I. AMHB: (ANTI)AROMATICITY-MODULATED HYDROGEN BONDING II. EVALUATION OF IMPLICIT SOLVATION MODELS FOR PREDICTING HYDROGEN BOND FREE ENERGIES Tayeb Kakeshpour By A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Chemistry—Doctor of Philosophy 2019 ABSTRACT FREE ENERGIES By Tayeb Kakeshpour I. AMHB: (ANTI)AROMATICITY-MODULATED HYDROGEN BONDING II. EVALUATION OF IMPLICIT SOLVATION MODELS FOR PREDICTING HYDROGEN BOND My doctoral research under Professor James E. Jackson focused on hydrogen bonding (H- bonding) using physical organic chemistry tools. In the first chapter, I present how I used quantum chemical simulations, synthetic organic chemistry, NMR spectroscopy, and X-ray crystallography to provide robust theoretical and experimental evidence for an interplay between (anti)aromaticity and H-bond strength of heterocycles, a concept that we dubbed (Anti)aromaticity-Modulated Hydrogen Bonding (AMHB). In the second chapter, I used accurately measured hydrogen bond energies for a range of substrates and solvents to evaluate the performance of implicit solvation models in combination with density functional methods for predicting solution phase hydrogen bond energies. This benchmark study provides useful guidelines for a priori modeling of hydrogen bonding-based designs. Coordinates of the optimized geometries and crystal structures are provided as supplementary materials. Copyright by TAYEB KAKESHPOUR 2019 ACKNOWLEDGEMENTS My doctoral study was a wonderful experience which would not have been possible without the love and support of many people to whom my gratitude cannot be fully conveyed in words. Beyond giving me the freedom to experience and explore various aspects of my interests from programming to synthetic chemistry himself, Dr. Jackson and his family have been a second family to me during the seven years I have been far from my own family. In addition, I want to thank our collaborators Dr. Judy I. Wu, Dr. Xuefei Huang, Dr. Babak Borhan, Dr. Jetze J. Tepe, Dr. Daniel C. Whitehead, and Dr. Carl L. Lira and my committee members Dr. Benjamin L. Levine and Dr. John L. McCracken who have been supportive of my research during these years. My research was made possible by the technical support and patience of many MSU staff members in explaining various tools to me. Among those I also want to express my gratitude to Dr. Daniel Holmes, Dr. Richard J. Staples, Dr. Chun-Min Chang, Paul Reed, and Robert Rasico. I also would like to express my appreciation towards the Jackson group members and the numerous high school and undergraduate students with whom I have worked with. Furthermore, I want to thank Hadi Gholami for both teaching me organic synthesis and being a supportive friend during my time at MSU. Lastly, I want to thank my parents, my sister, and my brother for their endless love and support. iv TABLE OF CONTENTS LIST OF TABLES ...................................................................................................................................................... vii LIST OF FIGURES ................................................................................................................................................... viii LIST OF SCHEMES ..................................................................................................................................................... x KEY TO SYMBOLS AND ABBREVIATIONS .................................................................................................... xi CHAPTER I: AMHB: (ANTI)AROMATICITY-MODULATED HYDROGEN BONDING ...................... 1 I.1. Introduction ................................................................................................................................................... 1 I.2. A broad in silico survey: generality and robustness of AMHB ................................................. 6 I.2.1. Designing examples to explore the generality of AMHB .................................................... 8 I.2.2. Nucleus-independent chemical shift ........................................................................................ 10 I.2.3. Energetic calculations ..................................................................................................................... 14 I.2.4. Aromaticity gain strengthens H-bonds .................................................................................... 15 I.2.5. Aromaticity loss weakens H-bonds ........................................................................................... 16 I.2.6. Antiaromaticity increase weakens H-bonds ......................................................................... 17 I.2.7. Antiaromaticity relief strengthens H-bonds ......................................................................... 18 I.3. Tuning association energies via AMHB ............................................................................................ 20 I.4. Remote AMHB effects in fused rings ................................................................................................. 23 I.5. Experimental measurement of the AMHB effect .......................................................................... 25 I.5.1. Energetic, geometric, and magnetic evidence for the interplay of aromaticity and H-bonding ........................................................................................................................................................ 35 I.5.2. Charge polarization vs. AMHB: Chemical shifts ................................................................... 37 I.5.3. Hybridization vs. AMHB: Energetics ......................................................................................... 38 I.5.4. Dipole-dipole interactions vs. AMHB: Energetics ............................................................... 39 I.6. Resonance-assisted H-bonding (RAHB) and AMHB ................................................................... 41 I.7. AMHB in redox systems .......................................................................................................................... 43 I.8. Conclusions .................................................................................................................................................. 49 I.9. Computational and experimental details ........................................................................................ 49 I.9.1. Computational details ..................................................................................................................... 49 I.9.2. Details of NMR measurements .................................................................................................... 51 I.9.3. Synthesis of compounds 1, 1’, 2 and 2’ .................................................................................... 52 CHAPTER II: EVALUATION OF IMPLICIT SOLVATION MODELS FOR PREDICTING H-BOND FREE ENERGIES ...................................................................................................................................................... 58 II.1. Introduction ................................................................................................................................................ 58 II.2. Experimental reference H-bond energies ..................................................................................... 60 II.3. CCSD(T)/CBS: a reference for gas-phase H-bond energies ................................................... 62 v II.4. The performance of DFT methods vs CCSD(T)/CBS in the gas-phase .............................. 63 II.5. Comparison of theory and experiment ........................................................................................... 68 II.6. Conclusions ................................................................................................................................................. 80 II.7. Experimental H-bond measurements ............................................................................................. 80 APPENDICES ............................................................................................................................................................ 82 APPENDIX A: Chemical shifts used for obtaining associations ..................................................... 83 APPENDIX B: Plots of fits for obtaining thermodynamic values from NMR spectra ........... 98 APPENDIX C: Stacked 1H NMR spectra used for obtaining dimerization energies ........... 105 APPENDIX D: NMR and IR spectra of compounds 1, 1’, 2 and 2’ ............................................... 141 APPENDIX E: Wavefunction-based energies ...................................................................................... 162 APPENDIX F: Calculated NICS values .................................................................................................... 179 APPENDIX G: The Python code for insertion of NICS probes ..................................................... 191 BIBLIOGRAPHY .................................................................................................................................................... 203 vi LIST OF TABLES Table I-1. Thermodynamic and chemical shift values (at 298.15 K and vs tetramethyl silane) obtained from NMR spectroscopy. ............................................................................ 33 Table I-2. Calculated dipole-dipole interaction energies (Ed-d). This table was adapted from Angewandte Chemie International Edition, 2017, 56, 9842. Copyright 2017 John Wiley and sons. ................................................................................................................................. 40 Table II-1. Measured H-bond thermodynamic values and extrapolated monomer and dimer chemical shifts. .................................................................................................................................. 61 Table II-2. Calculated H-bond electronic energies at CCSD(T)/CBS and a few less correlated wavefunction-based approximations. ..................................................................................... 63 Table II-3. Mean absolute errors (MAE) of calculated electronic energies of H-bonds using various levels of theory vs CCSD(T)/CBS. The energies are not counterpoise corrected. ............................................................................................................................................. 65 Table II-4. Extracted parameters from NMR measurements at 298.15 K. .................................... 81 vii LIST OF FIGURES Figure I-1. The structures of cycloheptatrienylium and cyclopentadienylium ions. This figure was recreated from Doering’s paper mentioned above.19 ................................ 4 Figure I-2. Intramolecular H-bond interaction in Stipitatic Acid. This figure was recreated from Dewar’s paper.20 .................................................................................................................... 5 Figure I-3. Archetype examples of AMHB. H-bond electronic energies were computed at the PBE0/aDZ level of theory. ............................................................................................................ 7 Figure I-4. The schematic presentation of the Python code written to perform the molecular rotation needed to prepare inputs for NICS(1)ZZ calculations. .................................. 12 Figure I-5. AMHB strengthens H-bonded dimers of 1 and 2 in contrast to their respective reference compounds 1’ and 2’. Nonbonding electron pairs not involved in π- delocalization are not shown. Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ................................................................................................................... 16 Figure I-6. AMHB weakens H-bonded dimers of 3 and 4 in contrast to their respective reference compounds 3’ and 4’. Nonbonding electron pairs not involved in π- delocalization are not shown. Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ................................................................................................................... 17 Figure I-7. AMHB weakens H-bonded dimers of 5 and 6 in contrast to their respective reference compounds 5’ and 6’. Nonbonding electron pairs not involved in π- delocalization are not shown. Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ................................................................................................................... 18 Figure I-8. AMHB strengthens H-bonded dimers of 7 and 8 in contrast to their respective reference compounds 7’ and 8’. Nonbonding electron pairs not involved in π- delocalization are not shown. Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ................................................................................................................... 19 Figure I-9. Comparison of X-ray crystal structure H-bond donor/acceptor distances for (A) 2a vs. 2a’ derivatives and (B) 3a vs. 3a’ derivatives. R groups may be H, alkyl, phenyl, 4-chlorophenyl, 4-trifluoromethylphenyl, and in a few cases, 4-methoxy and 3,4-dimethoxy phenyl, with the aryl group twisted out of the plane of the five-membered rings. ................................................................................................................... 20 Figure I-10. The dimerization energies of compound 9 and its hydrogenated analogues. The resonance forms that are enhanced upon H-bonding are shown. Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ............................................. 21 viii Figure I-11. Comparison of X-ray crystal structure H-bond donor-acceptor distances for 9dimer and 12dimer derivatives. .................................................................................................... 22 Figure I-12. (A) How to explain the AMHB effect in fused rings with extended p-systems. (B) Two cases where the enhanced aromaticity of one ring disrupts or enhances that of the second one calculated at DF-MP2/aQ5Z//MP2/aDZ using homodimers. .................................................................................................................................... 24 Figure I-13. Tautomerization energies for studied compounds. ....................................................... 28 Figure I-14. Stacked NMR spectra of the NH region of compound 1’ over a range of concentrations at four temperatures. ................................................................................... 31 Figure I-15. The plot of N-H chemical shift of compound 1’ by varying concentration at four temperatures. The markers are experimental data for the corresponding temperature and the grey lines are the best fits obtained from equation I-11. .. 32 Figure I-16. The two cases of aromaticity-modulated H-bonding. Enthalpies were measured in benzene via NMR spectroscopy. Aromatic rings are shown in red. .................... 36 Figure I-17. H-bonded heteroatom distances from X-ray structures of 1, 1t-butyl and 2 (left) vs their reference compounds 1’, 1’t-butyl and 2’ (right). Oxygen, nitrogen, carbon and hydrogen atoms are red, blue, gray and white respectively. .............................. 37 Figure I-18. Gas-phase dimerization electronic energies (kcal/mol). Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ............................................. 38 Figure I-19. Two examples of cases of RAHB. ............................................................................................ 41 Figure I-20. Two cases for evaluation of the magnitude of the RAHB effect. Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ............................................. 42 Figure I-21. Reduction energy modulations via AMHB. Energy (in kcal/mol) and NICS(1)zz (in ppm) values are respectively calculated at CCSD(T)/CBS and mPW91PW91 using MP2/aDZ geometries. ...................................................................................................... 45 Figure I-22. H-bonding modulation of flavin upon H-bonding. ......................................................... 48 Figure II-1. Sorted by sum of mean absolute errors of various levels of theory vs gas-phase CCSD(T)/CBS electronic energies and experimental H-bond free energies. ....... 71 Figure II-2. (A), (B), and (C) Individual signed errors for the three best-performing and (D) the most economical level of theory. ..................................................................................... 79 ix LIST OF SCHEMES Scheme I-1 . Timeline for the development of H-bonding, aromaticity and AMHB concepts. 6 Scheme I-2. Generating four cases for exploring the scope of AMHB. X can be NH, O, or S. .... 9 Scheme I-3. (A) Structures of compounds used for experimental evaluation of the AMHB concept, and (B) and (C) two examples showing the significance of their H- bond formation in two protein binding pockets. .......................................................... 27 Scheme II-1. (A) Complications from H-bonding polymerization in alcohols. (B) H-bonding species studied here. ................................................................................................................. 59 x Å ° °C K (anti)aromaticity H-bond AMHB RAHB NICS NICS(1)ZZ NMR ppm M mM µM SCF KEY TO SYMBOLS AND ABBREVIATIONS Angstrom; 10-10 meter degrees degree centigrade Kelvin Antiaromaticity and aromaticity Hydrogen Bond (Anti)aromaticity-Modulated Hydrogen Bonding Resonance-Assisted Hydrogen Bonding Nucleus-Independent Chemical Shift Dissected Nucleus-Independent Chemical Shift Nuclear Magnetic Resonance Parts per million Molar; moles per liter Millimolar; 10-3 molar Micromolar; 10-6 molar Self-consistent field xi DFT PBE0 HF MP2 CCSD(T) DF-HF DF-MP2 aDZ aTZ aQZ a5Z aQ5Z kcal/mol a.u. Density Functional Theory The PBE1PBE DFT method Hartree-Fock method 2nd order Møller–Plesset perturbation method Coupled Cluster with singles, doubles and perturbative triples Density-fitted HF method Density-fitted MP2 method Dunning aug-cc-pVDZ basis set Dunning aug-cc-pVTZ basis set Dunning aug-cc-pVQZ basis set Dunning aug-cc-pV5Z basis set Dunning Basis set extrapolation using cardinal numbers 4 and 5. Kilocalories per mol Hartree per particle; 1 a.u. = 627.509 kcal/mol xii CHAPTER I: AMHB: (ANTI)AROMATICITY-MODULATED HYDROGEN BONDING I.1. Introduction This chapter explores and generalizes an interplay between (anti)aromaticity and hydrogen bonding (H-bonding) of heterocycles which leads to modulations of their H-bond strengths. The concepts of aromaticity and H-bonding, which were formally developed during the first half of the 19th century, have been around for many decades.1,2 They have been used by chemists to explain chemical phenomena and to develop new chemical designs. However, their connection has remained underappreciated during these decades. The credit for the first mention of the H-bonding concept in the literature can be given to Moore and Winmill3 for their 1912 work on properties of aqueous solutions of ammonium salts. About two decades before the term H-bond was coined by Linus Pauling in his famous book titled “The Nature of the Chemical Bond”, they used the concept of H-bonding to rationalize the stronger basicity of tetramethyl ammonium hydroxide than that of trimethyl ammonium hydroxide.4 A definition of H-bonds, very similar to what we teach in general chemistry courses using Lewis structures, appeared in the literature in 1920 in a paper by Latimer and Rodebush working with G. N. Lewis on the structure and properties of water:5 "[A] free pair of electrons on one water molecule might be able to exert sufficient force on a hydrogen held by a pair of electrons on another water molecule to bind the two molecules together.... Such an explanation amounts to saying that the hydrogen nucleus held between 2 octets constitutes a weak 'bond'." 5 Interestingly, they called it a “bond” in this description. Despite these and a few more appearances of the H-bonding concept in the literature,6,7 the term “hydrogen bond” was 1 only dubbed by Pauling in his first edition of his book “The Nature of the Chemical Bond” in 1939:8 "[U]nder certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms, instead of only one, so that it may be considered to be acting as a bond between them. This is called the hydrogen bond" (taken from page 445 of the third edition published in 1959).8 "[A] hydrogen atom, with only one stable orbital, cannot form more than one pure covalent bond and that the attraction of two atoms observed in hydrogen-bond formation must be due largely to ionic forces."8 Although this definition looks like the classical definition of H-bonding presented earlier, he goes on to put it in firm quantum chemical terms a few pages later on page 450: In 1957, a symposium was held in Ljubljana, Yugoslavia on the topic of H-bonding which was attended by the most prominent names in chemical bonding and theory such as Pauling, Pople, and Pimentel. In this meeting Coulson presented his paper which was simply titled “The Hydrogen Bond”.9 In this landmark paper, which was a critical review of the current status of theory in understanding H-bonding, he went beyond the work of Lennard- Jones and Pople10 by dividing the H-bond interaction energy into four components: electrostatic, covalent, repulsive and dispersion. About 20 years later, Kitaura and Morokuma developed a SCF-based ab initio theory11–13 that decomposed the H-bond energy into five components: electrostatic (ES), polarization (PL), exchange repulsion (EX), charge transfer (CT), and coupling (MIX) components which set the foundation for the many energy 2 decomposition methods which continue to be further developed and improved even up to the present date.14 Finally, in their 1960 book simply called “The Hydrogen Bond”, Pimentel and McClellan provided a broad and practical definition for H-bonding that does not require the atoms (other than the hydrogen atom) involved in H-bonding to be limited to the three most electronegative atoms, nitrogen, oxygen and fluorine.15 "A H Bond exists between a functional group A-H and an atom or a group of atoms Β in the same or a different molecule when (a) there is evidence of bond formation (association or chelation), (b) there is evidence that this new bond linking A-H and Β specifically involves the hydrogen atom already bonded to A." 15 In about the same period, due to the explosion of knowledge in bonding theory and quantum chemistry, the concept of aromaticity was being developed in parallel. In contrast to H-bonding, the “aromaticity” term was proposed in the literature by August Wilhelm Hofmann in 1857, many decades before it was understood in terms of chemical bonding theory.16 This early naming was mainly based on the distinct odors of benzene and toluene rather than on bonding notions or spectroscopic behavior of related compounds, although the substitution vs addition behavior was seen as a hallmark of aromatic compounds even then. The word “aromatic” originates from the Greek word aroma and means having a pleasant and distinctive smell. However, it was a decade later in 1866 when the cyclohexatriene structure of benzene was proposed by August Kekulé.17 The term aromatic sextet was introduced for the first time in 1925 by Sir Robert Robinson who used it to explain 3 the resistance of the six electron system to disruption and the puzzling inertness of its compounds to addition reactions known for olefins.18 This stability was formulated in molecular orbital theory terms by Hückel in 1931; his concepts, however, remained unrecognized for two decades. Although the more subtle aromaticity of tropolone was explained by Dewar in 1945, the famous Hückel 4z+2 rule was first articulated formally and clearly by Doering in a 1951 article in the Journal of the American Chemical Society on the subject of the synthesis and properties of tropolone:19 “The general molecular orbital theory ascribing peculiar stability to cyclic molecular orbitals containing 2+4z electrons has, among others, the corollary that the cycloheptatrienylium ion (I) should be more stable than the cyclopentadienylium ion (II) whereas the stability of the anions, |}~} and |Ä~Ä, should be reversed.” 19 4 6 I II Figure I-1. The structures of cycloheptatrienylium and cyclopentadienylium ions. This figure was recreated from Doering’s paper mentioned above.19 Interestingly, even before the 4z+2 rule was recognized by the community in a widespread manner, Dewar in 1945 noted the interplay between aromaticity and H-bonding in a study on Stipitatic Acid, without explicitly invoking aromaticity:20 “When the appropriate triketocycloheptene carboxylic acid is written in the dienol forms (I) and (II), the possibility of resonance between them by hydrogen bond chelation becomes 4 evident; such a compound would be expected to show abnormal stability and lack of ketonic function.” 20 CO2H CO2H HO O H O HO O O H I II Dewar’s paper.20 Figure I-2. Intramolecular H-bond interaction in Stipitatic Acid. This figure was recreated from Fast forward to 2014, the first study to directly point out the reciprocal interplay between aromaticity and H-bonding was published in a collaboration between Dr. Judy I. Wu, a postdoctoral fellow in the laboratory of Paul von Ragué Schleyer and now an assistant professor at University of Houston, and Dr. James E. Jackson, my Ph.D. advisor. The rest of this chapter presents my work which comprises of two main parts. The first part uses quantum chemical simulations to examine the generality of the interplay between H-bonding and both aromaticity and antiaromaticity of heterocycles for a broad range of examples. It uses reference compounds to quantify the magnitude of the energetic effects and provides magnetic evidence for changes of ring currents upon H-bonding. The second part, which is experimental, provides geometrical, energetic, and magnetic evidence for the effect. A Schematic timeline for the above history is presented in Scheme I-1 below. The materials of this chapter were, in part, published and were adapted with permission form the publishers: (1) The Journal of the American Chemical Society, 2016, 138, 3427. Copyright 2016 American Chemical society. (2) Angewandte Chemie International Edition, 2017, 56, 9842. Copyright 2017 John Wiley and sons. 5 Linus Pauling “The Nature of Chemical Bond” the term H-bond was coined Latimer, Rodebush, and Lewis Lewis structure; a weak bond Moore and Winmill H-bonding and basicity Pimentel and McClellan “The Hydrogen Bond” book Coulson in Ljubljana Symposium the nature of H-bond and introduction of energy decomposition methods Wu, Jackson, and Schleyer AMHB in the 2-pyridone case Dewar stability of stipitatic acid via AMHB This thesis! 7 5 8 1 6 6 8 1 2 1 9 1 0 2 9 1 1 3 9 1 9 3 9 1 5 4 9 1 1 5 9 1 7 5 9 1 0 6 9 1 4 1 0 2 6 1 0 2 August Kekulé benzene structure Doering 4n + 2 rule August Wilhelm Hofmann the “aromaticity” term introduced timeline for: H-bonding aromaticity AMHB Dewar Tropolone aromatic structure Hückel Aromaticity in terms of MO theory Scheme I-1 . Timeline for the development of H-bonding, aromaticity and AMHB concepts. I.2. A broad in silico survey: generality and robustness of AMHB Since the C-N bond is not a complete double bond, 2-pyridone (case a in Figure I-3) is only partially aromatic. But when it dimerizes, a resonance form is enhanced in which the aromaticity of the ring, and thus the stability of the system (aromatic rings are shown in red) increases. Therefore, its H-bond should be stronger than in case e, which includes the same H-bonding moieties, but lacks a cyclic p-system. However, in case c, H-bonding enforces some antiaromaticity on the four-membered 4pÅ ring, since the C=N p-bond character of the amidine group is decreased upon H-bond formation. As a result, its H-bonding is weaker than that of case e, in which no antiaromaticity in involved. Conversely, in cases b and d, H- bond formation respectively disrupts (favorable) aromaticity and relieves (unfavorable) antiaromaticity effects leading to weaker and stronger H-bond energies than in case f, respectively. The measured homo-dimerization enthalpies of a and b by Inuzuka and co- workers 21,22 show that a binds 9.6 kcal/mol stronger than b (15.6 vs 6.0 kcal/mol). 6 Aromaticity-Modulated H-bonding Resonance-Assisted H-bonding O N H O N H N O H H a, ΔdimE = –21.97 enhanced aromaticity O N H H H e, ΔdimE = –15.05 O H N H H H N H H N O H N N H H Antiaromaticity-Modulated H-bonding O O H N N H N H O c, ΔdimE = –8.26 kcal/mol intensified antiaromaticity H N N NH N H N H N H N N N H N H H H H H H H H N H N H N H N H N H H f, ΔdimE = –15.23 b, ΔdimE = –11.01 disrupted aromaticity d, ΔdimE = –25.32 kcal/mol relieved antiaromaticity PBE0/aDZ level of theory. Figure I-3. Archetype examples of AMHB. H-bond electronic energies were computed at the While the above points all make sense intuitively, here, the questions are: how strong is the AMHB effect? And, these H-bonds are weakened and strengthened with respect to what? In other words, what are the appropriate reference compounds to compare these (anti)aromatic systems with to quantify the magnitude of the AMHB effect on H-bond strengths. These reference compounds should provide the same H-bonding moieties as the (anti)aromatic heterocycles under study but lack their conjugation to (anti)aromaticity. Fortunately, these structures can be easily constructed by hydrogenation of the double bonds in the rings. The described reference molecules for an (anti)aromatic heterocycle can be obtained simply by disconnecting the (anti)aromatic p-circuit via hydrogenation of a ring double bond. For a six-membered ring, e.g. 2-pyridone, two isomers are possible (four if hydrogenation of both double bonds and 1,4 hydrogenation are also considered). In addition, the flexibility of the hydrogenated ring might lead to multiple conformers, further complicating the study by increasing the number of structures that need to be calculated. Four-membered rings introduce strain and pyramidalization as additional issues. For these 7 reasons, five-membered rings, which can be designed to be aromatic (e.g. thiophene) or antiaromatic (e.g. cyclopentadienone) were chosen as the templates for this study. I.2.1. Designing examples to explore the generality of AMHB This section concentrates on designing a broad set of heterocycles capable of coupling (anti)aromaticity and H-bonding to investigate the generality of the AMHB concept (Scheme I-2). For this purpose, amide and amidine groups were used as H-bond moieties. These groups make two-point H-bonds that can polarize them to change their C=N p-bond orders. Considering the usual resonance structures, the amide group increases the p-bond character between C and N upon H-bonding. Conversely, in the amidine case, H-bonding decreases the p-bond character of the C=N bond. These changes in p-bond character can be coupled to both aromaticity and antiaromaticity depending on how many p-electrons are paired with them in a cycle. If amide or amidine groups are coupled to groups isoelectronic to the allyl cation, they form partially or fully antiaromatic rings respectively (total of four p-electrons in the ring). On the other hand, if these H-bonding groups form a cycle with groups that are isoelectronic with allyl anion, they form partially or fully aromatic rings. 8 (A) Generating cyclic 6πe- cases for aromaticity-modulated H-bonding (B) Generating cyclic 4πe- cases for antiaromaticity-modulated H-bonding X 4πe-, isoelectronic with allyl anion O NH amide O X 1(a-c) NH NH2 N amidine NH2 X N 3(a-c) or O or NH2 X X 2πe-, isoelectronic with allyl cation O NH amide X O 5(a-c) NH O or X or NH2 N amidine NH2 7(a-c) N NH2 2(a-c) NH X 4(a-c) N X NH 6(a-c) N 8(a-c) X X 4πe- disruption upon H-bonding 4πe- enhancement upon H-bonding disruption of 6πe- delocalization upon H-bonding 6πe- delocalization enhancement upon H-bonding Scheme I-2. Generating four cases for exploring the scope of AMHB. X can be NH, O, or S. The hypothesis is that these changes of p-bond character of the H-bond moieties could couple to the stabilizing and destabilizing effects of aromaticity or antiaromaticity. Hence, these perturbations should respond back and control the strength of H-bond. In this scenario, there are four possible cases upon H-bonding. The H-bond formation can 1. enhance aromaticity, and as a result thus be strengthened (lowered in energy upon association). 2. disrupt an aromatic ring and be weakened 3. relieve some antiaromaticity from a ring and be strengthened 4. enforce more antiaromaticity on the cycle and thus be weakened 9 Obtaining reference compounds in the abovementioned manner seems trivial for the AMHB case, but the challenge of designing reference compounds has led to controversial papers on the resonance-assisted hydrogen bonding concept (RAHB).23,24 With a wide range of examples for all the four possible cases of AMHB in hand, we put the hypothesis to test for its generality, but before that, the method used to follow the changes in magnetic properties of heterocycles, i.e. the degree of (anti)aromaticity, is discussed in the next section. I.2.2. Nucleus-independent chemical shift There is a number of descriptors for aromaticity that are based on geometric, energetic and magnetic consequences of aromatic stabilization. Each one has its own shortcomings and advantages.25 Among these methods, nucleus-independent chemical shift (NICS) is simple to implement, and complements the energetic calculations by providing magnetic evidence for changes in “ring current” and thus (anti)aromaticity of the studied heterocycles. Thus, this method was chosen to follow the changes of aromaticity or antiaromaticity of the p-conjugated heterocycles upon H-bonding. The NICS values are simply obtained by calculating the magnetic shielding of a ghost atom in shielding or deshielding cones of aromatic or antiaromatic rings, respectively. For convenience of interpretation in analogy with 1H NMR chemical shifts, the negative sign of the calculated shielding is usually reported, as recommended in the original paper.26 Since the so-called ghost atom is just a measurement location, with neither a positively charged nucleus nor any basis set or electrons, it does not perturb the probed molecule. Thus, the calculated wave function or electron density of the probed molecule is not affected during the NICS simulations. This is a major advantage over using experimental probes such as alkali metals (Li) or protons complexed to the systems, as the probe can be selectively placed in locations 10 close to the molecule’s site of interest to enhance the sensitivity of the method without interfering with the quantum mechanical calculations. The dissected version of NICS, which minimizes the effect of sigma electrons on the calculated magnetic shielding, was used in this study. The NICS probe in the original work of Schleyer et al.26 was placed at the center of the studied rings and the negative sign of the overall calculated shielding was used for reporting its value. However, the probe was later moved to 1 Å above the ring center and the negative sign of only the zz tensor of the magnetic shielding was used for reporting its value. Such a treatment not only decreases the effect of sigma electrons but also increases the sensitivity of the calculated shielding to p-electron ring currents by moving away from the former and closer to the latter. The notation of this dissected NICS is as NICS(1)ÉÉ, in which (1) stands for the 1 Å distance and zz refers to the used tensor of computed shielding. Calculation of NICS(1)ÉÉ values generally requires finding the plane of a ring and reorientation of the molecule in the Cartesian coordinate system. As mentioned above, the NICS(1)ÉÉ probe is, by definition, placed at one angstrom above (or below) the plane of the studied (anti)aromatic ring. Since, unlike benzene, many of the rings studied in this work are not completely flat, calculation of a least-squares mean plane was needed to be able to place the NICS(1)ÉÉ probe in a well-defined manner. Then, for the extracted zz tensor to be meaningful, the molecule needed to be rotated with the mean plane perpendicular to the z- axis of the Cartesian coordinate system. Figure I-4 shows the rotation required to prepare a NICS(1)ÉÉ input file, along with a schematic presentation of a Python27–29 code written to automate this tedious and repetitive work. 11 Input: Gaussian output Extract optimized geometry in xyz format using obabel. Read the geometry into a 2D matrix. Are the ring elements provided by the user? NO Sort the atom list from heavy to light. z-axis probes: NICS(1)zz NICS(0) YES Center the ring to the origin of the Cartesian system Find the mean plane vector. Use obabel to find the smallest set of smallest rings. Rotate the molecule and place NICS(0) and (1) probes. FOR EACH RING Write a Gaussian input file for NMR calculations. rotation needed to prepare inputs for NICS(1)ZZ calculations. Figure I-4. The schematic presentation of the Python code written to perform the molecular The code first uses open Babel30 to extract the coordinates of an optimized geometry from a Gaussian output file and reads it into a 2-D matrix. Then if the labels of the ring atoms are provided by the user, the code proceeds to find the mean plane of the specified ring, rotate the molecule, and place the NICS(1)ÉÉ probes before saving the Gaussian input file for NMR calculations. The centering (non-mass-weighted) of the ring is only for convenience and is not required; however, the NICS(1)ÉÉ probe is then convenient to place 1 Å above this ring center. Placement of the NICS(1)ÉÉ probe at the non-mass-weighted center of the ring is arbitrary. If the ring of interest is not specified by the user, the code again uses open Babel to find the smallest set of smallest rings (SSRs) in the structure and generates multiple NICS input files if more than one ring is found. The only reason the elements are sorted from heavy to light before searching for the SSRs is that the open Babel module removes the hydrogen 12 atoms before the SSRs search and as a result the indexing of the found ring atoms in the reported array may not match the original indexing of the structure. Considering that most non-flat rings may not be symmetrical on both faces, NICS(1)ÉÉ probes were in all cases placed on both “top” and “bottom” of the rings. The resulting NICS(1)ÉÉ values were averaged to eliminate the arbitrariness of choosing one face over the other one. To follow the ÑÖ|Ü(1)áá changes upon dimerization of aromatic and antiaromatic heterocycles, àÑÖ|Ü(1)áá was obtained as: ΔNICS(1)ÉÉ=NICS(1)ÉÉäãåçé−NICS(1)ÉÉåêëêåçé in which NICS(1)ÉÉäãåçé and NICS(1)ÉÉåêëêåçé refer to the calculated NICS(1)ÉÉ values for dimer and monomer, respectively. Since the negative sign of the calculated zz tensor of shielding is taken as the NICS(1)ÉÉ value, the reported values can be interpreted in a manner similar to 1H NMR chemical shifts. For example, the calculated NICS(1)ÉÉ value for benzene is -10.6 ppm31 as a proton in the shielding cone of an aromatic ring has a chemical shift of -4.0 ppm,32 both of which are large negative numbers. Presumably, the reason the experimental shift is 6.6 ppm more downfield than the NICS(1)ÉÉ value is: (1) there is no electron around the NICS(1)ÉÉ probe to shield it from the anisotropic magnetic field of benzene and (2) the NICS(1)ÉÉ probe is closer to the center of the benzene ring than any protons could experimentally be located; hence it experiences a larger magnetic shielding. In contrast, the calculated NICS(1)ÉÉ value for cyclobutadiene is +12.7 ppm, since the top of antiaromatic rings, where the NICS(1)ÉÉ probe is placed, is in the deshielding cone. For interpretation of the reported NICS(1)zz values in studying the cases of AMHB, the following short statement is helpful: A negative àÑÖ|Ü(1)áá value implies enhanced aromaticity or decreased 13 antiaromaticity, while a positive value means decreased aromaticity or increased antiaromaticity. O O H N N O N 2 x N H N monomer N H dimer The NICS(1)ÉÉ calculations were performed at the mPWPW91/6-311++G(3df,3pd) level of theory. Since these calculations are essentially NMR calculations, the choice of method was guided by benchmark study of 1H NMR calculations by Lodewyk et al.33 These authors have shown that the root mean square deviation (RMSD) of chemical sifts calculated wat mPWPW91/6-311+G(2d,p) is only 0.16 ppm from a wide range of experimental 1H NMR values. Here, the larger basis set 6-311++G(3df,3pd) was used. I.2.3. Energetic calculations Although in our original paper34 the energetic of effects of AMHB were calculated at the PBE0/6-311++G(3df,3pd) level of theory, all the energy calculations in this section are performed at the wavefunction-based CCSD(T)/CBS level of theory, the so-called “gold standard” method for non-covalent interactions.35 The geometries, however, were optimized at the MP2/aDZ level of theory, which is the highest wavefunction level of theory accessible for the studied systems considering the resources available. Here, CCSD(T)/CBS refers to a composite method that approximates the complete basis set by summing three components: in which Eíììéêî. óúü†°, and δü†°ïïñó(ò) are approximate CCSD(T)/CBS energy, density-fitted Hartree-Fock (DF-HF) energy, two-point extrapolated density-fitted MP2 (DF- MP2) correlation energy, and CCSD(T) correlation energy, all at the highest basis set Eíììéêî. ïïñó(ò)/ïôñ=Eçöçõ.óúùú+Eçîûéíìêö. ïïñó(ò)/ïôñ, Eçöçõ.óúùú, Eçîûéíìêö. óúü†°+δü†°ïïñó(ò) 14 possible, respectively. The CCSD(T) correlation energy is defined as the energy difference between MP2 and CCSD(T) methods at the aDZ basis set. That is why the δü†°ïïñó(ò) term has an “MP2” subscript. Considering the size of our systems and computational resources available at MSU, we were able to use a5Z, aQZ to a5Z extrapolated, and aDZ basis sets for Eçöçõ.óúùú, Eçîûéíìêö. óúü†°, and δü†°ïïñó(ò) calculations, respectively. Burns et al.36 have shown that the extrapolated DF-MP2 and CCSD(T) correlation energies obtained using the above basis sets for a variety of non-covalent interaction energies of small systems are each within about 0.1 kcal/mol of the corresponding correlation energies calculated at the highest computationally possible basis sets. Thus, the calculated energies here should be within 0.2 kcal/mol of directly extrapolated CCSD(T) energies using Dunning basis sets with the highest possible cardinal numbers (two-point extrapolation). I.2.4. Aromaticity gain strengthens H-bonds Compounds 1(a-c) and 2(a-c), are six cases of heterocycles that are partially aromatic (Figure I-5). They are called partially aromatic because the amide C-N has only a partial p- bond character. The partial aromaticity is also supported by their calculated small and negative NICS(1)ÉÉ values. Their aromaticity can then be enhanced upon H-bonding, which leads to stronger H-bonds. Indeed, in all the cases in Figure I-5, the H-bonds in the aromatic heterocycles are stronger than their respective reference compounds. The enhancement of aromatic character upon H-bonding is supported by negative values of the calculated ΔNICS(1)ÉÉ. Thus, energetic and magnetic calculations suggest that enhancement of aromaticity upon H-bonding can strengthen H-bonds to a significant degree. 15 O X 2 x N H O NH X N H O X 2 x O X O NH N H X 2(a-c) –13.5 to –11.3 ppm N H O X 2(a-c)dimer –18.8 to –16.2 ppm increased aromaticity 1(a-c)dimer –17.1 to –13.7 ppm increased aromaticity 1(a-c) –15.0 to –12.0 ppm O X 2 x N H O NH X O X O NH X 2 x O N H N H O 1'(a-c) 1'(a-c)dimer X 2'(a-c)dimer N H ∆dimE –20.4 –19.7 –18.9 –20.4 –19.2 –21.7 Cpd. 1a 1b 1c 2a 2b 2c X 2'(a-c) ∆∆dimE –4.4 –3.2 –3.0 –5.7 –1.8 –4.8 ∆dimE –16.0 –16.5 –15.9 –14.8 –17.4 –16.9 ∆NICS(1)zz X –2.1 ppm NH –1.6 ppm O –1.7 ppm S –6.1 ppm NH –4.9 ppm O –2.6 ppm S Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. Cpd. 1a’ 1b’ 1c’ 2a’ 2b’ 2c’ Figure I-5. AMHB strengthens H-bonded dimers of 1 and 2 in contrast to their respective reference compounds 1’ and 2’. Nonbonding electron pairs not involved in π-delocalization are not shown. I.2.5. Aromaticity loss weakens H-bonds Supported by their calculated large and negative NICS(1)ÉÉ values, all the main compounds 3(a-c) and 4(a-c) in Figure I-6 are strongly aromatic. Their aromaticity is disrupted upon H- bonding and hence their H-bonds are weaker than their respective reference compounds with the same H-bonding moieties but lacking aromaticity. The positive values of ΔNICS(1)ÉÉ for all the six compounds upon H-bonding point to the disrupted aromatic rings. Therefore, in contrast to the first case, aromatization of heterocycles weakens H-bonds of potential practical interest. These findings may have practical applications as the 2-aminoimidazole class of compounds covers a wide range of experimental and approved drugs. 16 H X N H N N H N X H 2 x 3(a-c)dimer –24.2 to –19.4 ppm disrupted aromaticity H N H H N H X N N X 4(a-c) –27.2 to –23.3 ppm N H N X 4(a-c)dimer H –25.7 to –21.6 ppm disrupted aromaticity H N H X 2 x N 3(a-c) –26.7 to –21.3 ppm H N H X 2 x N H N H N X H N H H N H X N X N H N 2 x N N H N H 3'(a-c) 3'(a-c)dimer X 4'(a-c)dimer H Cpd. 3a’ 3b’ 3c’ 4a’ 4b’ 4c’ Cpd. 3a 3b 3c 4a 4b 4c X 4'(a-c) ∆∆dimE +0.9 +0.8 +1.8 +3.3 +1.8 +2.6 ∆dimE –13.6 –14.3 –12.9 –8.9 –11.7 –10.7 ∆NICS(1)zz X +2.5 ppm NH +1.9 ppm O +2.4 ppm S +1.5 ppm NH +1.6 ppm O +2.0 ppm S Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ∆dimE –14.5 –15.1 –14.8 –12.2 –13.5 –13.3 Figure I-6. AMHB weakens H-bonded dimers of 3 and 4 in contrast to their respective reference compounds 3’ and 4’. Nonbonding electron pairs not involved in π-delocalization are not shown. I.2.6. Antiaromaticity increase weakens H-bonds All the six compounds 5(a-c) and 6(a-c) have four π-electrons in their cycles, and hence they are formally antiaromatic (Figure I-7). However, only compounds 5(a-c) show positive NICS values. The negative values in 6(a-c) are probably due to isolation of the endocyclic double bond from the nitrogen non-bonding electron pairs by the two electron withdrawing groups adjacent to it. The changes of NICS(1)ÉÉ upon H-bonding, however, suggest enhanced paratropicity, i.e. antiaromaticity, in the all the dimers. Energetic comparisons also confirm weaker H-bonds in the p-cyclic systems compared to their 17 respective reference compounds. These results, although small in some cases, are in line with the AMHB hypothesis. X 2 x O N H X O NH N H O X 2 x 5(a-c) +2.7 to +6.1 ppm 5(a-c)dimer +3.9 to +7.6 ppm increased antiaromaticity 6(a-c) –3.8 to –0.7 ppm O N H X X O NH N H O X 6(a-c)dimer –3.4 to –0.0 ppm increased antiaromaticity O N H X O NH N H O O O NH X X 2 x X 2 x O X 6'(a-c) N H 5'(a-c) 5'(a-c)dimer X 6'(a-c)dimer N H ∆dimE –16.0 –16.3 –16.7 –12.7 –12.5 –12.7 Cpd. 5a’ 5b’ 5c’ 6a’ 6b’ 6c’ Cpd. 5a 5b 5c 6a 6b 6c ∆∆dimE +1.3 +2.2 +1.5 +0.1 +0.8 +0.1 ∆NICS(1)zz X +1.2 ppm NH +1.5 ppm O +2.1 ppm S +0.4 ppm NH +0.7 ppm O +0.7 ppm S Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. ∆dimE –17.2 –18.5 –18.2 –12.8 –13.3 –12.8 Figure I-7. AMHB weakens H-bonded dimers of 5 and 6 in contrast to their respective reference compounds 5’ and 6’. Nonbonding electron pairs not involved in π-delocalization are not shown. I.2.7. Antiaromaticity relief strengthens H-bonds The last case of AMHB is the situation where relieving destabilization from antiaromatic p-system rings results in stronger H-bonds than the reference compounds. Compounds 7(a-c) and 8(a-c) in Figure I-8 are all formally antiaromatic, and hence their NICS(1)ÉÉ values are expected to be large and positive. This is true for the former group. However, the latter have small and negative values. Similar to the cases of 6(a-c), compounds 18 8(a-c) escape some antiaromaticity, by delocalizing the endocyclic C=N p-bonds outside the rings, isolating it from coupling to the other rings’ p-bonds. Despite the small effect in 8(a- c), all the antiaromatic compounds relieve some antiaromaticity upon H-bonding, as suggested by their positive ΔNICS(1)ÉÉ values. Accordingly, all the antiaromatic compounds form H-bonds stronger than those of their reference compounds. H N H N X 2 x X H N H N N H N 7(a-c) +10.7 to +19.6 ppm 7(a-c)dimer +9.2 to +15.3 ppm relieved antiaromaticity X H 2 x X 8(a-c) –3.6 to +0.6 ppm H N H N X H N H N N H N H X 8(a-c)dimer –3.7 to –0.2 ppm relieved antiaromaticity X H H N H N 7'(a-c) X 2 x H N H N X N H N X 2 x H N H N H N H N N H N 8'(a-c) 7'(a-c)dimer X 8'(a-c)dimer H Cpd. 7a’ 7b’ 7c’ 8a’ 8b’ 8c’ X ∆∆dimE –4.2 –4.8 –6.0 –1.0 –1.8 –0.4 ∆dimE –12.7 –13.0 –12.3 –15.8 –21.1 –23.3 Cpd. ∆dimE 7a –16.9 –17.8 7b –18.3 7c 8a –16.8 –22.9 8b 8c –23.7 ∆NICS(1)zz X –1.5 ppm NH –2.5 ppm O –6.6 ppm S –0.1 ppm NH –0.7 ppm O –0.6 ppm S Energies were calculated at CCSD(T)/CBS using MP2/aDZ geometries. Figure I-8. AMHB strengthens H-bonded dimers of 7 and 8 in contrast to their respective reference compounds 7’ and 8’. Nonbonding electron pairs not involved in π-delocalization are not shown. A survey of the online Cambridge X-ray Structural Database (WebCSD),37 in which H- bond donor-acceptor distances were compared, found that the average distance for 2a in five crystals of its derivatives38–42 is 0.116 Å shorter (2.707(6) vs 2.823(10) Å, Figure I-9-A) than 19 for 2a’ in nine crystal structures.43–50 In contrast, the average N----N distance in 3a derivatives in three crystal structures51–53 is 0.105 Å longer (3.013(6) vs. 2.908(6), Figure I-9-B) than 3a’ derivatives in four crystal structures.54–56 These observations offer strong experimental geometric support for the notion of aromaticity assisted H-bonding and aromaticity disrupted H-bonding in the cases of 2a and 3a, respectively. AMHB effect present AMHB effect NOT present A R O H R H N N R R N N O R R R R N N R R N R R O H H N O (average of 5 examples) (average of 9 examples) 2.707(6) Å 2a 2.823(10) Å 2a’ B R N R N R N R H H R R N R R N R R N N R 3.013(6) Å R R N R R N H N N H N R 2.908(6) Å 3a 3a’ (average of 5 examples) (average of 3 examples) twisted out of the plane of the five-membered rings. Figure I-9. Comparison of X-ray crystal structure H-bond donor/acceptor distances for (A) 2a vs. 2a’ derivatives and (B) 3a vs. 3a’ derivatives. R groups may be H, alkyl, phenyl, 4-chlorophenyl, 4- trifluoromethylphenyl, and in a few cases, 4-methoxy and 3,4-dimethoxy phenyl, with the aryl group I.3. Tuning association energies via AMHB 1H-imidazo[1,2-a]imidazole, compound 9 in Figure I-10, is a framework in which dimerization energy could in principle be predictably tuned via AMHB considerations from favorable to unfavorable through hydrogenation of different C=C p-bonds. In 9dimer, H- bonding enhances a resonance form in which an aromatic Clar sextet is formed as an 20 imidazolium ring while an imidazole sextet is disrupted. These described changes in ring currents are clearly supported by probing ΔNICS(1)ÉÉ for both rings A and B. The ΔNICS(1)ÉÉ is +2.5 ppm for the imidazole ring, whereas it is −0.8 ppm for the non-sextet ring (see Figure I-10 under each ring for the NICS(1)ÉÉ values). ΔdimE (kcal/mol) N –21.1 N N N H N N H 9dimer A = –23.5 ppm B = –28.0 ppm N H N N N N –21.4 N H 10dimer A = –12.1 ppm N N N –15.2 N H N N H 11dimer B = –22.0 ppm N H N N N –18.0 2 x N A B N H N 9 A = –22.6 ppm B = –30.4 ppm 2 x N N H A N 10 A = –9.3 ppm N H 2 x N B N 11 B = –23.5 ppm N H 2 x N N N N H 12dimer 12 CCSD(T)/CBS using MP2/aDZ geometries. Figure I-10. The dimerization energies of compound 9 and its hydrogenated analogues. The resonance forms that are enhanced upon H-bonding are shown. Energies were calculated at Comparison of dimerization energies between compounds 9 and 12, the related bicyclic with no cyclic p conjugation, reveals that the added 10§Å aromatic system and its further delocalization upon H-bonding leads to a 3.1 kcal/mol stronger H-bond in 9 than in 12. In 10dimer, an even higher dimerization energy is expected, since no imidazole sextet is 21 disrupted as the imidazolium sextet is enhanced. This difference, however, is quite small. On the other hand, dimerization of 11 should disrupt the imidazole sextet, weakening the H- bonding; this effect is observed as a 2.8 kcal/mol decrease in dimerization energy compared to 12dimer. In this case, the ΔNICS(1)ÉÉ =+2.4 ppm supports the idea that the diatropicity of the ring current is decreased upon dimerization. Such considerations for H-bonded system design would be of interest, since the H-bonding strength for the same guanidine moiety could be electronically tuned with a slight change in sterics, i.e. the hydrogenation of double bonds. Eventhough 9, 11, and 12 are known,49,51 compound 10 is not likely to be thermodynamically stable in a chemical environment; its computed electronic energy, without thermal corrections, is 9.3 kcal/mol above that of its isomer 11. Published crystal structures of derivatives of 9dimer and 12dimer also show shorter N-- -N distances in the former than the latter, in agreement with the calculated dimerization energies (Figure I-11). The H-bond length for 11dimer is 3.014(1), longer than those in both 9dimer and 12dimer (Figure I-17). N N H N N H N N 11dimer our crystal structure; see next section. R N N H N N H N N R N R N H N N H N R N R R 9dimer derivatives R = 2,4-dimethoxyphenyl one crystal structure: 3.014(1) Å Figure I-11. Comparison of X-ray crystal structure H-bond donor-acceptor distances for average of N----N distances in two crystal structures: 2.904(6) Å N----N distance in the crystal structure: 2.817(3) Å 9dimer and 12dimer derivatives. R R 12dimer derivatives R = H or phenyl 22 I.4. Remote AMHB effects in fused rings The p-electron delocalization of cyclic rings due to AMHB leads to alteration in the p- bond character inside the rings. An extreme case is that of benzene in which the two resonance forms lead to complete equalization of p-bonds around the ring leading to the highly symmetrical D6h point group. all bonds are equal (D6h symmetry) Hence, these p-bond order changes due to AMHB could, in principle, couple to (anti)aromaticity of a second ring fused to them. In previous sections, the resonance form shown in AMHB cases was only the one involving the amide or amidine moiety since that was enough to explain the changes of (anti)aromaticity of the rings upon H-bonding. However, in the fused rings studied in this section, the local functional group polarizations shown by the abovementioned resonance forms cannot be used to explain the effect of AMHB on the second ring. (Form I in Figure I-12-A) However, if the p-bonds of the ring in Form I are rotated, as shown using arrows in Figure I-12-A, resonance Form II is obtained, which can better describe the polarization effects of the first ring on the second one. In this case, the enhanced aromaticity of the first ring enhances the p-bond order of the bond shared between the two fused rings and hence the aromaticity of the second ring. 23 (A) How to interpret fused rings O N H dimerization O N H O N H Form I (involves only one ring) Form II (involves both rings) (B) Two cases of fused rings Case A: The aromaticity of both rings enhances upon H-bonding. O N H O N H O N H O N H O N H O N H 13 13dimer 13’ 13’dimer 13’’ 13’’dimer -26.79 -22.98 -23.04 Case B (two possible examples): The aromaticity of one ring is disrupted while the other one is enhanced. O N H 14 -20.41 O N H O N H 14dimer O N H O N H 14’ -22.86 O N H 14’dimer O N H O N H O H N 14’’ -22.66 O N H 14’’dimer O N H O N H 15 15dimer 15’ -21.58 -24.63 15’’ 15’’dimer 15’dimer Figure I-12. (A) How to explain the AMHB effect in fused rings with extended p-systems. (B) Two cases where the enhanced aromaticity of one ring disrupts or enhances that of the second one Two cases in which the enhanced aromaticity of the first ring upon H-bond formation can enhance (case A) or disrupt (case B) the aromaticity of the second one are shown in Figure I-12-B. In compound 13, both rings are partially aromatic as suggested by their calculated at DF-MP2/aQ5Z//MP2/aDZ using homodimers. -24.47 24 calculated NICS(1)ÉÉ values (see numbers inside respective rings). Upon H-bonding, the aromaticity of both rings is supposed to increase based on the resonance form shown. This hypothesis is supported by the upfield shifts of the NICS(1)ÉÉ values of both rings. This leads to a ca. 4 kcal/mol stronger H-bond in 13 when compared to 13’ or 13” in which the aromaticity of the second ring is breached by hydrogenation of any of the double bonds of the second ring. Conversely, in 14, the enhancement of aromaticity of the first ring upon H-bonding leads to the disruption of that of the second ring. Thus, the H-bond energy of 14 is ca. 2 kcal/mol weaker than those of 14’ or 14” in which the aromaticity of the second ring is eliminated via hydrogenation of any of the rings and cannot be disrupted. Notably, the H- bond energies of 13’, 13”, 14’ and 14” are only marginally different meaning the location of the second ring and p-patterns that are not cyclic do not significantly interfere with AMHB. Lastly, for the sake of completeness of the discussion, compound 15 and its reference compounds, 15’ and 15”, were explored. Similar to 14, the aromaticity of the second ring of 15 is disrupted upon H-bond formation, and hence its H-bond energy is ca. 3 kcal/mol weaker than either of its reference compounds 15’ or 15”. I.5. Experimental measurement of the AMHB effect In the previous section, quantum chemical analyses of H-bonding heterocycles, using the nucleus-independent chemical shift (NICS) method as an index of aromatic or antiaromatic π-delocalization, we found a systematic relationship between their (anti)aromaticity and H-bond association energies. Specifically, “H-bonding interactions that enhance aromaticity or relieve antiaromaticity are fortified, whereas those that intensify antiaromaticity or disrupt aromaticity are weakened, relative to analogues lacking full π- 25 circuits.”34 As H-bonds play key roles in the interactions of biologically important heterocycles such as DNA bases, enzyme cofactors, and drugs, such insights into the factors affecting H-bond strength are of broad interest and use.57–60 The interplay between aromaticity and H-bonding can be probed by experimentally comparing heterocyclic dimers with H-bonds that strengthen or weaken aromatic delocalization. Therefore, compounds 1 and 2 (Scheme I-3-A) were chosen for these two cases, respectively. To quantify the effect, their H-bond energies are compared with those of compounds 1’ and 2’, which have the same H-bonding motifs but lack π-conjugated circuits. Apart from their simplicity for this fundamental study, these heterocyclic frameworks can be found in many biologically active compounds. As an example for 1, compound A (Scheme I-3-B) accepts two H-bonds from Arg74 and Thr101, while donating one to Gln105 in the binding pocket of pseudomonas aeruginosa thymidylate kinase.61 A well-known instance involving ring 1’ is biotin, which reacts with avidin to form one of the tightest complexes known by accepting two H-bonds from residues Ser16 and Tyr33, and donating one to Asn118 (Scheme I-3-C).62 26 A) B) O N N H 1 Arg74 O N N H 1' C) 2.9 Å 2.6 Å Thr101 N H N H N N 2' N N 2 Ser16 Tyr33 2.7 Å 2.6 Å Asn118 2.7 Å Gln105 O N N H N 2.9 Å H H N O H N H S Biotin (vitamin) HO2C Ph Compound A (thymidylate kinase inhibitor) binding pockets. Scheme I-3. (A) Structures of compounds used for experimental evaluation of the AMHB concept, and (B) and (C) two examples showing the significance of their H-bond formation in two protein Measurements of association energetics in classic H-bonded systems such as alcohols or water are complicated by formation of a range of aggregates. To avoid this complexity, 1, 1’, 2, and 2’ were designed for simple pairwise homodimerization by blocking any extra H- bond donor moieties with methyl (in 1 and 1’) or ethanato (in 2 and 2’) groups. Another possible complication is tautomerization, as in 2-pyridone vs. 2-hydroxypyridine; such tautomeric equilibria are strongly affected by H-bonding media.63,64 However, G4(MP2)65 calculations find compounds 1, 1’, and 2 to be well below their tautomers in energy, both in the gas-phase, and in implicit benzene solvent (Figure I-13). 27 O N H O H N ΔtautE (kcal/mol) at G4(MP2) ΔtautE 2-py 1 1' 2 benzene/c-pcm Figure I-13. Tautomerization energies for studied compounds. gas-phase -1.1 +8.4 +16.7 +9.0 +0.8 +9.1 +17.7 +9.3 (2-hydroxypyridine) 2-hp 2-py (2-pyridone) Kò= [ó] [ü]• [D]=ïß[ü]° 2Kò[M]°+[M]−C¶=0 For compounds 1, 1’, 2, and 2’ in C6D6, the homodimerization equilibria were established faster than the NMR time scale, so observed chemical shifts appeared as weighted averages of monomer and dimer forms. The molar equilibrium constant KT (at temperature T) for the equilibrium between monomer M and its H-bonded dimer D can be written as follows: equation I-1 where [M] and [D] denote the molarities of M and D, respectively. In a solution with formal concentration of C0, i.e. C¶=[M]+2[D], the [D] could be written as a function of [M] equation I-2 substitution of equation I-2 in I-1 leads to a quadratic equation, after rearrangement: equation I-3 solving via the quadratic formula yields one positive and one negative answer for [M]. However, since negative molarities are not meaningful, the only real answer for the above equation would be: Since the dynamics of H-bonding equilibria are usually faster than the NMR time scale, the proton involved in H-bonding is observed as a weighted average δØ∞± of its monomer and dimer forms: [M]= ®©™´¨≠ïß© ƨ≠ equation I-4 28 δØ∞±=Xü(δü−δó)+δó equation I-5 Xü=[ü]ïß (δM-δD)+δD δAVG=®1+8KTC0-1 4KTC0 Kò=e∆≤≥¥µ∂≠∆≤≥¥∑ ∏≠ δü=δü¶+ dδü/dT(T−T¶) δó=δó¶+ dδó/dT(T−T¶) where XM is the mole fraction of the nucleus of interest in the monomer form, and δM and δD are the chemical shifts of that nucleus in the monomer and dimer forms at temperature T, respectively. For a solution with C0 concentration, XM can be written as: equation I-6 Substitution of [M] from equation I-4 in equation I-6, and then XM from equation I-6 in I-5 results in equation I-7: equation I-7 in which, Kò, δü, and δó can be replace by equation I-8 equation I-9 equation I-10 which results in ([δü¶+ dδü/dT(T−T¶)]-[δó¶+ dδó/dT(T−T¶)])+[δó¶+ δAVG=π1+8ç∂∆≤≥¥µ∂≠∆≤≥¥∑ C0-1 ∏≠ 4ç∂∆≤≥¥µ∂≠∆≤≥¥∑ C0 ∏≠ dδó/dT(T−T¶)] equation I-11 in which, ∆äãåH, ∆äãåS, δü¶, dδü/dT, δó¶, and dδó/dT are respectively, the enthalpy of dimerization (kcal/mol), the entropy of dimerization (kcal/molK), the monomer chemical shift at the lowest measurement temperature (ppm), temperature dependence of monomer chemical shift (ppm/K), dimer chemical shift at the lowest measurement temperature (ppm), and the temperature dependence of the dimer chemical shift (ppm/K). The constant R is in units of kcal/molK. Substitution of equations I-8, I-9 and I-10 into equation I-7 implies 29 that the ∫zªºis constrained to be a linear function of 1/Ω based on the van 't Hoff equation and the chemical shifts of monomer are dimer are assumed to be a linear function of temperature. The averaged chemical shifts, which are the only experimental observable, were then measured for series of samples over a range of concentrations at four temperatures to obtain the spectra presented in Figure I-14. Then, by varying the six independent variables, ∆äãåH, ∆äãåS, δü¶, dδü/dT, δó¶, and dδó/dT the best fit of equation I-11 to the experimental data was obtained.66,67 Figure I-15 is a visual presentation of the result of the fit for compound 1’. The markers show the experimental chemical shifts at various concentrations at four temperatures, and the grey lines are the plot of equation I-11 using the optimized values for the abovementioned six parameters. With the best values of these six parameters in hand, the thermodynamic and NMR parameters at 298.15 K were calculated. These quantities, along with Gibbs free energy ΔäãåG and equilibrium constant K values at 298.15 K, are summarized in Table I-1 for compounds 1, 1’, 2, and 2’, BA, IM in in four solvents. The near perfect fit of experimental data to equation I-11 supports the absence of aggregates larger than dimers in the temperature and concentration ranges chosen for this study. All measurements in benzene which are used in this chapter were performed in triplicate to calculate the standard deviations of enthalpies shown in Figure I-16. While about 90% data completeness was obtained and needed for species 1 and 2’ for 1’ and 2, data covering about 70% (due to solubility limitations) of the monomer-dimer chemical shift range was enough to obtain the uncertainties (standard deviation) seen in Figure I-16. Data coverage index is defined as the ratio of the range of chemical shift measured experimentally divided by the difference between extrapolated dimer and monomer chemical shifts multiplied by 100%. 30 1’ in benzene (NH) [Exp. 1] Figure I-14. Stacked NMR spectra of the NH region of compound 1’ over a range of concentrations at 31 01, 280.2 K, 129.0 mM 02, 280.2 K, 103.2 mM 03, 280.2 K, 77.4 mM 04, 280.2 K, 51.6 mM 05, 280.2 K, 25.8 mM 06, 280.2 K, 12.9 mM 07, 280.2 K, 2.6 mM 08, 280.2 K, 1.0 mM 09, 280.2 K, 516.2 (cid:80)M 10, 280.2 K, 129.0 (cid:80)M 11, 291.7 K, 129.0 mM 12, 291.7 K, 103.2 mM 13, 291.7 K, 77.4 mM 14, 291.7 K, 51.6 mM 15, 291.7 K, 25.8 mM 16, 291.7 K, 12.9 mM 17, 291.7 K, 2.6 mM 18, 291.7 K, 1.0 mM 19, 291.7 K, 516.2 (cid:80)M 20, 291.7 K, 129.0 (cid:80)M 21, 301.5 K, 129.0 mM 22, 301.5 K, 103.2 mM 23, 301.5 K, 77.4 mM 24, 301.5 K, 51.6 mM 25, 301.5 K, 25.8 mM 26, 301.5 K, 12.9 mM 27, 301.5 K, 2.6 mM 28, 301.5 K, 1.0 mM 29, 301.5 K, 516.2 (cid:80)M 30, 301.5 K, 129.0 (cid:80)M 31, 311.0 K, 129.0 mM 32, 311.0 K, 103.2 mM 33, 311.0 K, 77.4 mM 34, 311.0 K, 51.6 mM 35, 311.0 K, 25.8 mM 36, 311.0 K, 12.9 mM 37, 311.0 K, 2.6 mM 38, 311.0 K, 1.0 mM 39, 311.0 K, 516.2 (cid:80)M 40, 311.0 K, 129.0 (cid:80)M four temperatures. Figure I-15. The plot of N-H chemical shift of compound 1’ by varying concentration at four temperatures. The markers are experimental data for the corresponding temperature and the grey lines are the best fits obtained from equation I-11. 32 Table I-1. Thermodynamic and chemical shift values (at 298.15 K and vs tetramethyl silane) obtained from NMR spectroscopy. data exp. coverage (%) 1 in C6D6 (NH) 91 [exp. 1] 1 in C6D6 (NH) 89 [exp. 2] 1 in C6D6 (NH) 92 [exp. 3] 1' in C6D6 76 (NH) [exp. 1] 1' in C6D6 77 (NH) [exp. 2] 1' in C6D6 77 (NH) [exp. 3] 2 in C6D6 (NH) 65 [exp. 1] 2 in C6D6 (NH) 65 [exp. 2] 2 in C6D6 (NH) 65 [exp. 3] 2' in C6D6 86 (NH) [exp. 1] 2' in C6D6 83 (NH) [exp. 2] 2' in C6D6 83 (NH) [exp. 3] ΔS cal/molK -15.17 -15.18 -14.19 -15.32 -15.23 -15.65 -14.98 -14.91 -15.21 -18.01 -18.76 -18.14 ΔH kcal/mol -9.05 -9.03 -8.75 -6.55 -6.52 -6.64 -6.56 -6.54 -6.62 -8.85 -9.14 -8.89 dδM/dT ppb/K 1.5 1.3 -0.2 0.9 0.7 0.8 0.7 0.7 0.6 0.2 5.5 2.4 dδD/dT ppb/K -7.1 -6.5 -7.3 -9.4 -9.5 -9.4 -10.7 -10.7 -9.3 -8.6 -9.0 -7.8 ΔG kcal/mol -4.52 -4.50 -4.52 -1.98 -1.97 -1.98 -2.09 -2.09 -2.08 -3.48 -3.55 -3.48 Keq 1/M 2073.19 1995.22 2065.10 28.11 27.96 28.18 34.28 34.23 33.66 354.32 400.65 355.53 δD ppm 12.5257 12.5398 12.5287 8.0744 8.0710 8.0649 8.1583 8.1617 8.1856 9.5827 9.5174 9.5924 δM ppm 5.6646 5.6849 5.6952 3.2207 3.2178 3.2232 2.8941 2.8950 2.9005 3.1315 3.1039 3.0896 33 Because the N–H resonances show by far the largest changes in chemical shift between dimer and monomer forms, they were the primary data used in computing association constants. Between the monomer and dimer chemical shift values δM and δD of the studied compounds’ N–H sites, δD is uniformly several ppm downfield from δM due to H- bond induced deshielding. C6D6 was the solvent selected for the present study because: 1) It has weak interactions with solute due to its low polarity. 2) It dissolves all compounds studied. 3) It also has the minimum number of overlapping peaks in the chemical shift range where the studied N–H peaks appear. 4) its freezing and boiling temperatures allowed measurement in the temperature range available on MSU’s 900 MHz NMR instrument, i.e. ca. 5 to 40 °C. Deuterated methanol was used for temperature calibration of the cryogenic probe.68 To rigorously exclude water (which could hinder analyses by forming H-bonded complexes with the substrates)69 C6D6 was dried over molecular sieves, the substrates were sublimed before measurement, and samples were prepared in a dry box. In all experiments, no or negligible peaks were observed at 0.4 ppm, the chemical shift associated with residual water impurity in C6D6.70 For the dimerization energy differences between 1 and 2 and their reference compounds to be meaningful, accurate equilibrium data was needed. Though 1H NMR spectroscopy was a natural tool to use, MSU’s 500 and 600 MHz spectrometers did not allow measurements of sufficiently low concentrations to yield reliable association energies for compound 1. The high sensitivity of the 900 MHz NMR instrument equipped with a cryogenic probe (Bruker AVANCE) was the key to this problem, enabling useful spectra to be collected at concentrations as low as 10 µM. There, even compound 1, the strongest H-bonded dimer 34 studied, was substantially dissociated. Measured enthalpies of dimerization are presented in Figure I-16. The chemical shift values for monomers and dimers, and associated temperature coefficients were optimized as parameters to fit Equation I-11 to the experimental data. They are corrected to 298.15 K for the sake of comparison. The aromatic hydrogens of compounds 1 and 2 were assigned by NOE. The assignment of compound 1 was also confirmed by HMBC. The observed methine CH chemical shift changes upon dimerization serve as probes for the enhanced resonance forms shown in Figure I-16. The details of association measurements using NMR and peak assignments along with associated spectra are presented at the end of this chapter. To complement the NMR data, single crystals of compounds 1 and 2 (grown and characterized by X-ray crystallography) and known crystal structures of compounds 1t-butyl, 1′, 1′t-butyl, and 2′ were examined to assess the geometric effects of AMHB.56,71–73 Unlike 1’, compound 1 and the tert-butyl derivatives, 1t-butyl and 1’t-butyl, form simple dimers in their crystals. I.5.1. Energetic, geometric, and magnetic evidence for the interplay of aromaticity and H- bonding Experimental energetic, geometric, and magnetic evidence document the effects of aromaticity gain and its effect by H-bond strengthening. Upon dimerization of 1, cyclic six π- electron delocalization is enhanced in the five-membered rings of 1dimer (Figure I-16-A, top, red rings). The measured dimerization enthalpy is 2.37(15) kcal/mol more negative for 1 than it is for 1’ (∆fghi = –8.94 vs. –6.57 kcal/mol), the analogue with no π-conjugated ring and thus no possible AMHB. The N···O distance shortening (by 0.061(4) and 0.092(2) Å) in the structures of 1 vs. 1’ and 1t-butyl vs. 1’t-butyl (see top and middle in Figure I-17) also support 35 the stronger H-bonding in 1 and 1t-butyl. Downfield shifted 1H NMR signals for HA and HB in 1dimer (by 0.062(1) ppm and 0.597(1), relative to those of 1; see blue values, Figure I-16-A). These document the magnetic effects of AMHB. A) H-bond strengthening due to aromaticity enhancement N 2 x HA HA: 5.316 ppm HB: 5.211 ppm O N H HB 1 O N 2 x N H 1' N HA HA: 5.378 ppm HB: 5.808 ppm N O H N N N H O ΔdimH (kcal/mol) -8.94 aromaticity gain -2.37 N -6.57 no AMHB HB 1dimer O H N N H O 1'dimer B) H-bond weakening due to aromaticity disruption N 2 x HC HC: 6.198 ppm HD: 7.039 ppm N H N HD 2 N N H N N NH N HC HC: 6.187 ppm HD: 6.911 ppm HD 2dimer -6.57 aromaticity loss +2.39 N N N H N 2' N H N 2 x N -8.96 no AMHB N NH 2'dimer benzene via NMR spectroscopy. Aromatic rings are shown in red. Figure I-16. The two cases of aromaticity-modulated H-bonding. Enthalpies were measured in Dimerization of 2 decreases cyclic six π-electron aromaticity in the lower ring of 2dimer (Figure I-16-B), resulting in a 2.39(16) kcal/mol weaker dimerization enthalpy for 2 vs. 2’ (∆fghi=−6.57 vs. –8.96 kcal/mol, respectively), a 0.108(2) Å longer intermolecular N···N distance in 2dimer than in 2’dimer (see Figure I-17), and upfield shifts (by 0.011(1) and 0.128(1) 36 ppm) in the 1H NMR signals for HE and HF in 2dimer relative to those in 2 (see the blue values in Figure I-16-B).[10] AMHB effect present AMHB effect NOT present 2.866(4) Å 2.866(4) Å 1' 2.850(2) Å 1't-Butyl 2.805(2) Å 1 2.758(2) Å 1t-butyl 2 2.906(2) Å 2' 3.014(1) Å red, blue, gray and white respectively. Figure I-17. H-bonded heteroatom distances from X-ray structures of 1, 1t-butyl and 2 (left) vs their reference compounds 1’, 1’t-butyl and 2’ (right). Oxygen, nitrogen, carbon and hydrogen atoms are I.5.2. Charge polarization vs. AMHB: Chemical shifts The respective downfield and upfield shifts of the methine protons of compounds 1 and 2 upon dimerization qualitatively agree with expected AMHB trends. But these changes reflect not only π-delocalization effects; H-bond-induced polarization (expected to work in the same direction as aromaticity enhancement) must also be considered. For example, the 37 two methylene groups of compound 1’ shift by +0.502(4) and +0.126(19) ppm upon H- bonding. Thus, the methine peak shifts in 1 and 2 reflect both π-aromaticity perturbations and overall polarization effects (Figure I-16, resonance structures) for 1dimer, 1’dimer, and 2dimer; in 2’dimer, fast degenerate tautomerization averages resonances, complicating this analysis. Nonetheless, all the proton peaks of these compounds shift downfield upon dimerization, except those of the methine groups of compound 2; it is this exception that highlights the role of AMHB. I.5.3. Hybridization vs. AMHB: Energetics AMHB compounds reference compounds non-aromatic compounds with sp2 carbon centers in their rings O O O O O N N H N N H N N H N N H N N H 1-20.40 (0.00) N N H N 1'-15.77 (+4.63) N N H N 1x-16.92 (+3.49) N N H N 1y-16.03 (+4.37) N N H N 1z-17.13 (+3.28) N N H N 2-16.49 (0.00) 2'-17.76 (-1.27) 2x-19.72 (-3.23) 2y-18.29 (-1.79) 2z-19.91 (-3.42) sp2 carbon center CCSD(T)/CBS using MP2/aDZ geometries. Figure I-18. Gas-phase dimerization electronic energies (kcal/mol). Energies were calculated at Comparisons of the computed association energies of 1 and 2 to a series of reference compounds without a cyclic π-conjugated circuit, 1’ and 1x-z and 2’ and 2x-z (Figure I-18), show that ring carbon hybridizations of the reference compounds have little effect on AMHB. 38 As shown in Figure I-18, the computed ∆vwxE for 1 (two sp2 carbons) is consistently more negative than for 1’ (zero sp2 carbons), 1x and 1y (one sp2 carbon each), and 1z (two sp2 carbons), indicating aromaticity gain in 1dimer, while that of 2 (two sp2 carbons) is less negative compared to 2’ (zero sp2 carbons), 2x and 2y (one sp2 carbon each), and 2z (two sp2 carbons). These comparisons support the notion that aromaticity modulates H-bond strengths in a manner distinct from simple rehybridization effects. I.5.4. Dipole-dipole interactions vs. AMHB: Energetics Dipole moment (µ) is another property that changes upon going from compounds 1 and 2 to their corresponding reference compounds besides aromaticity. Thus, to understand the magnitude of the dipole effects on interaction energies vs AMHB, the µ vectors of monomers of 1, 1’, 2, and 2’ were calculated using their geometries found in the optimized Ci or C2h symmetry dimers without changing the Cartesian coordinates of the extracted monomers, at the MP2/aDZ level of theory using wB97X-D/aDZ geometries. This level of theory has been shown to predict dipole moment of a wide range of compounds with a mean absolute error of 0.08 D vs experimental values.74 Dipole-dipole distances (r) and angles (ϴ) were then obtained by center of symmetry operation on the calculated dipole moment vectors. They were then used in the following formula75 for antiparallel dipoles to calculate the dipole-dipole interaction energies (Evyv) that are listed in Table I-2. Evyv=−2µ(3coszθ−1) 4πε}r~ in which ε}=8.85×10yÄz F/m is the vacuum permittivity. Notably, for all four species, the µ values are about 5 D and the angles (ϴ) relating the antiparallel dipoles to the inter-dipole axes in the dimers are close to 54.74° (the magic 39 angle) making all the Ed-d values small. For 1 and 1’, these Ed-d values are close to zero and essentially negligible, whereas those of 2 and 2’ are slightly attractive. In both cases, the dipole effects are opposite to and substantially smaller than those of AMHB. Thus, dipole- dipole interactions do not account for the dimerization energy differences seen upon hydrogenation. Table I-2. Calculated dipole-dipole interaction energies (Ed-d). This table was adapted from Angewandte Chemie International Edition, 2017, 56, 9842. Copyright 2017 John Wiley and sons. Ed-d (kcal/mol) Cpd. 0.02 1 –0.05 1’ –0.44 2 –0.13 2’ In sum, experimental and theoretical evidence clearly point to significant geometric, energetic, and magnetic effects of AMHB. As illustrated herein, perturbations of aromaticity can modulate the H-bonding energies of heterocycles in the solution phase by as much as one-third. Quantum chemical calculations find that although hybridization and dipole effects are present, the effects due to changes in aromatic character are dominant. The reported NMR data for H-bonding interactions in the solvent medium may also serve as reference values for the evaluation and improvement of theoretical solvation models, enabling more realistic descriptions of molecules and their reactions in solution, which is the subject of the next chapter. d (Å) 5.313 5.424 5.171 5.299 ϴ (°) 54.52 55.27 58.83 56.63 µ (D) 4.3458 4.7805 4.6188 3.8340 40 I.6. Resonance-assisted H-bonding (RAHB) and AMHB Resonance-assisted hydrogen bonding (RAHB) is a concept explaining shorter H- bond distances seen in crystal structures of compounds in which the H-bond donor and acceptor sites are conjugated.76 This concept rationalizes the strong and short H-bonds in carboxylic acids, amides, DNA base pairs, etc. as a result of an increased contribution from the zwitterionic resonance form that strengthens H-bonds (Figure I-19). carboxylic acid H 2 x O O H amide H 2 x O HN H H O OH O H O H H O OH O H O O NHH O NHH H H H H H O HN H O HN H Figure I-19. Two examples of cases of RAHB. The concepts of RAHB and AMHB are closely related since they both correlate the polarizations of p-orbitals to those involved in H-bonding in the s-orbitals of H-bond donors and acceptors. Although RAHB is supported by broad surveys of the crystal database by Gilli and co-workers,76–78 it has been a controversial subject mainly, in my opinion, due to the ill- defined reference compounds chosen for the critical studies and ignorance of the effects of (anti)aromaticity in some cases.23,79,80 In this section, reference compounds are designed to quantitively evaluate the magnitude of the RAHB effect. 41 (A) amidine cases (B) imidic acid cases HN H -14.3 kca/mol HN H N 2 x N An1 HN H 2 x N -9.5 kca/mol (+4.8) N NHH 2 x An1dimer HN H N -22.1 kca/mol O H N Im1 O H -16.6 kca/mol O H N N OH Im1dimer O H N N OH N NHH 2 x N (+ 5.5) An2 cross-conjugation: no RAHB An2dimer Im2 cross-conjugation: no RAHB Im2dimer HN H -13.8 kca/mol HN H N 2 x N An3 N NHH 2 x An3dimer -22.4 kca/mol O H N Im3 O H N N OH Im3dimer O H An4dimer Im4 Im4dimer HN H 2 x N An4 2 x N O H N N NHH HN H N N OH -22.9 kca/mol -15.0 kca/mol at CCSD(T)/CBS using MP2/aDZ geometries. Figure I-20. Two cases for evaluation of the magnitude of the RAHB effect. Energies were calculated Upon H-bonding of An1 (Figure I-20), a resonance form is enhanced in which the charge separation as shown in An1dimer favors H-bonding, and thus its H-bond energy should be stronger than that of An2 in which such a resonance form is not possible due to cross- conjugation. Calculations show that this difference is significant (4.8 kcal/mol). They also show that hybridization changes of the ring carbons is not the main cause of this large difference since An3 and An4 have H-bond energies that are barely different from that of An1. Similarly, while calculated H-bond energies of Im1, Im3, and Im4 are within 1 kcal/mol of each other, they are significantly stronger than that of Im2. Specifically, Im1 is more tightly 42 bound than Im2 by 5.5 kcal/mol. An2 and Im2 have the same hybridization as An1 and Im2 on the atom centers involved in H-bonding respectively, so considering them as reference compounds, the RAHB effect is about 5 kcal/mol for both cases (Figure I-20). Therefore, these calculations provide strong evidence for a large RAHB effect at least in these two cases. I.7. AMHB in redox systems So far, it has been demonstrated how the H-bond strength of heterocycles can be modulated by their (anti)aromaticity. In this section, the energetic effects of H-bond formation on (anti)aromaticity of fused-ring heterocycles is probed via calculation of changes of reduction energies upon H-bonding. Figure I-21 (three pages long) shows the computational results. Importantly, p-electron counts vary by ± 2 potentially switching between aromatic and antiaromatic values. Given the opposite effects of AMHB on these two classes, a particularly pronounced modulation by AMHB of redox energy changes may be envisioned. The blue numbers are the H-bond electronic energy of the starting materials and the numbers under the arrows are the reduction electronic energies in the absence of formic acid. Compound A has a total of 8pÑy. Based on calculated NICS(1)ZZ values (shown outside the rings), while ring I is partially antiaromatic, ring II is weakly aromatic. Upon H-bonding, the antiaromaticity of ring I is increased, and aromaticity of ring II is disrupted, suggesting destabilization of the p-system upon H-bonding. On the other hand, the hydrogenated version of A, AH2, has two aromatic rings both of which increase in aromaticity upon H- bonding to formic acid. As a result of these (anti)aromaticity changes, the H-bond energy of AH2 is 3.84 kcal/mol stronger than that of A. This means the reduction of A to AH2 is favored by 3.84 kcal/mol in the presence of H-bonding to formic acid. This would translate into a difference in 2-electron reduction potential of 83 mV. Similar analysis can be used for 43 explaining the observed effect in the rest of compounds A-H in which effects as large as 6.37 kcal/mol are observed. In all these cases, the enhancement of aromaticity on both rings in the reduced product, and the enhancement of antiaromaticity on one or both rings in the starting upon H-bonding, favors the reduction in the presence of formic acid. Notably, in cases D, E, and G, in which the presence of two electron withdrawing groups (EWG) of carbonyls on ring II localizes its electrons, the ring I behaves like an isolated 2-pyridone and enhances in aromaticity upon H-bonding resulting in a smaller effect. This is supported by the upfield shifts of the calculated NICS(1)ÖÖ values on ring I in all these cases. I, J and M behave simply since the 2-pyridone ring is effectively isolated due to the presence of two carbonyl groups on ring II. As a consequence, H-bonding leads to enhancement of aromaticity on ring I and relief of antiaromaticity on ring II which leads to a stronger H-bonding than their reduced forms in which the aromaticity of both rings is enhanced upon H-bonding. This leads to weakly disfavoring of the reduction reaction in the presence of formic acid (the left column, small positive values). However, in the rest of the cases I-N, in which the two rings are strongly conjugated, the fused ring behaves as an antiaromatic 8ÜÑy system increasing in antiaromaticity upon H-bonding, which favors reduction in the presence of formic acid. In all the I-N cases, the rings do not act individually, and the aromaticity of both rings is enhanced upon H-bonding. This is presumably due to electron donating OH groups pushing electrons towards the electron deficient 2-pyridone rings. The very small or no effects are also supported by the calculated small ∆NICS(1)ÖÖ values. Cases O-U can be analyzed in a similar fashion. 44 O O +0.6 +0.7 -3.7 ring II N H +5.6 A . ring I O +0.6 +0.2 N -0.1 O +3.4 B NICS(1)zz of the ring O N N N +0.2 +0.6 -24.1 O +5.6 C O O +1.3 -2.4 +6.6 -6.8 D O +0.7 -2.7 +3.8 -8.2 E O O +0.5 +0.5 N +3.7 +1.0 F O N +1.0 -2.2 O +4.8 O -5.9 G +0.4 +0.6 N O H O H O H O H O H O H O H H-bond energy O -16.41 H O H2 -45.01 OH HO -2.9 -2.1 O H -15.89 H O O H NICS(1)zz shift upon H-bonding -13.5 Reduction energy without H-bonding H2 -42.94 -13.9 N -17.9 AH2 OH -2.7 -2.2 N -18.5 OH BH2 OH -13.79 H O O H -18.76 H O O H -18.46 H O O H -13.95 H O O H -18.17 H O O H H2 -10.98 H2 -35.24 H2 -25.77 H2 -24.91 H2 -30.53 -13.88 H O H2 -21.37 -12.9 -4.0 -1.7 N -17.0 OH CH2 N N HO OH -3.4 -3.4 -13.2 -13.3 DH2 OH -3.2 -3.6 -11.1 -13.7 OH EH2 OH -3.2 -2.6 -13.0 N -11.4 OH FH2 N -3.6 -3.4 HO -12.5 -14.6 OH GH2 Reduction energy change upon H-boning O H O H O H O H O H O O H H -3.84 -4.01 -5.68 -2.44 -2.18 -6.16 -2.72 O H O H O H O H O H O H O H O H O H O H O H O H O H O H O H -3.6 -2.6 N H O HO O -1.8 O O +2.1 H Figure I-21. Reduction energy modulations via AMHB. Energy (in kcal/mol) and NICS(1)zz (in ppm) values are respectively calculated at CCSD(T)/CBS and mPW91PW91 using MP2/aDZ geometries. -12.4 OH HH2 -6.37 -11.9 O H H 45 Figure I-21 (cont’d) O O +7.6 +0.3 -6.1 -2.6 H-bond energy O -19.32 H O H2 -62.34 -23.2 -8.9 N H O I +0.2 -3.1 N J O H H2 -51.79 -19.00 H O O H +5.4 O -7.5 OH -0.4 OH -2.9 N IH2 OH -2.9 N JH2 -0.5 -21.7 HO -8.2 Reduction energy change upon H-boning +2.17 +1.73 -2.03 -3.33 +0.12 -3.32 H O H O H O H O H O H O O H O H O H O H O H O H O H O H O H O H O H O H O H O H O H O H O H O +1.6 O +11.5 +6.0 +1.3 N K O -1.8 +0.1 +2.1 +0.3 N O L O +11.5 O -6.8 +0.1 -2.7 N M -0.1 +3.7 O +1.0 +0.2 N O N -16.56 H O O H -13.99 H O O H H2 -59.17 OH -0.3 HO -22.2 -8.6 -3.2 N KH2 OH H2 -36.46 -22.7 0.0 -7.8 -2.6 N OH LH2 H2 -48.67 -18.58 H O O H H2 -38.69 -14.03 H O O H HO -22.8 HO -7.7 -0.4 -3.2 N MH2 -0.1 -22.8 HO -7.0 -2.6 N OH NH2 46 Figure I-21 (cont’d) O +9.5 -18.2 O +1.5 N +0.5 O O -0.1 N +1.5 O +11.1 +0.6 P O +2.8 +0.2 N +2.9 +0.7 Q O -6.3 -2.3 N O +10.3 O +0.2 R O +8.0 -7.4 -2.5 N O -0.7 S +3.7 +1.1 N +10.5 O +1.6 T O -6.6 -2.4 +15.7 -1.7 U O N O H-bond energy O -16.82 H O O H -17.37 O H O H -16.66 H O O H -19.73 O H O H -15.51 O H O H -16.46 O H O H H O H O H O H O H O H O H -15.64 O H O H2 -47.80 H O H O H O H O H O H O H O H Reduction energy change upon H-boning -1.37 -0.50 -1.72 +0.64 -0.99 -2.55 -0.74 H O H O H O H O H O H O H O O H O H O H O H O H O H O H H2 HO -9.8 -2.4 -47.99 -25.5 -0.4 OH N OH2 OH H2 -59.61 -10.2 -2.6 N HO -22.8 -0.5 PH2 OH H2 -54.56 -10.0 -2.5 -22.7 -0.5 N QH2 OH H2 -45.18 H2 -35.50 H2 -53.19 -7.7 -3.1 N -1.0 HO -21.0 HO RH2 -7.7 -2.8 HO -20.2 -0.6 N OH SH2 -7.9 -3.1 N -0.8 -20.7 HO TH2 OH -7.1 -2.6 -21.8 -0.7 N OH UH2 OH 47 These calculations clearly show that while AMHB can affect the redox chemistry of fused rings, the interpretation of the results may be less straightforward, especially in cases where the comprising rings’ p-systems are not strongly coupled and act as individual ones. H-bond energy -15.25 O H O H O N N H O ring III ring II N -1.5 N -7.2 -0.5 -23.6 +0.8 ring I O N H O -0.1 N O H H H2 O -25.35 H N +0.3 N -1.1 +12.1 -0.4 -19.4 O N -0.4 N H H O Reduction energy change upon H-boning O H +0.32 O H Case I N N Case II -14.11 O H O H N NICS(1)zz shift upon H-bonding Reduction energy without H-bonding NICS(1)zz of the ring O H H O H H N N O O O O +0.8 -0.4 N N O N -19.4 H O H O H O 0.0 N H -0.3 N -1.67 +0.3 -23.6 H2 -25.35 N +0.3 N -7.2 H N +0.4 N -1.1 +12.1 Figure I-22. H-bonding modulation of flavin upon H-bonding. One biologically relevant case for which the redox chemistry could be affected by H- bond formation via AMHB is flavin. Flavin can H-bond in two modes which are shown as cases I and II (Figure I-22). In case I, the aromaticity of rings II and III is increased upon H- bonding. This is consistent with the calculated negative ∆NICS(1)ÖÖ values for these rings (see numbers inside the corresponding rings). A resonance form consistent with these magnetic changes is shown in Figure I-22. In this resonance form, the sum of rings II and III are similar to naphthalene, a bicyclic 10pey aromatic compound. This stabilization causes the reduction reaction to be favored towards the starting flavin, i.e. disfavoring the reduction by 0.32 kcal/mol. Conversely, in case II, H-bond formation favors a resonance form in flavin in which the rings II and III are not aromatic. This is consistent with the calculated ∆NICS(1)ÖÖ values (see numbers inside rings). As a result, the starting material’s p-system is destabilized leading to a more favored reduction reaction by 1.67 kcal/mol. Thus, the active 48 site binding mode found in the protein pockets of various flavin binding enzymes can potentially adjust the redox potential over this nontrivial range. I.8. Conclusions In conclusion, the generality of AMHB was demonstrated using a broad computational survey of heterocycles via calculations of energetic and magnetic effects of AMHB. Then, experimental measurements provided energetic, geometric and magnetic evidence for AMHB. These studies hinged on the clear definition of reference compounds in which the H-bonding sites were the same as (anti)aromatic heterocycles subjected to AMHB, except that their cyclic p-systems were breached via hydrogenation of rings’ p-bonds. The concept of AMHB was then used to explain remote H-bond energy modulations of bicyclic aromatic heterocycles. Calculations of the reduction of a wide range of heterocycles show that the energy modulations of cyclic p-systems upon H-bonding can be used to explain energy variations among redox active heterocycles such as flavin. I.9. Computational and experimental details I.9.1. Computational details All the geometries in this chapter were optimized at the MP281–85/aDZ86–90 level of theory, with the core electrons frozen, unless otherwise mentioned. Frequency calculations confirmed the stationary nature of the minima and the default geometry convergence criteria in Gaussian1691 after frequency calculations were used to confirm complete optimization. These default values for Maximum Force, RMS Force, Maximum Displacement, and RMS Displacement were 4.5×10yá, 3.0×10yá, 1.8×10y~, and 1.2×10y~ respectively. In cases where not all the four criteria were converged, if the Maximum Force and RMS Force were smaller than 4.5×10yá and 3.0×10yá the geometries were accepted as optimized. 49 êïyöõz/âóúò+ùöõz/âêò àâääãåç. ééèê(ë)=àíìíî.êïyñï/âóò+àíçôãâäåì. This exception was only used in cases where even optimizations with calculation of Hessian at each point did not resolve the issue and Gaussian16 itself accepted those geometries. In some cases, some dimers could form in two possible symmetries, Ci and C2. In those cases, the dimers were optimized in both symmetries and the lowest energy dimer was used for calculation of H-bond energies, after the CCSD(T)92–96 calculations described below. Using the optimized geometries, the wavefunction-based scheme recommended by Burns et al.36 was used to obtain reference H-bonding interaction energies in the gas-phase. ééèê(ë)/âêò The scheme is based on density-fitted97–105 Hartree-Fock (DF-HF)106 electronic energies calculated at DF-HF/a5Z, Eûüû†.°¢/£§•, DF-MP2 correlation energies extrapolated from aQZ to a5Z (abbreviated as DF-MP2/aQ5Z), Eû¶ß®£©™ü. ´¨z/£§ú•, and CCSD(T)/aDZ additional correlation ÆÆØ≠(∞)/£≠•, added on top of those of DF-MP2. The sum of these three components energies, δ´¨z/£≠• gives an approximation of the CCSD(T) energies extrapolated to the complete basis limit (CBS), denoted as E£©©®™¶. ÆÆØ≠(∞) in the above equation. The extrapolation scheme used for the DF- MP2 calculations is that of Halkier et al.107 in the form below E±†™®®.=E≤†™®®.+Any~ in which n is the cardinal number of the Dunning basis set, E±†™®®.is the calculated correlation energy using that basis set, A is a constant, and E≤†™®®. is the extrapolated correlation energy at cardinal number of infinity. By using two basis sets with consecutive cardinal numbers of n and n+1, the equation can be solved for E≤†™®®. E≤†™®®.= (n+1)~E±≥Ć™®®.−n~E±†™®®. (n+1)~−n~ 50 In our case where cardinal numbers n = 4 and n + 1 = 5 are used, the equation simplifies as follow ≠¢y´¨z/£§ú•=E≤†™®®.= 125×E£ú•†™®®.−64×E£§•†™®®. Eû¶ß®£©™ü. 61 After calculating the E£©©®™¶. ÆÆØ≠(∞) for each monomer and dimer, the electronic dimerization energies, ∆vwxE, were calculated as ÆÆØ≠(∞)(dimer)−2 E£©©®™¶. ÆÆØ≠(∞)(monomer) ∆vwxE=E£©©®™¶. in which the denotations are obvious. I.9.2. Details of NMR measurements Compounds 1, 1’, 2, and 2’ were sublimed and the sublimation apparatus was opened inside the nitrogen filled the dry box. The anhydrous C6D6 containing tetramethylsilane was prepared as follows: Tetramethylsilane (1 µL, NMR grade, Across Organics) and 3 Å molecular sieves (30 % v/v, Sigma-Aldrich) were added to a 10-gram bottle of C6D6 (99.5 % deuterated, Cambridge Isotope Laboratories) and the bottle was sealed for two days prior to the experiments. The C6D6 bottle was also opened inside the dry box, where all the samples were made. Thick-walled volumetric flasks (Corning Pyrex, 5- and 10 mL) were dried in an oven at ca. 140 °C for about 2 days followed by 2 hours at 300 °C. This drying procedure did not change the calibration of the flasks (vide infra). NMR tubes were dried at ca. 140 °C for 36- 48 hours. All the above items were transferred to the vacuum chamber of the dry box, while still hot, and were kept under 100 mTorr for overnight. Syringes (Hamilton, 50- and 500 µL) were dried at room temperature for overnight and were also kept under 100 mTorr for overnight. Samples were made by sequential dilution of a concentrated solution of the 51 analyte. After the solutions were made, the NMR tubes were capped with regular polyethylene caps, and the tops were wrapped with parafilm. All the volumetric glassware and syringes were calibrated, and their errors were determined by weighing water on a METTLER AE200 balance. A statistical. sample population of 10 was used for all the standard deviation determinations. The balance showed a repeatability of ±0.1 mg in our lab environment, which makes it suitable for calibration of the volumetric flasks and the 500-µL syringe but not the 50-µL one. Standard deviations of 7.5 and 15.7 µL was obtained for 5- and 10-mL flasks respectively, which are in agreement with the ±20 µL tolerance provided in the supplier catalog. This leads to an uncertainty less than 0.5 % in volumetric measurements carried out with these flasks. The 500 µL syringe however showed a standard deviation of 0.8 µL for measuring 100 µL, the smallest volume it was used for, which is again in good agreement with the 1% error provided in the supplier catalog. The 50 µL syringe gave standard deviation of 0.1 µL, which is in the range of repeatability of the balance. Since we were not able to estimate the error of the 50 µL syringe, we assumed the standard deviation of 0.1 µL which is provided by the supplier. Considering all the above standard deviations, errors of roughly up to 1% and 2% should be expected for the mM and µM concentration ranges, respectively. I.9.3. Synthesis of compounds 1, 1’, 2 and 2’ 1H NMR spectra were recorded on an Agilent DDR2 500 MHz spectrometer. Chemical shifts are reported in ppm from tetramethylsilane with the residual non-deuterated solvent resonance as the internal standard (CHCl3: δ 7.26 ppm). Data are reported as follows: chemical shift (multiplicity, coupling constant, number of hydrogens). Multiplicities are abbreviated as follows: s = singlet, d = doublet, t = triplet, q = quartet, m = multiplet. 13C 52 NMR spectra were also recorded on the above Agilent DDR2 500 MHz spectrometer with complete proton decoupling. Chemical shifts are reported in ppm from tetramethylsilane with the solvent resonance as the internal standard (CDCl3: δ 77.16 ppm). Infrared (IR) spectra were recorded on a JASCO FT/IR 6600 type A (ATR mode) spectrophotometer. Peaks are reported in cm−1. All synthetic procedures were carried out using reagent grade solvents in air unless otherwise mentioned. Reagents and chemicals were used as arrived, without further purification. Diethylenetriamine, sodium hydride (60% in mineral oil), 2,2-dimethoxy-N- methylethan-1-amine, 2-imidazolidinethione, imidazolidin-2-one, and 2,2-dimethoxyethan- 1-amine were purchased from Sigma-Aldrich. CS2 was purchased from Matheson Coleman and Bell. Methyl iodide was purchased from Alfa Aesar. 1-methyl-1,3-dihydro-2H-imidazol-2-one 1 (method A). This procedure was adapted from the literature.108 A solution of KOCN (1.20 g, 14.79 mmol) in water (2.6 mL) was added to a solution of 1S (1.20 g, 10.07 mmol) in HCl (4.0 mL, 3 M). The resulting solution was refluxed for 2 hours. Then, it was cooled down, saturated with sodium chloride, and extracted with dichloromethane (4 x 5 mL). Evaporation of all volatiles to dryness yielded a white solid (1.10 g). The solid was then dissolved in H2SO4 (1.1 mL, 0.25 N) and stirred at 57 °C for 2.2 hours. After that the solution was cooled down, saturated with NaCl (0.5 g), and extracted with dichloromethane (5 mL). After drying with magnesium sulfate, evaporation of all volatiles and subsequent sublimation (80 °C, 20 mTorr), compound 1 was obtained as 53 a white solid (70 mg, 7% isolated yield). Characterization data were in accordance with literature.109 1H NMR (500 MHz, CDCl3) δ 11.12 (s, 1H), 6.27 (t, J = 2.6 Hz, 1H), 6.16 – 6.11 (m, 1H), 3.24 (s, 3H). 13C NMR (126 MHz, CDCl3) δ 155.26, 112.51, 108.41, 30.00. IR (neat): 3107, 3030, 2994, 2843, 2809, 1655, 1469, 1402, 1280, 909, 785, 671, 531 cm-1. Single crystals suitable for X-ray diffraction were grown by slow evaporation of a solution in benzene. 1-methyl-1,3-dihydro-2H-imidazol-2-one 1 (method B). This method is an improved version of method A. A solution of KOCN (1.20 g, 14.79 mmol) in water (2.6 mL) was added to a solution of 1S (1.20 g, 10.07 mmol) in HCl (4.0 mL, 3 M). The resulting solution was refluxed for 30 minutes. Then, it was cooled down, saturated with sodium chloride (1.1 g), and extracted with dichloromethane (3 x 10 mL). After the organic phase was dried with MgSO4 and evaporated to dryness, a white solid (1.6 g) was obtained. The solid was then dissolved in dichloromethane (5 mL), trifluoroacetic acid (5 mL) was added, and the resulting solution was refluxed for 20 hours. After that, all the volatiles were evaporated under a stream of nitrogen, the residue was taken up in chloroform (30 mL), stirred with potassium carbonate (5 g) for 30 minutes, and the solids were filtered off. The neutralization with potassium carbonated was repeated, and all the volatiles were evaporated to obtain a yellowish white solid. After sublimation, a white solid (610 mg, 62%) was obtained. 1H NMR (500 MHz, CDCl3) δ 11.08 (s, 1H), 6.28 (t, J = 2.6 Hz, 1H), 6.14 (dd, J = 2.8, 2.2 Hz, 1H), 3.25 (s, 3H). 13C NMR (126 MHz, CDCl3) δ 155.21, 112.56, 108.44, 77.41, 77.16, 76.91, 30.03. 54 1-methylimidazolidin-2-one 1’. This procedure was adapted from the literature.110 A mixture of 2-imidazolidinone 3S (1.52 g, 96%, 16.95 mmol), sodium hydride (0.84 g, 60 % in mineral oil, 21.00 mmol), and 1,4-dioxane (20 mL, kept over 3 Å sieves for overnight) was stirred at 80 °C for 2.25 hours under an inert atmosphere of nitrogen. After that, the mixture was cooled down in an ice-water bath, and methyl iodide (2.0 mL, 31.80 mmol) was added. After stirring for one more day at ambient temperature, the solids were filtered off, and the filter cake was washed with more 1,4-dioxane (20 mL). Evaporation of all volatiles to dryness yielded crude 1’ which was purified via column chromatography using silica as the stationary phase and 10 % v/v methanol in dichloromethane as the eluent. Compound 1’ was isolated as a white solid (0.47 g, 28% isolated yield). Characterization data were in accordance with literature.110 1H NMR (500 MHz, CDCl3) δ 6.02 (s, 1H), 3.24 (s, 4H), 2.61 (s, 3H). 13C NMR (126 MHz, CDCl3) δ 163.38, 47.10, 37.62, 30.18. The pure compound was sublimed 60 °C under 50 mTorr and opened in the dry box. 2,3-dihydro-1H-imidazo[1,2-a]imidazole 2. This procedure was adapted from the literature.111 Methyl iodide (14.9 g, 105.0 mmol ) was added to a solution of 4S (9.82 g, 96.1 mmol) in methanol (20 mL), and the resulting mixture refluxed for 2 hours. After that, the solution was cooled down to room temperature, and ether (20 mL) was added. The precipitated white solid was filtrated and washed with more ether (50 mL). Recrystallization from methanol (15 mL) yielded 5S as a white solid (15.5 g, 66%). Characterization data were in accordance with literature.111 1H NMR (500 MHz, DMSO-d6) δ 9.91 (s, 2H), 3.87 (s, 4H), 55 2.62 (s, 3H). 13C NMR (126 MHz, DMSO-d6) δ 170.45, 45.37, 14.01. A solution of 5S (1.50 g, 6.2 mmol) and H2NCH2CH(OMe)2 (1.50 g, 14.3 mmol) in methanol (2.0 mL) was refluxed for 12 hours. After that, all the volatiles were evaporated and the resulting oil was further dried by heating at 110 °C under high vacuum for one hour. The residual gel was then dissolved in concentrated HCl (1.9 mL) and stirred at 55 °C for half an hour. After that, it was cooled down in an ice-water bath, and concentrated ammonium hydroxide (5.0 mL) and sodium chloride (4.0 g) were added, respectively. Insoluble solid was filtered off and the aqueous phase was extracted with dichloromethane (3 x 10 mL), and subsequently dried with magnesium sulfate. Evaporation of all volatiles to dryness yielded crude 2 which was purified via column chromatography using silica as the stationary phase and dichloromethane: triethylamine: methanol (7:2:1) as the eluent. After sublimation (80 °C, 50 mTorr), compound 2 was achieved as a white solid (0.21 g, 31% isolated yield). 1H NMR (500 MHz, CDCl3) δ 6.64 (d, J = 1.6 Hz, 1H), 6.54 (d, J = 1.6 Hz, 1H), 4.84 (s, 1H), 4.01 – 3.88 (m, 4H). 13C NMR (126 MHz, CDCl3) δ 158.40, 129.33, 110.36, 77.16, 76.90, 76.65, 47.94, 43.27. Single crystals were grown by slow evaporation of a solution in benzene. IR (neat): 3147, 3108, 2973, 2899, 1574, 1514, 1480, 1325, 1286, 1264, 1203, 1161, 1096, 1061, 1032, 939, 876, 848, 829, 738, 685, 620 cm-1. 2,3,5,6-tetrahydro-1H-imidazo[1,2-a]imidazole 2’. This procedure was adapted from the literature.112 CS2 (12.0 mL, 0.20 mol) was added to a stirring solution of diethylenetriamine (20.6 g, 0.20 mol) in xylenes (300 mL), and the resulting mixture was 56 refluxed under an inert atmosphere of nitrogen for 13 days. After that, about two-third of the solvent was evaporated by blowing nitrogen on top of the condenser. The remaining solution was then decanted into an Erlenmeyer flask while still hot and cooled down slowly overnight to precipitate a brownish white solid (15.3 g). Sublimation (60 °C, 50 mTorr) of a portion of this solid (1.00 g) yielded compound 2’ as a yellowish white solid (0.50 g). Characterization data were in accordance with literature.112 1H NMR (500 MHz, CDCl3) δ 6.76 (s, 1H), 3.76 (t, J = 7.0 Hz, 4H), 3.01 (t, J = 7.1 Hz, 4H). 13C NMR (126 MHz, CDCl3) δ 171.52, 52.70, 49.53. 57 CHAPTER II: EVALUATION OF IMPLICIT SOLVATION MODELS FOR PREDICTING H-BOND FREE ENERGIES II.1. Introduction Accurate methods to predict the strengths of H-bonds are of value in the design and analysis of molecular systems across various fields of chemistry. The development of such tools relies on systematic datasets of accurately measured solution phase H-bond energies. However, many simple compounds of interest, such as alcohols, aggregate via multi-species equilibria in solution, placing H-bonds in a complex mixture of different settings. To probe H-bonding, no common spectroscopic tool is ideal: fast exchange averages NMR peaks for H- bonding species, while IR spectra show broad overlapping bands with widely varying frequency-dependent extinction coefficients. The above issues have hindered quantitative molecular-level determination of association energetics for most H-bonds among simple compounds such as water, alcohols, or amines in solution (Scheme II-1-A). A number of H-bonded small-molecule systems have been studied in the gas-phase using specialized spectroscopic methods.113 Modern high-level quantum chemical protocols can compute energetics for such gas-phase systems at levels of accuracy that rival experiment.114,115 Thus, high-level calculations generally serve well as reference methods for gas-phase systems (vide infra).116,117 Yet the condensed phase is the context of broadest interest. Recent years have seen the development of sophisticated and general continuum methods to simulate solvent environments. These methods are mostly optimized to compute free energies of solvation.118 In this chapter, H-bonded association energies as another metric to assess the performance of such tools are explored. 58 A) Complicated hydrogen bonding equilibria of alcohols R O H υγ R O H υα At least five overlapping peaks in infrared spectra or averaged peaks in NMR spectra. R O H υγ R O H υβ R O H υδ R O H υβ etc. B) Simple dimerization equilibria studied here O N IM H δM O H N O N H δD O O N H N N H N H N H N N O Ph N 1 2 N H N O 1' 2' BA studied here. Scheme II-1. (A) Complications from H-bonding polymerization in alcohols. (B) H-bonding species One way to get around the measurement challenges noted above is to design systems that establish simple “2×π∫ª∫πѺ⇌æøπѺ" equilibria in solution (Scheme II-1-B). Systems chosen for this study only form dimers, mostly via two-point H-bond homodimerization of amide or carboxylic acid functional groups (six cases). Though tautomerization to the 2-hydroxypyridine structure complicates the analysis of 2-pyridone, for the amides examined here, the potential tautomeric forms are strongly disfavored, as confirmed by quantum chemical simulations. In rigorously dry solvents, the systems studied herein show simple monomer-dimer equilibria that accurately fit an analytical expression for the observed NMR data, enabling extraction of thermodynamic and extrapolated spectroscopic parameters. While NMR instruments with common field values and probes are limited in sensitivity for measurements of strongly bound systems, MSU's 900 MHz NMR 59 spectrometer, equipped with a cryogenic probe, enabled accurate quantification of H-bonds as strong as 4.5 kcal/mol. The solvents chosen for this study were benzene, dichloromethane, chloroform, and acetonitrile covering a range of dielectric constants from 2.3 to 37.5. These are among the most common organic solvents, and their polarity ranges from strongly polar to hydrophobic, roughly the range seen in the binding sites of various proteins. H-bonding solvents and those with exchangeable protons were not considered here. The computational survey includes a wide range of common popular and newer density functional methods, with solvation effects incorporated using the implicit solvation models IEF-PCM C-PCM, and SMD models.118–121 Gas-phase benchmark studies have shown that some DFT methods can compete in accuracy (≤0.5-1.0 kcal/mol) with highly correlated wavefunction-based levels of theory.122 The use of continuum solvation models entails manageably small numbers of modest-sized calculations, obviating the need for explicit quantum chemical calculations on the dynamically variable clusters of solvent molecules that form the solvation shell of a given solute. Therefore, a survey of combinations of DFT methods and continuum solvation models constitutes the main part of this study. II.2. Experimental reference H-bond energies As mentioned earlier, NMR spectroscopy was used to measure solution phase H-bond energies. Samples were prepared at concentrations chosen to access a range of monomer:dimer ratios, and measured at four temperatures in the range of 5-35 °C. From these measurements, enthalpy, entropy and free energies of dimerization were extracted. The details of procedures and data fitting are similar to those presented in chapter I of this 60 dissertation. The N-H or O-H proton chemical shifts were used as the primary peaks for extracting thermodynamic data for IM and BA respectively. Table II-1. Measured H-bond thermodynamic values and extrapolated monomer and dimer chemical shifts. Keq Compound DdimH DdimG dD dM DdimS (kcal/mol) (kcal/mol) (ppm) (ppm) (1/M) (cal/molK) or solvent Benzene -4.52 -8.94 5.682 12.531 2044.50 -14.85 1 -1.98 -6.57 8.070 28.08 -15.40 3.221 1' -6.57 -2.09 8.169 34.06 2.897 -15.03 2 -3.50 -8.96 9.564 -18.30 3.108 370.17 2' -2.17 -7.30 9.079 -17.22 4.165 38.93 IM -9.18 -3.78 5.864 13.981 593.29 -18.1 BA Chloroform -2.82 -5.84 -10.11 6.956 11.637 117.52 1 -3.39 -0.40 7.185 1.98 4.137 -10.02 1' -0.06 -1.99 6.991 -6.48 3.870 1.10 2 -0.87 -4.41 8.735 -11.88 4.001 4.31 2' -3.63 -0.62 2.85 8.573 5.329 -10.08 IM -3.48 -8.16 6.794 13.383 355.86 -15.68 BA Dichloromethane -6.59 -2.70 95.76 -13.04 6.948 11.599 1 -0.19 -4.01 -12.8 4.095 7.248 1.39 1' -3.33 -0.33 1.74 7.228 3.851 -10.07 2 -1.54 -5.48 13.46 -13.2 4.021 8.496 2' -0.42 -4.44 -13.48 5.287 8.5044 2.03 IM -8.18 -3.14 6.977 13.390 200.28 -16.91 BA Acetonitrile -4.43 -0.98 5.2 7.797 11.413 -11.57 1 0.65 -3.03 -12.34 4.618 7.175 0.33 1' 0.45 -2.71 -10.59 4.305 7.196 0.47 2 -0.84 -5.87 -16.88 4.516 4.12 8.824 2' 5.827 -12.41 -3.09 0.35 8.445 0.62 IM 1.44 -3.81 9.391 18.542 -17.6 0.09 BAa gave: DdimG = +0.84 kcal/mol, DdimH = -1.75 kcal/mol, DdimS = -8.71 cal/mol/K, dM = 9.38 ppm, and ddM/dt = -5.8 ppb/K aLocking down the dimer chemical shift to 13.40 ppm and its temperature dependence to 6.1 ppb/K 61 Table II-1 presents the thermodynamic data extracted for all compounds studied. As expected, going from non-polar to polar solvents, the dimerization energies weakened for all compounds. The dimerization energies in CDCl3 and CD2Cl2 are very similar. Interestingly, the AMHB effect34,123,124 manifests itself in dimerization energies across all solvents, even though its effect is smaller in the more polar CD3CN solvent. The free energies were used as reference points as they are reported in this table. II.3. CCSD(T)/CBS: a reference for gas-phase H-bond energies The wavefunction-based scheme recommended by the Sherrill group 36 was used to obtain reference H-bonding interaction energies in the gas phase. The geometries used for these calculations were fully optimized at MP2/aDZ using the Gaussian16 software. As described in detail in the previous chapter, the CCSD(T)/CBS energy is the sum of the DF- HF/a5Z total electronic energy, DF-MP2 correlation energy extrapolated from aQZ to a5Z basis set, and CCSD(T) correlation energy calculated using the aDZ basis set. DF-MP2 correlation energy is the difference between DF-MP2 and DF-HF total electronic energies calculated using the same basis set. Likewise, the CCSD(T) correlation energy is the difference between the CCSD(T) and MP2 (not DF-MP2) energies calculated at the same basis set. Both CCSD(T) and DF-MP2 correlation energies are negative. Table II-2 shows the DF-HF,/a5Z extrapolated DF-MP2/aQ5Z, and CCSD(T)/aDZ interaction energies as well as the estimated CCSD(T)/CBS values for all the dimers studies here in various symmetries. While DF-HF interaction energies were off by a few kcal/mol, extrapolated DF- MP2/aQ5Z and CCSD(T)/aDZ were close to the CCSD(T)/CBS reference methods, with the former performing slightly better. The poorer performance of CCSD(T)/aDZ is likely due to 62 DF-MP2/aQ5Z −21.09 −15.65 −15.59 −17.14 −16.95 −18.66 −18.62 −17.43 −16.30 −16.31 slow convergence of the correlation energy and use of the smallest aDZ Dunning basis set.107 The CCSD(T)/CBS energies were used as reference values in the following discussion. Table II-2. Calculated H-bond electronic energies at CCSD(T)/CBS and a few less correlated wavefunction-based approximations. DF-HF/a5Z CCSD(T)/aDZ Cpd. (sym.) CCSD(T)/CBS −22.26 −12.36 −20.40 1 (C2h) −9.55 −17.23 −15.77 1' (C2) −9.47 −17.13 −15.69 1' (Ci) −18.57 −8.23 −16.49 2 (C2) −8.64 −18.29 −16.39 2 (Ci) −9.98 −19.51 −17.76 2' (C2) −17.66 −19.34 −9.82 2' (Ci) −12.53 −18.88 −17.79 BA (C2h) −9.53 −17.76 −16.31 IM (C2) −16.32 −17.78 −9.52 IM (Ci) II.4. The performance of DFT methods vs CCSD(T)/CBS in the gas-phase Deviations for calculated H-bond electronic energies vs the CCSD(T)/CBS composite level of theory for 1, 1’, 2, 2’, BA and IM as well as their mean absolute errors (MAE, the right column) are presented in Table II-3. For reference, the CCSD(T)/CBS energies of each species is shown on top of their corresponding columns. The deviations (signed errors) for each species at various DFT methods and basis sets (DFT/base), denoted as D¶≠¢∞, were calculated as in which, E¶≠¢∞/√£ƒû and E¶ÆÆØ≠(∞)/Æ≈Ø are total electronic energies of dimerization for species X (X = 1, 1’, 2, 2’, BA, or IM) at DFT/base and CCSD(T)/CBS levels of theory, respectively. The values of D¶≠¢∞/√£ƒû are presented in columns 2-7 of Table II-3. The MAE values for each level of theory over the 6 complexes were then calculated as D¶≠¢∞/√£ƒû=E¶≠¢∞/√£ƒû−E¶ÆÆØ≠(∞)/Æ≈Ø 63 6 ∆«à=|EÄ≠¢∞/√£ƒû|+|EÄ…≠¢∞/√£ƒû|+|Ez≠¢∞/√£ƒû|+|Ez…≠¢∞/√£ƒû|+|E≈ ≠¢∞/√£ƒû|+|EÀ´≠¢∞/√£ƒû| Consistent with recommendations from the Thanthiriwatte et al. study of formic acid, formamide and formamidine homo- and hetero-dimers,122 methods such as wB97X-D,125 PBE,126,127 or M06-2X128 produce H-bond energies with MAE values of less than 0.5 kcal/mol is some combinations with a large basis sets such as 6-311++G(3df,3pd), aDZ or aTZ. To shorten denotation of large Gaussian basis sets, their ‘6-311++’ term is replaced by ‘L’. This simplifies these basis sets as: 6-311++G(3df,3pd) = LG(3df,3pd), 6-311++G(2df,2p) = LG(2df,2p), and 6-311++G(d,p) = LG(d,p). It is notable that PBE0 (also known as PBE1PBE),129 M06-2X, and PBE (not to be confused with PBE0) can achieve high accuracy when used in combination with the moderate 6-31+G(d,p) basis set saving hugely in computational resources. Using this relatively small basis set, methods such as MN15130 and wB97X-D also perform acceptably. However, LC-wHPBE131 and TPSS132 produce errors of 1-2 kcal/mol, and APFD133 and B3LYP methods are not recommended to be used with this basis set. The use of HF and S-VWN134– 136 is to be avoided with any basis set. While the calculated energies of the former method are under-bound by up to 6 kcal/mol, the latter method predicts H-bond energies that are over-bound by up to 19 kcal/mol. In addition to these two methods, the use of Dunning’s double zeta basis set without augmentation, DZ, should be avoided. This basis set is the smallest one in this study. On the other hand, the augmented version of this basis set, aDZ, appears to construct the best performing levels of theory when used in conjunction with appropriate DFT methods. It is notable that as opposed to wavefunction-based methods, for density functional methods, the increase of basis set size does not necessarily lead to more 64 accurate H-bond energies. For example, the PBE method used with the aDZ basis set leads to more accurate results than the significantly larger basis set aTZ. On a second-row element such as carbon, there are 14, 15, 19, 22, 23, 30, 34, 39, and 46 basis functions for DZ, 6- 31G(d), 6-31+G(d,p), LG(d,p), aDZ, TZ, LG(2df,2p), LG(3df,3pd), and aTZ basis sets, respectively. Table II-3. Mean absolute errors (MAE) of calculated electronic energies of H-bonds using various levels of theory vs CCSD(T)/CBS. The energies are not counterpoise corrected. MAE IM kcal/mol –16.32 CCSD(T)/CBS values: 0.45 0.03 wB97X-D/LG(3df,3pd) 0.46 0.12 wB97X-D/aTZ 0.02 0.46 PBE/aDZ 0.46 0.47 M06-2X/aDZ 0.47 0.42 PBE0/aDZ 0.43 0.48 M11/LG(d,p) 0.26 0.48 MN15/aDZ 0.53 –0.07 wB97X-D/LG(2df,2p) 0.64 0.55 PBE0/6–31+G(d,p) 0.76 0.57 M06-2X/6–31+G(d,p) 0.45 0.59 PBE/6–31+G(d,p) 0.59 0.45 PBE0/TZ 0.26 0.61 M11/6–31+G(d,p) 0.54 0.63 M06-2X/TZ 0.38 0.66 M05-2X/aDZ 0.67 0.98 M06-2X/LG(d,p) 0.67 0.68 M05-2X/LG(d,p) 0.98 0.68 PBE0/LG(d,p) 0.26 0.68 M05-2X/TZ 0.70 –0.53 M11/aDZ –0.11 0.70 PBE/TZ 0.50 0.71 M11/TZ 0.81 0.72 PBE/LG(d,p) 0.75 0.69 M05-2X/6–31+G(d,p) 0.98 0.80 PBE/LG(2df,2p) –0.28 0.83 wB97X-D/LG(d,p) 0.97 0.83 PBE/aTZ 0.85 0.73 M11/LG(2df,2p) 0.95 0.88 PBE/LG(3df,3pd) –0.41 0.90 wB97X-D/6–31+G(d,p) 0.88 0.95 MN15/TZ 0.97 1.00 MN15/6–31+G(d,p) 1.22 0.99 PBE0/LG(2df,2p) 2' –17.76 –0.85 –0.88 –0.79 0.41 –0.01 0.21 0.23 –1.15 –0.02 0.43 –0.46 –0.28 0.60 0.46 0.88 0.42 0.61 –0.09 0.77 –0.65 –1.07 0.63 –0.54 0.97 0.11 –1.81 0.22 0.88 0.34 –1.52 0.82 1.03 0.60 BA –17.79 –0.73 –0.55 –0.73 –0.27 –0.50 –0.93 –0.96 –0.63 –0.90 –0.70 –1.04 –0.93 –1.60 –0.88 –0.32 –0.21 –0.44 –0.22 –1.08 –1.66 –1.41 –0.85 –0.21 –0.55 –0.17 –0.79 –0.22 –0.68 –0.39 –1.23 –0.67 –0.69 –0.07 1 –20.40 0.40 0.47 0.59 0.34 0.56 0.53 0.50 0.33 0.65 0.47 0.88 0.80 –0.16 0.58 0.53 1.00 0.91 1.34 0.53 –0.68 0.71 0.73 1.58 0.64 1.72 0.14 1.65 0.91 1.68 –0.35 1.38 1.17 1.57 1' –15.77 –0.04 0.09 0.49 0.51 0.67 0.22 0.14 –0.14 0.58 0.43 0.62 0.68 0.05 0.51 0.55 0.73 0.53 1.00 0.37 –0.41 0.36 0.48 1.02 0.46 1.27 –0.43 1.33 0.61 1.27 –0.63 0.81 0.69 1.32 2 –16.49 –0.64 –0.61 –0.16 0.80 0.68 0.54 0.80 –0.84 0.49 0.65 –0.08 0.40 0.97 0.81 1.30 0.65 0.90 0.46 1.11 0.26 –0.56 1.11 –0.13 1.17 0.52 –1.53 0.61 1.30 0.64 –1.29 1.15 1.22 1.18 65 Table II-3 (cont’d) M06-2X/aTZ MN15/LG(d,p) M05-2X/aTZ LC–wHPBE/6–31G(d) M11/LG(3df,3pd) PBE0/aTZ wB97X-D/aDZ M06-2X/LG(2df,2p) PBE0/LG(3df,3pd) wB97X-D/TZ M05-2X/LG(2df,2p) TPSS/TZ B3LYP/6–31G(d) MN15/aTZ M06-2X/LG(3df,3pd) M11/aTZ TPSS/aDZ M05-2X/LG(3df,3pd) TPSS/6–31+G(d,p) MN15/LG(2df,2p) TPSS/6–31G(d) MN15/LG(3df,3pd) LC–wHPBE/TZ B3LYP/TZ LC–wHPBE/aDZ TPSS/LG(d,p) LC–wHPBE/6–31+G(d,p) MN15/6–31G(d) B3LYP/DZ B3LYP/aDZ M05-2X/6–31G(d) LC–wHPBE/DZ M06-2X/6–31G(d) B3LYP/6–31+G(d,p) LC–wHPBE/LG(d,p) TPSS/LG(2df,2p) TPSS/LG(3df,3pd) APFD/aTZ APFD/LG(3df,3pd) APFD/LG(2df,2p) TPSS/aTZ PBE0/6–31G(d) M05-2X/DZ M06-2X/DZ TPSS/DZ B3LYP/LG(d,p) LC–wHPBE/LG(2df,2p) 1.04 1.69 0.89 –0.53 1.16 1.57 –0.67 1.38 1.54 –0.32 1.36 2.04 –0.58 1.59 1.31 1.29 1.77 1.30 1.91 1.96 –0.60 1.97 2.19 2.29 1.86 2.61 2.03 –1.14 –1.10 2.10 –1.54 –1.32 –1.62 2.30 2.68 2.82 2.76 –1.32 –1.35 –1.31 2.91 –1.51 –1.80 –1.87 –1.30 2.94 2.95 0.99 0.95 0.82 –0.74 0.85 1.45 –0.78 1.16 1.36 –0.71 1.03 1.72 –0.85 1.11 1.21 1.12 1.77 1.10 1.73 1.31 –0.80 1.31 1.90 1.81 1.82 2.16 1.85 –1.54 –1.12 1.89 –1.62 –1.16 –1.54 1.98 2.18 2.42 2.43 –1.37 –1.46 –1.48 2.62 –1.60 –1.57 –1.48 –1.17 2.32 2.56 1.51 1.15 1.75 –0.65 1.70 1.32 –1.37 1.48 1.32 –1.59 1.85 1.08 –0.80 1.63 1.62 1.99 1.38 1.98 1.39 1.88 –1.24 1.97 1.88 1.79 2.06 1.35 2.01 –1.18 –1.57 2.07 –1.19 –1.48 –1.57 2.22 1.85 1.95 2.05 –2.02 –2.04 –2.16 2.14 –1.85 –1.62 –1.96 –2.13 2.17 2.69 1.25 0.88 1.44 –1.26 1.39 0.80 –1.83 1.16 0.87 –1.98 1.52 0.68 –1.24 1.25 1.46 1.54 0.93 1.82 1.12 1.60 –1.71 1.75 1.36 1.51 1.50 1.07 1.68 –1.65 –2.01 1.66 –1.65 –2.20 –2.02 2.10 1.45 1.65 1.87 –2.58 –2.52 –2.78 1.88 –2.59 –2.00 –2.36 –2.67 2.02 2.27 –0.28 –0.31 –0.56 –2.23 –0.42 –0.07 –1.05 0.10 –0.29 –1.37 0.00 –0.15 –2.24 –0.15 –0.27 –0.19 0.33 –0.42 –0.10 0.02 –2.67 –0.17 0.37 0.59 0.72 0.71 0.53 –3.24 –3.22 1.12 –2.80 –3.55 –2.87 0.80 1.04 0.80 0.55 –3.12 –3.35 –3.13 0.87 –3.17 –3.94 –3.61 –3.88 1.47 1.27 1.09 1.20 0.78 –0.93 0.94 1.31 –0.85 1.33 1.24 –0.74 1.05 1.25 –1.27 1.27 1.34 1.16 1.24 1.10 1.53 1.51 –1.51 1.51 1.82 1.61 1.72 1.89 2.06 –1.65 –1.42 1.66 –1.88 –1.30 –1.69 2.03 2.29 2.08 2.06 –1.40 –1.47 –1.47 2.21 –2.00 –1.82 –1.60 –1.81 2.32 2.58 1.03 1.03 1.04 1.06 1.08 1.09 1.09 1.10 1.10 1.12 1.14 1.15 1.16 1.17 1.20 1.21 1.24 1.29 1.30 1.38 1.42 1.45 1.59 1.60 1.62 1.63 1.70 1.73 1.74 1.75 1.78 1.84 1.88 1.90 1.92 1.95 1.95 1.97 2.03 2.05 2.11 2.12 2.13 2.15 2.16 2.21 2.39 66 –1.85 –1.47 2.98 –2.43 3.03 3.19 3.19 3.16 –2.16 –2.36 –2.21 3.28 –2.10 3.31 –2.00 –2.33 –3.11 –3.13 –2.83 4.60 5.29 5.15 5.51 –4.27 5.81 5.89 5.98 –5.14 –9.10 –9.19 –9.15 –9.13 –10.04 –10.03 –10.79 –11.95 –14.07 –1.87 –1.74 2.65 –2.35 2.78 2.62 2.65 2.69 –2.15 –2.16 –1.96 2.63 –2.17 2.60 –2.27 –2.64 –2.54 –3.11 –2.77 3.72 4.27 4.45 4.57 –4.34 4.74 4.90 5.02 –4.81 –8.54 –8.66 –8.65 –8.75 –9.17 –9.48 –9.92 –11.47 –12.86 –1.86 –2.87 2.88 –1.57 2.88 2.77 2.88 2.86 –2.77 –2.70 –2.66 3.12 –3.00 3.43 –3.12 –3.52 –2.43 –4.50 –4.16 4.71 5.01 5.53 5.33 –5.18 5.69 5.89 5.91 –6.14 –9.18 –9.23 –9.43 –10.18 –9.94 –10.33 –10.65 –12.66 –14.40 –4.46 –3.21 1.10 –3.89 1.36 1.60 1.42 1.60 –3.93 –3.54 –4.24 1.96 –3.99 1.88 –4.02 –3.37 –5.31 –4.48 –5.55 3.43 4.00 4.21 4.23 –6.05 4.45 4.37 4.62 –7.36 –13.73 –13.93 –13.90 –13.67 –14.99 –14.86 –14.57 –16.31 –19.49 –1.91 –1.65 2.65 –2.58 2.77 2.56 2.56 2.58 –1.97 –2.31 –2.31 2.84 –2.27 2.83 –3.01 –2.83 –2.77 –3.26 –3.40 4.21 4.64 4.70 4.82 –4.61 5.06 5.24 5.33 –5.04 –8.88 –8.99 –8.93 –8.93 –9.33 –9.93 –10.43 –12.25 –13.58 –2.37 –3.46 2.59 –2.19 2.50 2.61 2.82 2.73 –3.37 –3.45 –3.49 3.07 –3.69 3.26 –3.71 –3.97 –3.25 –5.00 –4.84 4.83 5.24 5.84 5.45 –5.89 5.90 6.24 6.20 –6.96 –10.64 –10.63 –10.97 –11.73 –11.55 –11.98 –12.66 –14.27 –16.38 Table II-3 (cont’d) 2.39 MN15/DZ 2.40 APFD/LG(d,p) 2.48 LC–wHPBE/LG(3df,3pd) 2.50 M11/6–31G(d) 2.55 LC–wHPBE/aTZ 2.56 B3LYP/LG(2df,2p) 2.59 B3LYP/LG(3df,3pd) 2.60 B3LYP/aTZ 2.73 APFD/6–31+G(d,p) 2.75 APFD/aDZ 2.81 PBE0/DZ 2.81 HF/DZ 2.87 APFD/TZ 2.89 HF/6–31G(d) 3.02 PBE/6–31G(d) 3.11 wB97X-D/6–31G(d) 3.24 M11/DZ 3.91 wB97X-D/DZ 3.92 PBE/DZ 4.25 HF/6–31+G(d,p) 4.74 HF/LG(d,p) 4.98 HF/aDZ 4.98 HF/TZ 5.06 APFD/6–31G(d) 5.27 HF/LG(2df,2p) 5.42 HF/LG(3df,3pd) 5.51 HF/aTZ 5.91 APFD/DZ 10.01 S–VWN/aTZ 10.10 S–VWN/LG(3df,3pd) 10.17 S–VWN/LG(2df,2p) 10.40 S–VWN/LG(d,p) 10.84 S–VWN/6–31+G(d,p) 11.10 S–VWN/TZ 11.50 S–VWN/aDZ 13.15 S–VWN/6–31G(d) 15.13 S–VWN/DZ To summarize this part, the combined choice of basis set and DFT method is critical for achieving high accuracy for gas phase H-bond energies. The results obtained here are consistent with those of the previous study by Sherrill’s group,122 but inclusion of smaller basis sets in this work enables recommendations suitable for larger systems without 67 compromise in the accuracy. Specifically, the use of PBE0, M06-2X and PBE functionals is recommended in combination with the 6-31+G(d,p) basis set when quick calculations of small molecules are needed or the system of study is too large for use of more complete basis sets. II.5. Comparison of theory and experiment With CCSD(T)/CBS energies as reference for gas-phase “electronic energies” and experimental dimerization “free energies” as reference for solution phase, the performance of various combinations of DFT methods (and HF) and basis sets can be evaluated both in the gas- and in the solution phases. For the latter, implicit solvation models SMD, C-PCM, and IEF-PCM were used to simulate the four studied solvents. The geometries for both gas-phase and solution phase structures were fully optimized at the specified level of theory in the corresponding medium. All the DFT calculations were performed using Gaussian 16. Due to the large number of calculations (about 30,000 geometry optimizations) the convergence of the geometries, maximum force, RMS force, maximum displacement, and RMS displacement were only checked before frequencies. The default Gaussian16 values were used for these four criteria of geometry convergence. Since the experimental free energies used as reference were at room temperature (298.15 K), no special correction was made to the calculated thermal corrections to free energies and standard solvent parameters as they were implemented in Gaussian16 were used. The harmonic frequencies for each fully optimized structure were calculated in the solution phase and used for calculation of thermal correction to free energy. The following formula was used to calculate the dimerization free energies: ∆vwxG=Gvwxû®−2×Gx™±™xû®−1.89 kcal/mol 68 in which Œfghíã and Œhåœåhíã are dimer and monomer free energies which were directly extracted from the thermochemistry section of the Gaussian output files by searching for the “Sum of electronic and thermal Free Energies” string. The 1.89 kcal/mol is the correction for free energy of dimerization that originates from the contraction from gas-phase standard conditions (1 atm) to ∆G(1 atm→1 M)=nRTln(VÄ£ßx—£ƒVÄ´ƒ™ü) the solution-phase standard conditions (1 M) at 298.15 K. This value was obtained using the following formula in which n=1 mol, R=1.987×10y~ kcal/molK, T=298.15 K, VÄ´ƒ™ü=1 “, and VÄ£ßx—£ƒ for an idea gas at these conditions was calculated using PV=nRT to be 24.465 L. Substituting all these values in the above equation, ∆G(1atm→1M)=+1.89 kcal/mol was obtained, which is also reported in the original SMD parametrization paper.118 The harmonic frequencies for each fully optimized structure were calculated in the solution phase and used for calculation of thermal correction to free energy. Monomers of 1 and BA were optimized in Cs symmetry. However, in some cases, the symmetric monomer of 1 led to an imaginary frequency. In those cases, the symmetry was broken. Dimers of 1 and BA were optimized in C2h symmetry. For dimers of 1, again, this symmetry resulted in imaginary frequencies in some cases, so Ci and C2 symmetry geometries were also optimized for the dimers of 1. For the rest of the molecules (1’, 2, 2’ and IM), the monomers were optimized in C1 symmetry and the dimers were optimized in both C2 and Ci symmetries. For extraction of data, a home-made python code was used. If the Cs symmetry monomer of 1 had an imaginary frequency, then the C1 one was used. Similarly, for the dimer of 1 if the geometry with C2h symmetry had any imaginary frequencies then the C2 and Ci were compared and the one with lowest energy and no imaginary frequency was used. For BA, the Cs monomers and C2h dimers 69 did not have any imaginary frequency at any level of theory. For the other cases with C2 and Ci dimer, the symmetry with the lowest energy and no imaginary frequency was used. The criteria for the best-performing levels of theory, though somewhat arbitrary, was the sum of gas-phase electronic energy MAEs vs CCSD(T)/CBS reference, and the solution phase free energies vs experimental values. Figure II-1, which is extended to a few pages, shows the plots comparing the performance of the studied methods. The Y-axis shows various levels of theory and the X-axis is the sum of gas-phase and solution phase MAEs, by which the Y-axis is sorted. Looking at the end of the plot, it is obvious that choosing HF and S-VWN methods in combination with any basis set leads to large errors in both the gas- and solution-phase. It is also clear that while using the DZ basis set (the smallest one in this study) in combination with any method leads to substantial errors, its augmented version, the aDZ basis set, is among the best performing ones when used with DFT methods such as PBE0, MN15, M06-2X, M05-2X or PBE. The colors of the bars show the solvation model used as guided in the legend, and the MAE for the corresponding levels of theory both in the gas- phase and solution phase are labeled on each bar. Nominally, PBE0/aDZ/C-PCM is the best performing method among all. Its MAE values for gas- and solution phases are 0.47 and 0.60 kcal/mol respectively. Changing the solvation model from C-PCM to IEF-PCM leads to a slight increase of 0.06 kcal/mol in its MAE. However, using the SMD solvation model with this level of theory leads to solution phase MAE of 1.47 kcal/mol. This comparison points out to the importance of the choice of implicit solvation model in addition to the DFT method and basis set. 70 0.66 0.600.710.800.790.800.720.620.840.84 0.470.470.480.460.480.470.550.660.450.460.550.670.680.47 0.630.47 0.590.480.53 0.660.680.46 0.680.590.570.450.480.45 0.680.46 0.610.570.460.530.48 0.67 0.970.590.72 1.030.53 0.750.70 1.00 PBE0/aDZ PBE0/aDZ MN15/aDZ ѡB97XD/aTZ M11/LG(d,p) M06-2X/aDZ PBE0/6-31+G(d,p) M05-2X/aDZ ѡB97XD/LG(3df,3pd) PBE/aDZ PBE0/6-31+G(d,p) 0.77 M06-2X/LG(d,p) 0.680.67 M05-2X/LG(d,p) M06-2X/aDZ 0.89 M06-2X/TZ 0.730.90 M06-2X/aDZ PBE0/TZ 0.770.86 M11/LG(d,p) 0.91 ѡB97XD/LG(2df,2p) M05-2X/aDZ 0.730.95 PBE0/LG(d,p) 0.72 ѡB97XD/aTZ PBE0/LG(d,p) 0.730.850.950.99 PBE/6-31+G(d,p) 0.82 M06-2X/6-31+G(d,p) ѡB97XD/LG(3df,3pd) 0.98 MN15/aDZ ѡB97XD/LG(3df,3pd) M05-2X/LG(d,p) 0.771.00 PBE/aDZ M11/6-31+G(d,p) 0.860.90 M06-2X/6-31+G(d,p) ѡB97XD/aTZ 1.030.961.01 ѡB97XD/LG(2df,2p) MN15/aDZ M06-2X/LG(d,p) 0.820.91 MN15/6-31+G(d,p) 0.530.81 PBE0/TZ PBE/LG(d,p) MN15/LG(d,p) 0.500.80 ѡB97XD/LG(2df,2p) 1.01 M05-2X/6-31+G(d,p) PBE/TZ 0.85 0.00 5.00 4.00 Figure II-1. Sorted by sum of mean absolute errors of various levels of theory vs gas-phase CCSD(T)/CBS electronic energies and experimental H-bond free energies. C-PCM IEF-PCM SMD 2.00 3.00 gas 71 Figure II-1 (cont’d) PBE/6-31+G(d,p) 0.970.96 PBE/LG(2df,2p) 0.77 M11/6-31+G(d,p) PBE/LG(2df,2p) 0.77 M05-2X/TZ 0.890.87 M11/TZ PBE/LG(d,p) 0.88 MN15/6-31+G(d,p) 0.62 PBE0/TZ 1.01 M11/LG(2df,2p) 0.75 M05-2X/6-31+G(d,p) 0.85 MN15/LG(d,p) 0.580.76 M11/LG(2df,2p) PBE/aDZ 1.15 M05-2X/TZ 0.93 M11/aDZ 0.93 PBE/LG(3df,3pd) 0.75 M06-2X/aTZ 0.61 PBE/LG(3df,3pd) 0.770.82 PBE/aTZ PBE/aTZ 0.82 M11/TZ 0.941.09 M06-2X/6-31+G(d,p) M11/TZ 0.97 M06-2X/aTZ 0.670.601.03 M06-2X/LG(2df,2p) M05-2X/TZ ѡB97XD/LG(d,p) 0.921.30 MN15/TZ 0.80 M11/LG(d,p) ѡB97XD/6-31+G(d,p) 0.88 MN15/aTZ 0.64 MN15/aTZ 0.64 MN15/TZ 0.861.151.12 M06-2X/LG(d,p) M11/aDZ M06-2X/LG(3df,3pd) 0.621.13 M11/aDZ PBE0/LG(2df,2p) 0.84 M06-2X/TZ 1.22 M06-2X/LG(3df,3pd) 0.650.78 M11/LG(3df,3pd) TPSS/TZ 0.72 0.00 0.59 0.800.61 0.800.680.710.72 0.970.59 0.850.75 1.030.850.46 0.680.70 0.88 1.030.880.830.830.710.570.71 1.031.100.680.83 0.950.48 0.90 1.171.170.950.670.70 1.200.70 0.990.63 1.201.081.15 1.00 2.00 3.00 4.00 C-PCM IEF-PCM SMD gas 72 5.00 Figure II-1 (cont’d) M05-2X/aTZ M11/LG(3df,3pd) TPSS/TZ ѡB97XD/aDZ M05-2X/LG(2df,2p) M05-2X/aTZ PBE/6-31+G(d,p) PBE0/LG(2df,2p) M06-2X/TZ PBE0/aDZ M11/aTZ PBE0/LG(3df,3pd) M11/aTZ M05-2X/LG(2df,2p) MN15/LG(2df,2p) M05-2X/aDZ MN15/TZ ѡB97XD/LG(d,p) M11/6-31+G(d,p) PBE0/LG(3df,3pd) LC-ѡHPBE/6-31G(d) ѡB97XD/6-31+G(d,p) MN15/LG(3df,3pd) ѡB97XD/TZ MN15/LG(2df,2p) M05-2X/LG(3df,3pd) PBE0/aTZ M05-2X/LG(3df,3pd) M05-2X/LG(d,p) MN15/LG(3df,3pd) PBE0/6-31+G(d,p) ѡB97XD/LG(d,p) PBE/LG(d,p) ѡB97XD/6-31+G(d,p) TPSS/aDZ PBE/TZ TPSS/aDZ PBE0/LG(d,p) B3LYP/6-31G(d) ѡB97XD/aDZ M11/LG(2df,2p) M05-2X/6-31+G(d,p) PBE/LG(2df,2p) 0.00 0.840.81 0.74 0.81 0.77 0.870.93 1.33 1.30 1.47 0.73 0.850.76 0.84 0.601.04 1.32 1.17 1.42 0.931.13 0.98 0.61 0.94 0.680.99 0.79 0.810.69 1.431.60 1.331.29 1.47 0.97 1.60 1.10 1.67 1.201.551.651.60 1.28 1.00 1.041.081.151.091.141.040.59 0.990.630.47 1.211.101.211.14 1.380.66 0.950.830.61 1.101.060.90 1.451.12 1.381.291.09 1.290.68 1.45 0.55 0.830.72 0.90 1.240.70 1.240.68 1.161.090.850.750.80 2.00 3.00 4.00 C-PCM IEF-PCM SMD gas 73 5.00 Figure II-1 (cont’d) TPSS/6-31+G(d,p) MN15/6-31+G(d,p) PBE/LG(3df,3pd) B3LYP/TZ PBE/aTZ M06-2X/aTZ PBE/TZ M06-2X/LG(2df,2p) TPSS/6-31+G(d,p) LC-ѡHPBE/TZ MN15/LG(d,p) ѡB97XD/aDZ B3LYP/TZ TPSS/TZ M06-2X/LG(3df,3pd) LC-ѡHPBE/TZ M11/LG(3df,3pd) M05-2X/aTZ TPSS/LG(d,p) TPSS/6-31G(d) M05-2X/LG(2df,2p) MN15/aTZ LC-ѡHPBE/aDZ LC-ѡHPBE/6-31G(d) PBE0/LG(2df,2p) TPSS/LG(d,p) ѡB97XD/TZ M05-2X/LG(3df,3pd) PBE0/LG(3df,3pd) M11/aTZ LC-ѡHPBE/aDZ PBE0/aTZ LC-ѡHPBE/6-31G(d) APFD/aTZ MN15/LG(2df,2p) B3LYP/aDZ ѡB97XD/TZ MN15/LG(3df,3pd) APFD/LG(2df,2p) LC-ѡHPBE/6-31+G(d,p) APFD/LG(3df,3pd) B3LYP/6-31G(d) TPSS/LG(3df,3pd) 0.00 1.12 1.461.551.63 0.86 1.451.40 1.79 1.22 0.941.46 1.50 0.98 1.461.411.651.70 1.05 1.20 1.421.711.69 1.29 1.87 1.94 1.321.88 1.721.931.822.02 1.48 2.05 1.141.74 1.382.04 1.74 1.151.23 1.52 2.14 1.38 1.00 1.300.970.88 1.600.83 1.030.70 1.10 1.30 1.591.031.09 1.601.151.20 1.591.081.04 1.631.421.141.17 1.621.060.99 1.631.12 1.291.101.21 1.621.091.06 1.971.38 1.751.12 1.45 2.051.70 2.03 1.16 1.95 2.00 3.00 C-PCM IEF-PCM SMD gas 74 4.00 5.00 Figure II-1 (cont’d) B3LYP/aDZ TPSS/LG(2df,2p) LC-ѡHPBE/6-31+G(d,p) TPSS/aDZ LC-ѡHPBE/LG(d,p) B3LYP/6-31G(d) TPSS/LG(3df,3pd) B3LYP/TZ TPSS/LG(2df,2p) M05-2X/6-31G(d) MN15/6-31G(d) B3LYP/6-31+G(d,p) LC-ѡHPBE/LG(d,p) TPSS/6-31+G(d,p) LC-ѡHPBE/DZ LC-ѡHPBE/TZ TPSS/aTZ B3LYP/DZ B3LYP/6-31+G(d,p) TPSS/aTZ APFD/LG(d,p) B3LYP/LG(d,p) PBE0/6-31G(d) M06-2X/6-31G(d) TPSS/6-31G(d) TPSS/LG(d,p) B3LYP/LG(d,p) TPSS/6-31G(d) LC-ѡHPBE/aDZ APFD/6-31+G(d,p) APFD/aTZ LC-ѡHPBE/LG(3df,3pd) B3LYP/aDZ LC-ѡHPBE/LG(2df,2p) APFD/LG(2df,2p) LC-ѡHPBE/6-31+G(d,p) APFD/aDZ APFD/LG(3df,3pd) HF/DZ APFD/aTZ TPSS/LG(3df,3pd) LC-ѡHPBE/LG(3df,3pd) B3LYP/LG(2df,2p) 0.00 1.591.65 1.39 2.11 1.472.29 1.521.55 1.88 1.751.82 1.66 1.65 2.31 1.792.041.95 1.52 1.80 1.67 1.391.812.052.42 1.70 2.52 1.86 2.69 2.57 1.53 2.35 1.88 2.62 2.032.37 2.74 1.70 2.45 1.67 2.54 2.60 2.08 2.00 1.00 1.75 1.951.701.24 1.92 1.16 1.951.60 1.951.781.73 1.901.921.30 1.841.59 2.111.74 1.902.11 2.402.212.121.881.421.63 2.21 1.421.62 2.73 1.97 2.481.75 2.392.051.70 2.752.03 2.81 1.971.95 2.482.56 3.00 2.00 C-PCM IEF-PCM SMD gas 75 4.00 5.00 Figure II-1 (cont’d) B3LYP/LG(3df,3pd) M11/6-31G(d) TPSS/LG(2df,2p) APFD/LG(2df,2p) TPSS/DZ M05-2X/6-31G(d) M05-2X/DZ APFD/LG(3df,3pd) HF/DZ MN15/6-31G(d) LC-ѡHPBE/LG(d,p) LC-ѡHPBE/aTZ B3LYP/LG(2df,2p) B3LYP/DZ B3LYP/LG(3df,3pd) M05-2X/6-31G(d) M06-2X/DZ B3LYP/6-31+G(d,p) LC-ѡHPBE/DZ B3LYP/aTZ TPSS/aTZ MN15/6-31G(d) B3LYP/DZ HF/6-31G(d) LC-ѡHPBE/DZ M06-2X/6-31G(d) PBE0/6-31G(d) APFD/LG(d,p) HF/6-31G(d) MN15/DZ M06-2X/6-31G(d) B3LYP/LG(d,p) PBE0/6-31G(d) APFD/TZ APFD/LG(d,p) LC-ѡHPBE/LG(2df,2p) HF/DZ LC-ѡHPBE/LG(3df,3pd) APFD/6-31+G(d,p) PBE0/DZ TPSS/DZ APFD/aDZ B3LYP/LG(2df,2p) 0.00 2.00 2.102.662.472.53 2.57 2.88 2.64 1.862.96 2.79 2.182.183.01 2.18 3.01 2.652.89 2.96 2.22 2.77 3.153.17 2.063.15 3.172.96 2.70 2.25 2.752.97 3.273.14 2.423.13 2.89 2.713.13 2.883.54 2.83 2.95 3.20 2.00 2.592.501.952.052.161.78 2.132.03 2.811.731.92 2.552.561.74 2.591.78 2.151.901.84 2.602.111.731.74 2.891.841.882.122.40 2.892.391.88 2.212.12 2.872.402.39 2.812.48 2.732.812.16 2.752.56 4.00 6.00 8.00 C-PCM IEF-PCM SMD gas 76 10.00 Figure II-1 (cont’d) B3LYP/LG(2df,2p) B3LYP/LG(3df,3pd) APFD/6-31+G(d,p) M11/6-31G(d) ѡB97XD/6-31G(d) B3LYP/aTZ TPSS/DZ M05-2X/DZ HF/6-31G(d) APFD/aDZ M05-2X/DZ M11/6-31G(d) M06-2X/DZ PBE/6-31G(d) M06-2X/DZ M11/DZ MN15/DZ MN15/DZ APFD/TZ APFD/TZ PBE0/DZ ѡB97XD/6-31G(d) PBE0/DZ ѡB97XD/6-31G(d) PBE/6-31G(d) PBE/6-31G(d) M11/DZ ѡB97XD/DZ M11/DZ HF/6-31+G(d,p) HF/6-31+G(d,p) PBE/DZ HF/TZ HF/LG(d,p) ѡB97XD/DZ HF/TZ ѡB97XD/DZ HF/LG(d,p) HF/aDZ HF/6-31+G(d,p) HF/aDZ PBE/DZ HF/LG(2df,2p) 0.00 3.203.18 3.06 3.29 2.693.23 3.72 3.76 3.01 3.153.87 3.54 3.91 3.103.04 4.00 3.90 4.09 3.633.963.78 3.80 4.143.944.45 4.264.29 3.71 4.49 3.68 3.87 4.34 3.673.92 4.79 3.864.16 4.94 4.03 4.77 4.275.46 4.28 2.00 2.562.592.732.50 3.112.602.162.13 2.892.752.13 2.502.15 3.022.15 3.242.392.39 2.872.872.813.112.813.113.023.023.24 3.913.24 4.254.253.92 4.984.743.91 4.983.91 4.744.984.25 4.983.92 5.27 6.00 8.00 4.00 C-PCM IEF-PCM SMD gas 77 10.00 Figure II-1 (cont’d) PBE/DZ HF/TZ APFD/6-31G(d) HF/LG(3df,3pd) HF/LG(2df,2p) HF/LG(d,p) HF/LG(3df,3pd) HF/aTZ HF/aDZ HF/aTZ HF/LG(2df,2p) HF/LG(3df,3pd) APFD/6-31G(d) HF/aTZ APFD/6-31G(d) APFD/DZ APFD/DZ APFD/DZ S-VѡN/aTZ S-VѡN/LG(3df,3pd) S-VѡN/LG(2df,2p) S-VѡN/LG(d,p) S-VѡN/6-31+G(d,p) S-VѡN/aTZ S-VѡN/LG(3df,3pd) S-VѡN/LG(2df,2p) S-VѡN/aTZ S-VѡN/LG(3df,3pd) S-VѡN/LG(2df,2p) S-VѡN/LG(d,p) S-VѡN/LG(d,p) S-VѡN/TZ S-VѡN/aDZ S-VѡN/6-31+G(d,p) S-VѡN/6-31+G(d,p) S-VѡN/TZ S-VѡN/aDZ S-VѡN/TZ S-VѡN/aDZ S-VѡN/6-31G(d) S-VѡN/6-31G(d) S-VѡN/6-31G(d) S-VѡN/DZ S-VѡN/DZ S-VѡN/DZ 0.00 3.92 4.985.065.425.274.745.425.514.985.515.275.425.065.515.065.915.915.91 5.66 4.684.62 4.33 4.494.54 5.02 4.47 5.075.315.305.445.77 4.67 5.80 5.97 6.95 7.12 9.019.079.009.219.59 10.63 10.72 10.66 10.90 10.98 10.92 10.91 11.17 10.56 10.18 11.2612.14 11.52 11.77 12.39 12.03 12.81 14.24 14.49 15.23 16.62 16.86 8.00 10.01 10.10 10.1710.4010.8410.01 10.10 10.17 10.01 10.10 10.17 10.4010.40 11.10 11.5010.8410.8411.10 11.5011.10 11.5013.1513.1513.1515.1315.1315.13 24.00 16.00 C-PCM IEF-PCM SMD gas 78 32.00 (A) PBE0/aDZ/C-PCM (B) PBE0/aDZ/IEF-PCM Interestingly, as opposed to wave function methods, using substantially larger basis sets than aDZ such as aTZ, LG(3df,3pd), or LG(2df,2p) does not lead to systematic improvement of accuracy. For example, replacing the aDZ basis set with the substantially larger aTZ basis set for the best-performing level of theory (PBE0/aDZ/C-PCM), in fact, increases the gas and solution phase MAE values to 1.09 and 0.99 kcal/mol, respectively. PBE0/6-31+G(d,p)/C-PCM seems to be a good balance between accuracy and computational resource demand. Its solution and gas-phase MAE values are only about. 0.1 kcal/mol larger than those of the best-performing level of theory, which uses the aDZ basis set with all the same other parameters. -5-4-3-2-1012 -5-4-3-2-1012 1' 1 MAE Benzene Acetonitrile gas-phase Figure II-2. (A), (B), and (C) Individual signed errors for the three best-performing and (D) the The individual signed errors for the three best-performing levels of theory as well as PBE0/6-31+G(d,p)/C-PCM are shown in Figure II-2. While most errors are small, those of -5-4-3-2-1012 -5-4-3-2-1012 IM BA 1' 1 Dichloromethane Benzene Acetonitrile most economical level of theory. 1' 1 IM BA (D) PBE0/6-31+G(d,p)/C-PCM Dichloromethane Acetonitrile Benzene 2 2' Chloroform 1' BA (C) MN15/aDZ/C-PCM Benzene Dichloromethane ) l o m / l a c k ( e c n e r e f e r m o r f r o r r E ) l o m / l a c k ( e c n e r e f e r m o r f r o r r E BA Dichloromethane IM IM MAE gas-phase 2 2' Chloroform 2 2' Chloroform MAE gas-phase MAE gas-phase 2 2' Chloroform 1 Acetonitrile ) l o m / l a c k ( e c n e r e f e r m o r f r o r r E ) l o m / l a c k ( e c n e r e f e r m o r f r o r r E 79 BA in acetonitrile appear to be all negative and about 4 kcal/mol. This is presumably due to slight strong polarization of the carboxylate group in acetonitrile that can be challenging to model via implicit solvation models. Finding the best-performing method based on MAE values calculated by eliminating the BA in acetonitrile data did not change the conclusion from Figure II-1 significantly. In this condition, the order changed very slightly and MN15/aDZ/C-PCM appeared as the best-performing level of theory. II.6. Conclusions Gas-phase CCSD(T)/CBS electronic energies and experimental solution phase free energies were used as reference to assess the performance of DFT method in the gas-phase as well as in the solution phase when used in combination with implicit solvation models. The benchmark study shows that in addition to the solvation model, the choice of both method and basis set is critical in choosing a level of theory for simulation of H-bond free energies in solution; using a long-range corrected DFT method or a large basis set does not guarantee a more accurate result. PBE0/aDZ/C-PCM appeared to be the best-performing level of theory with gas- and solution phase MAE values of 0.47 and 0.60 kcal/mol. The benchmark study also recommends the use of PBE0/6-31+G(d,p)/C-PCM levels of theory when calculation of larger systems is needed. The MAE values for both gas- and solution phases are only about 0.1 kcal/mol different from those of PBE0/aDZ/C-PCM. II.7. Experimental H-bond measurements The H-bond energies for species studied in this chapter were measured as described in the previous chapter. The NMR and thermodynamic values corrected for 298.15 K are shown in Table II-4. Data coverage is defined as the ratio of the measured shift range to the difference of the extrapolated monomer and dimer shifts multiplied by 100%. 80 exp. 1 in CD3CN (NH) 1 in CDCl3 (NH) 1 in CD2Cl2 (NH) 1' in CD3CN (NH) 1' in CDCl3 (NH) [exp. 1] 1' in CDCl3 (NH) [exp. 2] 1' in CDCl3 (NH) [exp. 3] 1' in CD2Cl2 (NH) 2 in CD3CN (NH) 2 in CDCl3 (NH) [exp. 1] 2 in CDCl3 (NH) [exp. 2] 2 in CD2Cl2 (NH) 2' in CD3CN (NH) 2' in CDCl3 (NH) 2' in CD2Cl2 (NH) BA in CD3CN (OH) BA in C6D6 (OH) BA in CDCl3 (OH) BA in CD2Cl2 (OH) Im in CD3CN (NH) Im in C6D6 (NH) Im in CDCl3 (NH) Im in CD2Cl2 (NH) Table II-4. Extracted parameters from NMR measurements at 298.15 K. ΔH dδD/dT ppb/K kcal/mol -4.43 -5.9 -5.84 -4.2 -4.1 -6.59 -3.03 -3.1 -3.44 -8.2 -3.29 -8.3 -8.2 -3.39 -4.01 -3.5 -2.71 -9.1 -1.94 -8.9 -8.2 -2.04 -3.33 -6.1 -5.87 2.2 -4.41 -6.2 -6.4 -5.48 -3.81 92.0 -9.12 -7.4 -8.16 -6.3 -6.2 -8.18 -3.09 -3.2 -7.30 -10.2 -3.63 -5.4 -4.2 -4.44 ΔS cal/molK -11.57 -10.11 -13.04 -12.34 -10.14 -9.65 -10.02 -12.80 -10.59 -6.32 -6.63 -10.07 -16.88 -11.88 -13.20 -17.60 -17.91 -15.68 -16.91 -12.41 -17.22 -10.08 -13.48 δD ppm 11.4131 11.6371 11.5988 7.1753 7.1034 7.1876 7.1848 7.2477 7.1961 6.9976 6.9838 7.2284 8.8239 8.7345 8.4964 18.5424 13.9893 13.3832 13.3895 8.4454 9.0788 8.5734 8.5044 ΔG kcal/mol -0.98 -2.82 -2.70 0.65 -0.42 -0.42 -0.40 -0.19 0.45 -0.06 -0.06 -0.33 -0.84 -0.87 -1.54 1.44 -3.78 -3.48 -3.14 0.62 -2.17 -0.62 -0.42 Keq 1/M 5.20 117.52 95.76 0.33 2.04 2.02 1.98 1.39 0.47 1.10 1.10 1.74 4.12 4.31 13.46 0.09 588.95 355.86 200.28 0.35 38.93 2.85 2.03 δM ppm 7.7974 6.9555 6.9484 4.6176 4.1408 4.1396 4.1367 4.0950 4.3054 3.8711 3.8690 3.8512 4.5160 4.0005 4.0211 9.3908 5.8759 6.7941 6.9767 5.8274 4.1653 5.3294 5.2873 dδM/dT ppb/K -4.2 -3.1 -2.3 -3.2 -1.9 -1.9 -1.9 -1.6 -2.4 -1.8 -1.7 -1.5 -3.5 -2.0 -0.6 -5.9 -1.3 -5.8 -4.8 -3.5 1.6 -2.6 -2.1 data coverage (%) 57 82 86 32 34 54 50 49 19 38 44 50 45 63 74 13 72 81 88 39 85 67 63 81 APPENDICES 82 APPENDIX A: Chemical shifts used for obtaining associations 83 conc. (mM) 1.85E+02 1.39E+02 9.25E+01 4.63E+01 2.31E+01 5.78E+00 2.31E+00 1.16E+00 5.78E-01 conc. (mM) 3.19E+01 2.55E+01 1.92E+01 1.28E+01 6.39E+00 3.19E+00 6.39E-01 2.55E-01 1.28E-01 3.19E-02 1.28E-02 1 in acetonitrile (NH) 277.05 K --- 9.8531 9.6093 9.1797 8.7710 8.2061 8.0239 7.9610 7.9268 Chemical Shifts (ppm) 296.61 K 286.82 K 9.8130 9.4222 9.2476 9.6453 8.9981 9.3953 8.9690 8.6047 8.2827 8.5865 7.9319 8.0958 7.9593 7.8333 7.7961 7.9002 7.8743 7.7866 1 in benzene (NH) [exp. 1] Chemical Shifts (ppm) 301.25 K 291.50 K 12.0769 11.6730 11.5960 12.0268 11.4880 11.9500 11.8229 11.2803 10.8730 11.5410 10.3371 11.1580 8.6950 9.7980 8.7800 7.6200 7.9590 6.6210 6.1000 6.1145 5.8660 --- 280.15 K 12.2766 12.2399 12.1876 12.0878 11.8710 11.5729 10.4560 9.5320 8.7320 --- --- 305.95 K 9.4222 9.2476 8.9981 8.6047 8.2827 7.9319 7.8333 7.7961 7.7866 310.50 K 11.6730 11.5960 11.4880 11.2803 10.8730 10.3371 8.6950 7.6200 --- 6.1145 5.8660 84 311.00 K 11.6085 11.5210 11.3970 11.1880 10.7480 10.1820 8.4360 7.3900 6.7810 6.0550 --- 310.50 K 11.6110 11.5240 11.3980 11.1890 10.7530 10.1790 8.4580 --- --- 6.0500 5.8400 conc. (mM) 2.70E+01 2.16E+01 1.62E+01 1.08E+01 5.40E+00 2.70E+00 5.40E-01 2.16E-01 1.08E-01 2.70E-02 1.08E-02 conc. (mM) 2.65E+01 2.12E+01 1.59E+01 1.06E+01 5.30E+00 2.65E+00 5.30E-01 2.12E-01 1.06E-01 2.65E-02 1.06E-02 1 in benzene (NH) [exp. 2] 280.15 K 12.2458 12.2010 12.1420 12.0360 11.8080 11.4700 10.2870 9.3220 8.4800 overlap 6.3100 Chemical Shifts (ppm) 301.04 K 291.40 K 12.0348 11.6085 11.5210 11.9794 11.3970 11.8950 11.7560 11.1880 10.7480 11.4570 10.1820 11.0451 9.6060 8.4360 7.3900 8.5520 6.7810 7.7390 6.5100 6.0550 6.0570 --- 1 in benzene (NH) [exp. 3] Chemical Shifts (ppm) 301.76 K 291.82 K 11.6110 12.0315 11.9750 11.5240 11.3980 11.8950 11.1890 11.7510 10.7530 11.4470 11.0350 10.1790 9.6061 8.4580 8.5384 280.04 K 12.2440 12.2013 12.1377 12.0316 11.8000 11.4730 10.2910 9.3040 8.5030 overlap 6.3310 --- --- 6.0500 5.8400 --- 6.5200 6.0700 85 304.01 K 10.8766 10.8059 10.6992 10.5522 10.1962 9.6946 8.6237 7.9593 7.5736 --- --- 299.58 K 10.7711 10.6936 10.5782 10.3932 9.9940 9.5185 8.4095 7.7874 7.4479 7.1007 conc. (mM) 1.86E+02 1.48E+02 1.11E+02 7.42E+01 3.71E+01 1.86E+01 4.64E+00 1.86E+00 9.28E-01 4.64E-01 2.32E-01 conc. (mM) 1.50E+02 1.20E+02 9.02E+01 6.01E+01 3.01E+01 1.50E+01 3.76E+00 1.50E+00 7.52E-01 1.88E-01 1 in chloroform (NH) Chemical Shifts (ppm) 296.53 K 286.70 K 11.1235 10.8766 10.8059 11.0680 10.6992 10.9846 10.8681 10.5522 10.1962 10.5815 9.6946 10.1582 9.1616 8.6237 7.9593 8.4427 7.9558 7.5736 7.5686 277.05 K 11.2470 11.1994 11.1281 11.0272 10.7778 10.4018 9.4754 8.7547 8.2227 7.7812 7.4721 1 in dichloromethane (NH) --- --- --- Chemical Shifts (ppm) 291.74 K 283.91 K 10.7711 11.0288 10.9692 10.6936 10.5782 10.8794 10.3932 10.7331 9.9940 10.4078 9.9983 9.5185 8.4095 8.9392 7.7874 8.2326 7.7841 7.4479 7.1007 7.2456 276.10 K 11.1476 11.0960 11.0176 10.8905 10.6028 10.2325 9.2297 8.5059 8.0098 7.3557 86 conc. (mM) 5.79E+02 4.63E+02 3.47E+02 2.32E+02 1.16E+02 5.79E+01 1.45E+01 5.79E+00 2.89E+00 1.45E+00 conc. (mM) 1.29E+02 1.03E+02 7.74E+01 5.16E+01 2.58E+01 1.29E+01 2.58E+00 1.03E+00 5.16E-01 1.29E-01 1' in acetonitrile (NH) Chemical Shifts (ppm) 296.48 K 286.73 K 5.3192 5.1343 5.0591 5.2351 4.9714 5.1337 5.0140 4.8713 4.7468 4.8601 4.6747 4.7654 4.6827 4.6153 4.6012 4.6635 4.5984 4.6588 4.6603 4.5952 277.11 K 5.4236 5.3352 5.2271 5.0986 4.9239 4.8166 4.7207 4.6987 4.6938 4.6903 1' in benzene (NH) [exp. 1] Chemical Shifts (ppm) 291.71 K 301.45 K 6.1967 6.7850 6.0400 6.6269 6.4468 5.8380 5.5231 6.1609 4.9635 5.6130 4.4298 5.0284 3.8990 3.6042 3.3897 3.5305 3.3150 3.3857 3.2600 3.2526 280.04 K 7.0830 6.9760 6.8120 6.5618 6.0450 5.4634 4.1819 3.6845 3.4720 3.2810 305.76 K 5.1343 5.0591 4.9714 4.8713 4.7468 4.6747 4.6153 4.6012 4.5984 4.5952 311.10 K 6.1967 6.0400 5.8380 5.5231 4.9635 4.4298 3.6042 3.3897 3.3150 3.2526 87 conc. (mM) 1.35E+02 1.08E+02 8.08E+01 5.39E+01 2.69E+01 1.35E+01 2.69E+00 1.08E+00 5.39E-01 1.35E-01 5.39E-02 conc. (mM) 1.36E+02 1.09E+02 8.14E+01 5.43E+01 2.71E+01 1.36E+01 2.71E+00 1.09E+00 5.43E-01 1.36E-01 5.43E-02 1' in benzene (NH) [exp. 2] Chemical Shifts (ppm) 301.45 K 291.71 K 6.7740 6.2155 6.0693 6.6477 5.8608 6.4710 6.1890 5.5507 4.9972 5.6489 4.4492 5.0515 3.9005 3.6049 3.3962 3.5386 3.3157 3.3895 3.2600 3.2465 3.2333 3.2380 280.26 K 7.0982 6.9873 6.8080 6.5852 6.0790 5.4894 4.1833 3.6960 3.4780 3.2800 3.2440 1' in benzene (NH) [exp. 3] Chemical Shifts (ppm) 301.45 K 291.61 K 6.2286 6.7830 6.6597 6.0802 5.8724 6.4800 5.5614 6.1982 4.9967 5.6506 5.0702 4.4660 3.6270 3.9362 3.3986 3.5458 3.3967 3.3203 3.2543 3.2683 3.2380 3.2426 280.26 K 7.1068 7.0032 6.8429 6.5896 6.0811 5.5076 4.2260 3.7061 3.4876 3.2865 3.2420 311.10 K 6.2155 6.0693 5.8608 5.5507 4.9972 4.4492 3.6049 3.3962 3.3157 3.2465 3.2333 310.90 K 6.2286 6.0802 5.8724 5.5614 4.9967 4.4660 3.6270 3.3986 3.3203 3.2543 3.2426 88 conc. (mM) 1.12E+02 8.97E+01 6.72E+01 4.48E+01 2.24E+01 1.12E+01 2.24E+00 8.97E-01 4.48E-01 1.12E-01 conc. (mM) 3.81E+02 3.05E+02 2.29E+02 1.52E+02 7.62E+01 3.81E+01 9.53E+00 3.81E+00 1.91E+00 9.53E-01 4.76E-01 1' in chloroform (NH) [exp. 1] Chemical Shifts (ppm) 297.58 K 286.68 K 5.0437 4.8218 4.7306 4.9392 4.6231 4.8113 4.6533 4.4935 4.3365 4.4509 4.2388 4.3171 4.1964 4.1535 4.1389 4.1756 4.1364 4.1696 4.1635 4.1305 277.10 K 5.1836 5.0725 4.9348 4.7599 4.5299 4.3714 4.2229 4.1974 4.1900 4.1836 1' in chloroform (NH) [exp. 2] Chemical Shifts (ppm) 286.63 K 296.41 K 5.4432 5.6985 5.3286 5.5825 5.4268 5.1798 4.9930 5.2268 --- 4.5929 4.2975 4.2200 4.1925 4.1773 4.1700 --- 4.4498 4.2250 4.1693 4.1513 4.1411 4.1339 277.21 K 5.8488 5.7329 5.5777 5.3727 --- 4.6902 4.3460 4.2516 4.2176 4.1994 4.1908 304.04 K 4.8218 4.7306 4.6231 4.4935 4.3365 4.2388 4.1535 4.1389 4.1364 4.1305 303.84 K 5.4432 5.3286 5.1798 4.9930 --- 4.4498 4.2250 4.1693 4.1513 4.1411 4.1339 89 conc. (mM) 3.88E+02 3.10E+02 2.33E+02 1.55E+02 7.76E+01 3.88E+01 3.10E+01 1.55E+01 7.76E+00 conc. (mM) 3.98E+02 3.18E+02 2.39E+02 1.59E+02 7.95E+01 3.98E+01 3.18E+01 3.98E+00 conc. (mM) 2.01E+02 1.61E+02 1.21E+02 8.05E+01 4.02E+01 2.01E+01 5.03E+00 2.01E+00 1.01E+00 5.03E-01 1' in chloroform (NH) [exp. 3] Chemical Shifts (ppm) 302.37 K 292.66 K 5.6065 5.3302 5.2171 5.4899 5.0765 5.3409 5.1324 4.8871 4.6060 4.8076 4.3920 4.5372 4.4778 4.3469 4.2428 4.3348 4.2502 4.1833 283.01 K 5.7553 5.6391 5.4881 5.2737 4.9273 4.6271 4.5605 4.3933 4.2898 1' in dichloromethane (NH) 276.21 K 5.6930 5.5785 5.4257 5.2080 4.8551 4.5709 4.5066 4.1930 Chemical Shifts (ppm) 291.76 K 283.92 K 5.5655 5.3303 5.2135 5.4500 5.0636 5.2950 5.0786 4.8650 4.5764 4.7497 4.3685 4.4933 4.3232 4.4365 4.1693 4.1271 2 in acetonitrile (NH) Chemical Shifts (ppm) 292.56 K 302.25 K 4.6088 4.7551 4.5536 4.6868 4.6113 4.4934 4.4280 4.5268 4.3557 4.4297 4.3763 4.3145 4.2838 4.3344 x4.2751 4.2749 4.2738 4.3205 4.3198 --- 283.04 K 4.8420 4.7666 4.6819 4.5859 4.4735 4.4109 4.3608 --- 4.3449 4.3449 311.81 K 5.3302 5.2171 5.0765 4.8871 4.6060 4.3920 4.3469 4.2428 4.1833 299.57 K 5.3303 5.2135 5.0636 4.8650 4.5764 4.3685 4.3232 4.1271 311.55 K 4.6088 4.5536 4.4934 4.4280 4.3557 4.3145 4.2838 x4.2751 4.2749 4.2738 90 conc. (mM) 4.20E+01 3.36E+01 2.52E+01 1.68E+01 8.39E+00 4.20E+00 8.39E-01 3.36E-01 1.68E-01 8.39E-02 conc. (mM) 3.95E+01 3.16E+01 2.37E+01 1.58E+01 7.90E+00 3.95E+00 7.90E-01 3.16E-01 1.58E-01 7.90E-02 5.53E-02 2 in benzene (NH) [exp1] 280.26 K 6.5024 6.3369 6.1036 5.7616 5.1277 4.4731 3.3952 3.1130 3.0052 2.9510 Chemical Shifts (ppm) 301.45 K 291.61 K 6.0749 5.3822 5.1903 5.8917 4.9343 5.6418 5.2844 4.5880 4.0420 4.6587 3.5950 4.0676 3.2259 3.0765 2.9767 3.0357 2.9402 2.9680 2.9330 2.9225 2 in benzene (NH) [exp2] Chemical Shifts (ppm) 291.71 K 301.45 K 5.3286 6.0227 5.1374 5.8415 5.5870 4.8794 4.5299 5.2214 3.9879 4.5927 3.5649 4.0255 3.2067 3.0645 2.9721 3.0295 2.9403 2.9622 2.9250 2.9212 2.9170 2.9210 280.26 K 6.4566 6.2920 6.0545 5.7044 5.0625 4.4254 3.3686 3.1001 2.9965 2.9408 2.9290 310.90 K 5.3822 5.1903 4.9343 4.5880 4.0420 3.5950 3.0765 2.9767 2.9402 2.9225 311.10 K 5.3286 5.1374 4.8794 4.5299 3.9879 3.5649 3.0645 2.9721 2.9403 2.9212 2.9170 91 conc. (mM) 4.03E+01 3.23E+01 2.42E+01 1.61E+01 8.06E+00 4.03E+00 8.06E-01 3.23E-01 1.61E-01 8.06E-02 conc. (mM) 3.32E+02 2.65E+02 1.99E+02 1.33E+02 6.63E+01 3.32E+01 8.29E+00 3.32E+00 1.66E+00 8.29E-01 4.15E-01 conc. (mM) 4.65E+02 3.72E+02 2.79E+02 1.86E+02 9.29E+01 4.65E+01 1.16E+01 4.65E+00 5.81E-01 2 in benzene (NH) [exp3] Chemical Shifts (ppm) 301.45 K 291.71 K 6.0421 5.3488 5.1583 5.8605 4.9046 5.6128 5.2240 4.5512 4.0017 4.6098 3.5764 4.0419 3.2331 3.0830 2.9760 3.0330 2.9403 2.9658 2.9351 2.9249 280.04 K 6.4741 6.3088 6.0860 5.7247 5.0762 4.4455 3.4040 3.1070 3.0020 2.9510 2 in chloroform (NH) [exp. 1] 276.87 K 5.1195 5.0051 4.8473 4.6443 4.3676 4.1647 --- Chemical Shifts (ppm) 286.73 K 296.39 K 4.8416 5.0149 4.7366 4.9024 4.7503 4.5956 4.4238 4.5589 4.2001 4.3016 4.0441 4.1180 3.9142 3.8816 3.8716 3.8673 3.8639 --- 3.9384 3.9234 3.9178 3.9129 2 in chloroform (NH) [exp. 2] 3.9170 3.9039 3.8994 3.8957 276.19 K 5.3126 5.1951 5.0350 4.8152 4.5006 4.2510 4.0073 3.9496 3.9135 Chemical Shifts (ppm) 295.71 K 285.86 K 5.0123 5.2033 5.0861 4.9058 4.7588 4.9291 4.5635 4.7174 4.4226 4.3022 4.1066 4.1950 3.9308 overlap 3.9266 3.8895 3.8653 3.8953 92 310.90 K 5.3488 5.1583 4.9046 4.5512 4.0017 3.5764 3.0830 2.9760 2.9403 2.9249 303.61 K 4.8416 4.7366 4.5956 4.4238 4.2001 4.0441 3.9142 3.8816 3.8716 3.8673 3.8639 303.43 K 5.0123 4.9058 4.7588 4.5635 4.3022 4.1066 3.9308 3.8895 3.8653 conc. (mM) 3.71E+02 2.97E+02 2.22E+02 1.48E+02 7.41E+01 3.71E+01 1.85E+01 3.71E+00 conc. (mM) 8.32E+01 6.66E+01 4.99E+01 3.33E+01 1.66E+01 8.32E+00 4.16E+00 1.66E+00 conc. (mM) 5.04E+01 4.03E+01 3.02E+01 2.02E+01 1.01E+01 5.04E+00 1.01E+00 4.03E-01 2.02E-01 1.01E-01 7.05E-02 2 in dichloromethane (NH) 276.12 K 5.6215 5.5002 5.3335 5.0869 4.7062 4.3886 4.1754 3.9555 Chemical Shifts (ppm) 291.73 K 283.95 K 5.4986 5.2634 5.1426 5.3763 4.9772 5.2051 4.9706 4.7560 4.4290 4.6048 4.1869 4.3135 4.1228 4.0368 3.8926 3.9323 2' in acetonitrile (NH) 279.15 K 6.4010 6.2366 6.0430 5.7634 5.3463 5.0276 4.8353 4.6928 Chemical Shifts (ppm) 298.69 K 288.82 K 5.6357 6.1270 5.9750 5.5001 5.3267 5.7686 5.1144 5.5048 5.1429 4.8379 4.6631 4.8786 4.5867 4.7350 4.6296 4.5287 2' in benzene (NH) [exp1] Chemical Shifts (ppm) 301.25 K 291.61 K 8.7875 8.2084 8.0770 8.6949 7.8848 8.5582 8.3392 7.5847 6.9739 7.8736 6.2807 7.3036 5.6852 4.6569 3.8693 4.6103 3.5616 4.0619 3.6920 3.3850 3.5590 --- 280.15 K 9.0822 9.0121 8.9008 8.7330 8.3582 7.8855 6.4173 5.2648 4.5750 4.0367 3.8270 299.55 K 5.2634 5.1426 4.9772 4.7560 4.4290 4.1869 4.0368 3.8926 308.43 K 5.6357 5.5001 5.3267 5.1144 4.8379 4.6631 4.5867 4.5287 310.10 K 8.2084 8.0770 7.8848 7.5847 6.9739 6.2807 4.6569 3.8693 3.5616 3.3850 --- 93 conc. (mM) 5.07E+01 4.06E+01 3.04E+01 2.03E+01 1.01E+01 5.07E+00 1.01E+00 4.06E-01 2.03E-01 1.01E-01 conc. (mM) 4.72E+01 3.78E+01 2.83E+01 1.89E+01 9.45E+00 4.72E+00 9.45E-01 3.78E-01 1.89E-01 conc. (mM) 3.18E+02 2.55E+02 1.91E+02 1.27E+02 6.37E+01 3.18E+01 7.96E+00 3.18E+00 1.59E+00 2' in benzene (NH) [exp2] 280.04 K 9.0866 9.0145 8.9130 8.7375 8.3639 7.8983 6.5648 5.3180 4.6400 4.0470 Chemical Shifts (ppm) 301.45 K 291.71 K 8.7936 8.2189 8.0846 8.7008 7.9000 8.5671 8.3473 7.5959 6.9840 7.8818 6.2999 7.3203 5.8407 4.7956 3.9113 4.6610 4.1360 3.6298 3.6914 --- 2' in benzene (NH) 280.15 K 9.0570 8.9830 8.8740 8.6990 8.3120 7.8250 6.2510 5.2100 4.4840 Chemical Shifts (ppm) 291.40 K 301.45 K 8.1574 8.7527 8.0291 8.6600 8.5239 7.8390 7.5306 8.2980 6.9103 7.8221 6.2010 7.2320 5.5248 4.5310 3.8480 4.5590 3.9900 3.5220 2' in chloroform (NH) Chemical Shifts (ppm) 296.54 K 286.76 K 6.8722 6.4690 6.3107 6.7192 6.0763 6.4961 6.1708 5.7497 5.2129 5.6043 4.7665 5.0895 4.3920 4.2339 4.0953 4.1872 4.1143 4.0504 277.02 K 7.1011 6.9650 6.7584 6.4250 5.8560 5.3090 4.5068 4.2536 4.1612 310.90 K 8.2189 8.0846 7.9000 7.5959 6.9840 6.2999 4.7956 3.9113 3.6298 --- 310.70 K 8.1574 8.0291 7.8390 7.5306 6.9103 6.2010 4.5310 3.8480 3.5220 303.81 K 6.4690 6.3107 6.0763 5.7497 5.2129 4.7665 4.2339 4.0953 4.0504 94 conc. (mM) 2.37E+02 1.89E+02 1.42E+02 9.46E+01 4.73E+01 2.37E+01 5.92E+00 2.37E+00 1.18E+00 2.96E-01 conc. (mM) 4.57E+02 3.66E+02 2.74E+02 1.83E+02 9.15E+01 4.57E+01 2.29E+01 9.15E+00 4.57E+00 conc. (mM) 8.60E+00 7.74E+00 6.88E+00 5.16E+00 3.44E+00 1.72E+00 8.60E-01 2.15E-01 2' in dichloromethane (NH) 276.18 K 7.5115 7.4179 7.2860 7.0681 6.5801 6.0052 4.9763 4.5061 4.2949 4.1305 Chemical Shifts (ppm) 291.77 K 283.91 K 7.3374 7.0093 6.8837 7.2287 6.6876 7.0609 6.8216 6.4044 5.8983 6.3452 5.3494 5.7682 4.8064 4.5430 4.2276 4.3999 4.1452 4.2308 4.1105 4.0850 BA in acetonitrile (OH) 276.10 K 10.2738 10.1437 10.0075 9.8610 9.6968 9.6115 9.5599 9.5384 9.5328 Chemical Shifts (ppm) 282.98 K 294.68 K 9.9416 10.1966 9.8350 10.0727 9.9413 9.7230 9.6056 9.8017 9.4762 9.6463 9.4115 9.5662 9.5178 9.3715 9.3560 9.4983 9.4937 9.3548 BA in benzene (OH) Chemical Shifts (ppm) 298.46 K 288.62 K 12.2956 11.2723 11.1517 12.2064 11.0310 12.1171 11.8676 10.7000 10.1858 11.4592 9.2491 10.6590 9.7409 8.3182 6.8460 7.8614 279.04 K 12.7324 12.6601 12.5878 12.3801 12.0366 11.3449 10.5080 8.5840 299.54 K 7.0093 6.8837 6.6876 6.4044 5.8983 5.3494 4.5430 4.2276 4.1452 4.0850 305.90 K 9.9416 9.8350 9.7230 9.6056 9.4762 9.4115 9.3715 9.3560 9.3548 307.55 K 11.2723 11.1517 11.0310 10.7000 10.1858 9.2491 8.3182 6.8460 95 conc. (mM) 2.10E+02 1.68E+02 1.26E+02 8.40E+01 4.20E+01 2.10E+01 5.25E+00 2.10E+00 1.05E+00 5.25E-01 conc. (mM) 1.65E+02 1.32E+02 9.92E+01 6.62E+01 3.31E+01 1.65E+01 4.14E+00 1.65E+00 8.27E-01 2.07E-01 conc. (mM) 8.25E+02 6.60E+02 4.95E+02 3.30E+02 1.65E+02 8.25E+01 2.06E+01 4.13E+00 BA in chloroform (OH) Chemical Shifts (ppm) 298.56 K 288.59 K 13.0204 12.6729 12.6076 12.9770 12.5113 12.9114 12.8038 12.3508 11.9890 12.5555 11.5332 12.2325 11.2173 10.2156 9.2088 10.3195 8.4867 9.5635 8.7740 7.8436 279.00 K 13.1634 13.1277 13.0772 12.9998 12.7934 12.5305 11.6784 10.8811 10.1701 9.3687 BA in dichloromethane (OH) 276.16 K 13.0834 13.0355 12.9620 12.8454 12.5851 12.2330 11.1942 10.2922 9.5494 8.1981 Chemical Shifts (ppm) 283.95 K 291.84 K 12.6126 12.9418 12.5337 12.8836 12.7961 12.4106 12.2179 12.6548 11.8002 12.3455 11.2623 11.9309 10.7602 9.8737 8.9106 9.8035 8.2771 9.0690 7.8679 7.4199 IM in acetonitrile (NH) Chemical Shifts (ppm) 285.87 K 295.72 K 6.5353 6.7291 6.4481 6.6354 6.5181 6.3446 6.2125 6.3685 6.0390 6.1699 6.0346 5.9327 5.8423 5.9147 5.8817 5.8182 276.22 K 6.8452 6.7499 6.6269 6.4713 6.2529 6.0992 5.9590 5.9169 307.67 K 12.6729 12.6076 12.5113 12.3508 11.9890 11.5332 10.2156 9.2088 8.4867 7.8436 299.62 K 12.6126 12.5337 12.4106 12.2179 11.8002 11.2623 9.8737 8.9106 8.2771 7.4199 303.43 K 6.5353 6.4481 6.3446 6.2125 6.0390 5.9327 5.8423 5.8182 96 conc. (mM) 2.49E+02 1.99E+02 1.49E+02 9.96E+01 4.98E+01 2.49E+01 6.23E+00 2.49E+00 1.25E+00 3.11E-01 conc. (mM) 6.19E+02 4.95E+02 3.71E+02 2.47E+02 1.24E+02 6.19E+01 1.55E+01 6.19E+00 3.09E+00 7.73E-01 conc. (mM) 6.66E+02 5.33E+02 4.00E+02 2.66E+02 1.33E+02 6.66E+01 1.67E+01 6.66E+00 8.33E-01 IM in benzene (NH) 276.10 K 8.6470 8.5701 8.4584 8.2814 7.8951 7.4717 6.3519 5.5454 5.0364 4.4226 Chemical Shifts (ppm) 295.59 K 285.94 K 8.4149 7.9250 7.7951 8.3177 7.6183 8.1841 7.9793 7.3581 6.8410 7.5373 6.3385 7.0798 5.9333 5.2705 4.7396 5.2019 4.4787 4.7820 4.3283 4.2433 IM in chloroform (NH) Chemical Shifts (ppm) 283.93 K 291.82 K 7.2186 7.4532 7.1106 7.3515 7.2066 6.9583 6.7383 6.9899 6.3593 6.6023 6.0108 6.2189 5.6778 5.5551 5.4297 5.5094 5.3820 5.4433 5.3902 5.3414 276.09 K 7.5596 7.4703 7.3246 7.1215 6.7336 6.3411 5.7484 5.5554 5.4786 5.4133 IM in dichloromethane (NH) 276.18 K 7.4135 7.3168 7.1703 6.9551 6.5765 6.1944 5.6536 5.4835 --- Chemical Shifts (ppm) 283.92 K 291.82 K 7.0254 7.2821 6.9193 7.1788 7.0359 6.7629 6.5347 6.8067 6.1762 6.4303 6.0618 5.8450 5.4706 5.5820 5.4385 5.3655 --- --- 97 305.28 K 7.9250 7.7951 7.6183 7.3581 6.8410 6.3385 5.2705 4.7396 4.4787 4.2433 299.57 K 7.2186 7.1106 6.9583 6.7383 6.3593 6.0108 5.5551 5.4297 5.3820 5.3414 299.53 K 7.0254 6.9193 6.7629 6.5347 6.1762 5.8450 5.4706 5.3655 --- APPENDIX B: Plots of fits for obtaining thermodynamic values from NMR spectra 98 99 100 101 102 103 104 APPENDIX C: Stacked 1H NMR spectra used for obtaining dimerization energies 105 BA in benzene (OH) 01, 279.0 K, 8.6 mM 02, 279.0 K, 6.9 mM 03, 279.0 K, 5.2 mM 04, 279.0 K, 3.4 mM 05, 279.0 K, 1.7 mM 06, 279.0 K, 859.8 (cid:80)M 07, 279.0 K, 214.9 (cid:80)M 08, 288.6 K, 8.6 mM 09, 288.6 K, 6.9 mM 10, 288.6 K, 5.2 mM 11, 288.6 K, 3.4 mM 12, 288.6 K, 1.7 mM 13, 288.6 K, 859.8 (cid:80)M 14, 288.6 K, 214.9 (cid:80)M 15, 298.5 K, 8.6 mM 16, 298.5 K, 6.9 mM 17, 298.5 K, 5.2 mM 18, 298.5 K, 3.4 mM 19, 298.5 K, 1.7 mM 20, 298.5 K, 859.8 (cid:80)M 21, 298.5 K, 214.9 (cid:80)M 22, 307.5 K, 8.6 mM 23, 307.5 K, 6.9 mM 24, 307.5 K, 5.2 mM 25, 307.5 K, 3.4 mM 26, 307.5 K, 1.7 mM 27, 307.5 K, 859.8 (cid:80)M 28, 307.5 K, 214.9 (cid:80)M 106 BA in chloroform (OH) 01, 279.0 K, 210.0 mM 02, 279.0 K, 168.0 mM 03, 279.0 K, 126.0 mM 04, 279.0 K, 84.0 mM 05, 279.0 K, 42.0 mM 06, 279.0 K, 21.0 mM 07, 279.0 K, 5.3 mM 08, 279.0 K, 2.1 mM 09, 279.0 K, 1.1 mM 10, 279.0 K, 525.1 (cid:80)M 11, 279.0 K, 262.5 (cid:80)M 12, 288.6 K, 210.0 mM 13, 288.6 K, 168.0 mM 14, 288.6 K, 126.0 mM 15, 288.6 K, 84.0 mM 16, 288.6 K, 42.0 mM 17, 288.6 K, 21.0 mM 18, 288.6 K, 5.3 mM 19, 288.6 K, 2.1 mM 20, 288.6 K, 1.1 mM 21, 288.6 K, 525.1 (cid:80)M 22, 288.6 K, 262.5 (cid:80)M 23, 298.6 K, 210.0 mM 24, 298.6 K, 168.0 mM 25, 298.6 K, 126.0 mM 26, 298.6 K, 84.0 mM 27, 298.6 K, 42.0 mM 28, 298.6 K, 21.0 mM 29, 298.6 K, 5.3 mM 30, 298.6 K, 2.1 mM 31, 298.6 K, 1.1 mM 32, 298.6 K, 525.1 (cid:80)M 33, 298.6 K, 262.5 (cid:80)M 34, 307.7 K, 210.0 mM 35, 307.7 K, 168.0 mM 36, 307.7 K, 126.0 mM 37, 307.7 K, 84.0 mM 38, 307.7 K, 42.0 mM 39, 307.7 K, 21.0 mM 40, 307.7 K, 5.3 mM 41, 307.7 K, 2.1 mM 42, 307.7 K, 1.1 mM 43, 307.7 K, 525.1 (cid:80)M 44, 307.7 K, 262.5 (cid:80)M 107 BA in dichloromethane (OH) 01, 276.2 K, 165.4 mM 02, 276.2 K, 132.3 mM 03, 276.2 K, 99.2 mM 04, 276.2 K, 66.2 mM 05, 276.2 K, 33.1 mM 06, 276.2 K, 16.5 mM 07, 276.2 K, 4.1 mM 08, 276.2 K, 1.7 mM 09, 276.2 K, 827.0 (cid:80)M 10, 276.2 K, 206.8 (cid:80)M 11, 284.0 K, 165.4 mM 12, 284.0 K, 132.3 mM 13, 284.0 K, 99.2 mM 14, 284.0 K, 66.2 mM 15, 284.0 K, 33.1 mM 16, 284.0 K, 16.5 mM 17, 284.0 K, 4.1 mM 18, 284.0 K, 1.7 mM 19, 284.0 K, 827.0 (cid:80)M 20, 284.0 K, 206.8 (cid:80)M 21, 291.8 K, 165.4 mM 22, 291.8 K, 132.3 mM 23, 291.8 K, 99.2 mM 24, 291.8 K, 66.2 mM 25, 291.8 K, 33.1 mM 26, 291.8 K, 16.5 mM 27, 291.8 K, 4.1 mM 28, 291.8 K, 1.7 mM 29, 291.8 K, 827.0 (cid:80)M 30, 291.8 K, 206.8 (cid:80)M 31, 299.6 K, 165.4 mM 32, 299.6 K, 132.3 mM 33, 299.6 K, 99.2 mM 34, 299.6 K, 66.2 mM 35, 299.6 K, 33.1 mM 36, 299.6 K, 16.5 mM 37, 299.6 K, 4.1 mM 38, 299.6 K, 1.7 mM 39, 299.6 K, 827.0 (cid:80)M 40, 299.6 K, 206.8 (cid:80)M 108 BA in acetonitrile (OH) 01, 276.1 K, 457.3 mM 02, 276.1 K, 365.9 mM 03, 276.1 K, 274.4 mM 04, 276.1 K, 182.9 mM 05, 276.1 K, 91.5 mM 06, 276.1 K, 45.7 mM 07, 276.1 K, 22.9 mM 08, 276.1 K, 9.1 mM 09, 276.1 K, 4.6 mM 10, 283.0 K, 457.3 mM 11, 283.0 K, 365.9 mM 12, 283.0 K, 274.4 mM 13, 283.0 K, 182.9 mM 14, 283.0 K, 91.5 mM 15, 283.0 K, 45.7 mM 16, 283.0 K, 22.9 mM 17, 283.0 K, 9.1 mM 18, 283.0 K, 4.6 mM 19, 294.7 K, 457.3 mM 20, 294.7 K, 365.9 mM 21, 294.7 K, 274.4 mM 22, 294.7 K, 182.9 mM 23, 294.7 K, 91.5 mM 24, 294.7 K, 45.7 mM 25, 294.7 K, 22.9 mM 26, 294.7 K, 9.1 mM 27, 294.7 K, 4.6 mM 28, 305.9 K, 457.3 mM 29, 305.9 K, 365.9 mM 30, 305.9 K, 274.4 mM 31, 305.9 K, 182.9 mM 32, 305.9 K, 91.5 mM 33, 305.9 K, 45.7 mM 34, 305.9 K, 22.9 mM 35, 305.9 K, 9.1 mM 36, 305.9 K, 4.6 mM 109 1 in benzene (NH) [exp. 3] 01, 280.0 K, 26.5 mM 02, 280.0 K, 21.2 mM 03, 280.0 K, 15.9 mM 04, 280.0 K, 10.6 mM 05, 280.0 K, 5.3 mM 06, 280.0 K, 2.7 mM 07, 280.0 K, 530.0 (cid:80)M 08, 280.0 K, 212.0 (cid:80)M 09, 280.0 K, 106.0 (cid:80)M 10, 280.0 K, 26.5 (cid:80)M 11, 280.0 K, 10.6 (cid:80)M 12, 291.8 K, 26.5 mM 13, 291.8 K, 21.2 mM 14, 291.8 K, 15.9 mM 15, 291.8 K, 10.6 mM 16, 291.8 K, 5.3 mM 17, 291.8 K, 2.7 mM 18, 291.8 K, 530.0 (cid:80)M 19, 291.8 K, 212.0 (cid:80)M 20, 291.8 K, 106.0 (cid:80)M 21, 291.8 K, 26.5 (cid:80)M 23, 301.8 K, 26.5 mM 24, 301.8 K, 21.2 mM 25, 301.8 K, 15.9 mM 26, 301.8 K, 10.6 mM 27, 301.8 K, 5.3 mM 28, 301.8 K, 2.7 mM 29, 301.8 K, 530.0 (cid:80)M 30, 301.8 K, 212.0 (cid:80)M 31, 301.8 K, 106.0 (cid:80)M 32, 301.8 K, 26.5 (cid:80)M 34, 310.9 K, 26.5 mM 35, 310.9 K, 21.2 mM 36, 310.9 K, 15.9 mM 37, 310.9 K, 10.6 mM 38, 310.9 K, 5.3 mM 39, 310.9 K, 2.7 mM 40, 310.9 K, 530.0 (cid:80)M 41, 310.9 K, 212.0 (cid:80)M 42, 310.9 K, 106.0 (cid:80)M 43, 310.9 K, 26.5 (cid:80)M 110 1 in benzene (NH) [exp. 1] 01, 280.2 K, 39.9 mM 02, 280.2 K, 25.5 mM 03, 280.2 K, 19.2 mM 04, 280.2 K, 12.8 mM 05, 280.2 K, 6.4 mM 06, 280.2 K, 3.2 mM 07, 280.2 K, 638.7 (cid:80)M 08, 280.2 K, 255.5 (cid:80)M 09, 280.2 K, 127.7 (cid:80)M 10, 280.2 K, 31.9 (cid:80)M 11, 280.2 K, 12.8 (cid:80)M 12, 291.5 K, 39.9 mM 13, 291.5 K, 25.5 mM 14, 291.5 K, 19.2 mM 15, 291.5 K, 12.8 mM 16, 291.5 K, 6.4 mM 17, 291.5 K, 3.2 mM 18, 291.5 K, 638.7 (cid:80)M 19, 291.5 K, 255.5 (cid:80)M 20, 291.5 K, 127.7 (cid:80)M 21, 291.5 K, 31.9 (cid:80)M 22, 291.5 K, 12.8 (cid:80)M 23, 301.3 K, 39.9 mM 24, 301.3 K, 25.5 mM 25, 301.3 K, 19.2 mM 26, 301.3 K, 12.8 mM 27, 301.3 K, 6.4 mM 28, 301.3 K, 3.2 mM 29, 301.3 K, 638.7 (cid:80)M 30, 301.3 K, 255.5 (cid:80)M 31, 301.3 K, 127.7 (cid:80)M 32, 301.3 K, 31.9 (cid:80)M 33, 301.3 K, 12.8 (cid:80)M 34, 310.5 K, 31.9 mM 35, 310.5 K, 25.5 mM 36, 310.5 K, 19.2 mM 37, 310.5 K, 12.8 mM 38, 310.5 K, 6.4 mM 39, 310.5 K, 3.2 mM 40, 310.5 K, 638.7 (cid:80)M 41, 310.5 K, 255.5 (cid:80)M 42, 310.5 K, 127.7 (cid:80)M 43, 310.5 K, 31.9 (cid:80)M 44, 310.5 K, 12.8 (cid:80)M 111 1 in benzene (NH) [exp. 2] 01, 280.2 K, 27.0 mM 02, 280.2 K, 21.6 mM 03, 280.2 K, 16.2 mM 04, 280.2 K, 10.8 mM 05, 280.2 K, 5.4 mM 06, 280.2 K, 2.7 mM 07, 280.2 K, 539.7 (cid:80)M 08, 280.2 K, 215.9 (cid:80)M 09, 280.2 K, 107.9 (cid:80)M 10, 280.2 K, 27.0 (cid:80)M 11, 280.2 K, 10.8 (cid:80)M 12, 291.5 K, 27.0 mM 13, 291.5 K, 21.6 mM 14, 291.5 K, 16.2 mM 15, 291.5 K, 10.8 mM 16, 291.5 K, 5.4 mM 17, 291.5 K, 2.7 mM 18, 291.5 K, 539.7 (cid:80)M 19, 291.5 K, 215.9 (cid:80)M 20, 291.5 K, 107.9 (cid:80)M 21, 291.5 K, 27.0 (cid:80)M 22, 291.5 K, 10.8 (cid:80)M 23, 301.2 K, 27.0 mM 24, 301.2 K, 21.6 mM 25, 301.2 K, 16.2 mM 26, 301.2 K, 10.8 mM 27, 301.2 K, 5.4 mM 28, 301.2 K, 2.7 mM 29, 301.2 K, 539.7 (cid:80)M 30, 301.2 K, 215.9 (cid:80)M 31, 301.2 K, 107.9 (cid:80)M 32, 301.2 K, 27.0 (cid:80)M 33, 301.2 K, 10.8 (cid:80)M 34, 310.5 K, 27.0 mM 35, 310.5 K, 21.6 mM 36, 310.5 K, 16.2 mM 37, 310.5 K, 10.8 mM 38, 310.5 K, 5.4 mM 39, 310.5 K, 2.7 mM 40, 310.5 K, 539.7 (cid:80)M 41, 310.5 K, 215.9 (cid:80)M 42, 310.5 K, 107.9 (cid:80)M 43, 310.5 K, 27.0 (cid:80)M 44, 310.5 K, 10.8 (cid:80)M 112 1 in acetonitrile (NH) 01, 277.1 K, 138.8 mM 02, 277.1 K, 92.5 mM 03, 277.1 K, 46.3 mM 04, 277.1 K, 23.1 mM 05, 277.1 K, 5.8 mM 06, 277.1 K, 2.3 mM 07, 277.1 K, 1.2 mM 08, 277.1 K, 578.4 (cid:80)M 09, 286.8 K, 185.1 mM 10, 286.8 K, 138.8 mM 11, 286.8 K, 92.5 mM 12, 286.8 K, 46.3 mM 13, 286.8 K, 23.1 mM 14, 286.8 K, 5.8 mM 15, 286.8 K, 2.3 mM 16, 286.8 K, 1.2 mM 17, 286.8 K, 578.4 (cid:80)M 18, 296.6 K, 185.1 mM 19, 296.6 K, 138.8 mM 20, 296.6 K, 92.5 mM 21, 296.6 K, 46.3 mM 22, 296.6 K, 23.1 mM 23, 296.6 K, 5.8 mM 24, 296.6 K, 2.3 mM 25, 296.6 K, 1.2 mM 26, 296.6 K, 578.4 (cid:80)M 27, 305.9 K, 185.1 mM 28, 305.9 K, 138.8 mM 29, 305.9 K, 92.5 mM 30, 305.9 K, 46.3 mM 31, 305.9 K, 23.1 mM 32, 305.9 K, 5.8 mM 33, 305.9 K, 2.3 mM 34, 305.9 K, 1.2 mM 35, 305.9 K, 578.4 (cid:80)M 113 1 in chloroform (NH) 01, 277.1 K, 163.7 mM 02, 277.1 K, 131.0 mM 03, 277.1 K, 98.2 mM 04, 277.1 K, 65.5 mM 05, 277.1 K, 32.7 mM 06, 277.1 K, 16.4 mM 07, 277.1 K, 4.1 mM 08, 277.1 K, 1.6 mM 09, 277.1 K, 818.7 (cid:80)M 10, 277.1 K, 409.4 (cid:80)M 11, 277.1 K, 204.7 (cid:80)M 12, 286.7 K, 163.7 mM 13, 286.7 K, 131.0 mM 14, 286.7 K, 98.2 mM 15, 286.7 K, 65.5 mM 16, 286.7 K, 32.7 mM 17, 286.7 K, 16.4 mM 18, 286.7 K, 4.1 mM 19, 286.7 K, 1.6 mM 20, 286.7 K, 818.7 (cid:80)M 21, 286.7 K, 409.4 (cid:80)M 22, 286.7 K, 204.7 (cid:80)M 23, 296.5 K, 163.7 mM 24, 296.5 K, 131.0 mM 25, 296.5 K, 98.2 mM 26, 296.5 K, 65.5 mM 27, 296.5 K, 32.7 mM 28, 296.5 K, 16.4 mM 29, 296.5 K, 4.1 mM 30, 296.5 K, 1.6 mM 31, 296.5 K, 818.7 (cid:80)M 32, 296.5 K, 409.4 (cid:80)M 33, 296.5 K, 204.7 (cid:80)M 34, 304.0 K, 163.7 mM 35, 304.0 K, 131.0 mM 36, 304.0 K, 98.2 mM 37, 304.0 K, 65.5 mM 38, 304.0 K, 32.7 mM 39, 304.0 K, 16.4 mM 40, 304.0 K, 4.1 mM 41, 304.0 K, 1.6 mM 42, 304.0 K, 818.7 (cid:80)M 43, 304.0 K, 409.4 (cid:80)M 44, 304.0 K, 204.7 (cid:80)M 114 1 in dichloromethane (NH) 01, 276.1 K, 150.3 mM 02, 276.1 K, 120.3 mM 03, 276.1 K, 90.2 mM 04, 276.1 K, 60.1 mM 05, 276.1 K, 30.1 mM 06, 276.1 K, 15.0 mM 07, 276.1 K, 3.8 mM 08, 276.1 K, 1.5 mM 09, 276.1 K, 751.7 (cid:80)M 10, 276.1 K, 187.9 (cid:80)M 11, 283.9 K, 150.3 mM 12, 283.9 K, 120.3 mM 13, 283.9 K, 90.2 mM 14, 283.9 K, 60.1 mM 15, 283.9 K, 30.1 mM 16, 283.9 K, 15.0 mM 17, 283.9 K, 3.8 mM 18, 283.9 K, 1.5 mM 19, 283.9 K, 751.7 (cid:80)M 20, 283.9 K, 187.9 (cid:80)M 21, 291.7 K, 150.3 mM 22, 291.7 K, 120.3 mM 23, 291.7 K, 90.2 mM 24, 291.7 K, 60.1 mM 25, 291.7 K, 30.1 mM 26, 291.7 K, 15.0 mM 27, 291.7 K, 3.8 mM 28, 291.7 K, 1.5 mM 29, 291.7 K, 751.7 (cid:80)M 30, 291.7 K, 187.9 (cid:80)M 31, 299.6 K, 150.3 mM 32, 299.6 K, 120.3 mM 33, 299.6 K, 90.2 mM 34, 299.6 K, 60.1 mM 35, 299.6 K, 30.1 mM 36, 299.6 K, 15.0 mM 37, 299.6 K, 3.8 mM 38, 299.6 K, 1.5 mM 39, 299.6 K, 751.7 (cid:80)M 40, 299.6 K, 187.9 (cid:80)M 115 1’ in acetonitrile (NH) 01, 277.1 K, 590.7 mM 02, 277.1 K, 472.5 mM 03, 277.1 K, 354.4 mM 04, 277.1 K, 236.3 mM 05, 277.1 K, 118.1 mM 06, 277.1 K, 59.1 mM 07, 277.1 K, 14.8 mM 08, 277.1 K, 5.9 mM 09, 277.1 K, 3.0 mM 10, 277.1 K, 1.5 mM 11, 286.7 K, 590.7 mM 12, 286.7 K, 472.5 mM 13, 286.7 K, 354.4 mM 14, 286.7 K, 236.3 mM 15, 286.7 K, 118.1 mM 16, 286.7 K, 59.1 mM 17, 286.7 K, 14.8 mM 18, 286.7 K, 5.9 mM 19, 286.7 K, 3.0 mM 20, 286.7 K, 1.5 mM 21, 296.5 K, 590.7 mM 22, 296.5 K, 472.5 mM 23, 296.5 K, 354.4 mM 24, 296.5 K, 236.3 mM 25, 296.5 K, 118.1 mM 26, 296.5 K, 59.1 mM 27, 296.5 K, 14.8 mM 28, 296.5 K, 5.9 mM 29, 296.5 K, 3.0 mM 30, 296.5 K, 1.5 mM 31, 305.8 K, 590.7 mM 32, 305.8 K, 472.5 mM 33, 305.8 K, 354.4 mM 34, 305.8 K, 236.3 mM 35, 305.8 K, 118.1 mM 36, 305.8 K, 59.1 mM 37, 305.8 K, 14.8 mM 38, 305.8 K, 5.9 mM 39, 305.8 K, 3.0 mM 40, 305.8 K, 1.5 mM 116 1’ in chloroform (NH) [exp. 3] 01, 283.0 K, 388.0 mM 02, 283.0 K, 310.4 mM 03, 283.0 K, 232.8 mM 04, 283.0 K, 155.2 mM 05, 283.0 K, 77.6 mM 06, 283.0 K, 38.8 mM 07, 283.0 K, 31.0 mM 08, 283.0 K, 15.5 mM 09, 283.0 K, 7.8 mM 10, 292.7 K, 388.0 mM 11, 292.7 K, 310.4 mM 12, 292.7 K, 232.8 mM 13, 292.7 K, 155.2 mM 14, 292.7 K, 77.6 mM 15, 292.7 K, 38.8 mM 16, 292.7 K, 31.0 mM 17, 292.7 K, 15.5 mM 18, 292.7 K, 7.8 mM 19, 302.4 K, 388.0 mM 20, 302.4 K, 310.4 mM 21, 302.4 K, 232.8 mM 22, 302.4 K, 155.2 mM 23, 302.4 K, 77.6 mM 24, 302.4 K, 38.8 mM 25, 302.4 K, 31.0 mM 26, 302.4 K, 7.8 mM 27, 311.8 K, 388.0 mM 28, 311.8 K, 310.4 mM 29, 311.8 K, 232.8 mM 30, 311.8 K, 155.2 mM 31, 311.8 K, 77.6 mM 32, 311.8 K, 38.8 mM 33, 311.8 K, 31.0 mM 34, 311.8 K, 15.5 mM 35, 311.8 K, 7.8 mM 117 1’ in chloroform (NH) [exp. 1] 01, 277.1 K, 112.1 mM 02, 277.1 K, 89.7 mM 03, 277.1 K, 67.2 mM 04, 277.1 K, 44.8 mM 05, 277.1 K, 22.4 mM 06, 277.1 K, 11.2 mM 07, 277.1 K, 2.2 mM 08, 277.1 K, 896.5 (cid:80)M 09, 277.1 K, 448.3 (cid:80)M 10, 277.1 K, 112.1 (cid:80)M 11, 286.7 K, 112.1 mM 12, 286.7 K, 89.7 mM 13, 286.7 K, 67.2 mM 14, 286.7 K, 44.8 mM 15, 286.7 K, 22.4 mM 16, 286.7 K, 11.2 mM 17, 286.7 K, 2.2 mM 18, 286.7 K, 896.5 (cid:80)M 19, 286.7 K, 448.3 (cid:80)M 20, 286.7 K, 112.1 (cid:80)M 21, 297.6 K, 112.1 mM 22, 297.6 K, 89.7 mM 23, 297.6 K, 67.2 mM 24, 297.6 K, 44.8 mM 25, 297.6 K, 22.4 mM 26, 297.6 K, 11.2 mM 27, 297.6 K, 2.2 mM 28, 297.6 K, 896.5 (cid:80)M 29, 297.6 K, 448.3 (cid:80)M 30, 297.6 K, 112.1 (cid:80)M 31, 304.0 K, 112.1 mM 32, 304.0 K, 89.7 mM 33, 304.0 K, 67.2 mM 34, 304.0 K, 44.8 mM 35, 304.0 K, 22.4 mM 36, 304.0 K, 11.2 mM 37, 304.0 K, 2.2 mM 38, 304.0 K, 896.5 (cid:80)M 39, 304.0 K, 448.3 (cid:80)M 40, 304.0 K, 112.1 (cid:80)M 118 1’ in chloroform (NH) [exp. 2] 01, 277.2 K, 381.0 mM 02, 277.2 K, 304.8 mM 03, 277.2 K, 228.6 mM 04, 277.2 K, 152.4 mM 05, 277.2 K, 38.1 mM 06, 277.2 K, 9.5 mM 07, 277.2 K, 3.8 mM 08, 277.2 K, 1.9 mM 09, 277.2 K, 952.6 (cid:80)M 10, 277.2 K, 476.3 (cid:80)M 11, 286.6 K, 381.0 mM 12, 286.6 K, 304.8 mM 13, 286.6 K, 228.6 mM 14, 286.6 K, 152.4 mM 15, 286.6 K, 38.1 mM 16, 286.6 K, 9.5 mM 17, 286.6 K, 3.8 mM 18, 286.6 K, 1.9 mM 19, 286.6 K, 952.6 (cid:80)M 20, 286.6 K, 476.3 (cid:80)M 21, 296.4 K, 381.0 mM 22, 296.4 K, 304.8 mM 23, 296.4 K, 228.6 mM 24, 296.4 K, 152.4 mM 25, 296.4 K, 38.1 mM 26, 296.4 K, 9.5 mM 27, 296.4 K, 3.8 mM 28, 296.4 K, 1.9 mM 29, 296.4 K, 952.6 (cid:80)M 30, 296.4 K, 476.3 (cid:80)M 31, 303.8 K, 381.0 mM 32, 303.8 K, 304.8 mM 33, 303.8 K, 228.6 mM 34, 303.8 K, 152.4 mM 35, 303.8 K, 38.1 mM 36, 303.8 K, 9.5 mM 37, 303.8 K, 3.8 mM 38, 303.8 K, 1.9 mM 39, 303.8 K, 952.6 (cid:80)M 40, 303.8 K, 476.3 (cid:80)M 119 1’ in dichloromethane (NH) 01, 276.2 K, 397.5 mM 02, 276.2 K, 318.0 mM 03, 276.2 K, 238.5 mM 04, 276.2 K, 159.0 mM 05, 276.2 K, 79.5 mM 06, 276.2 K, 39.8 mM 07, 276.2 K, 31.8 mM 08, 276.2 K, 4.0 mM 09, 283.9 K, 397.5 mM 10, 283.9 K, 318.0 mM 11, 283.9 K, 238.5 mM 12, 283.9 K, 159.0 mM 13, 283.9 K, 79.5 mM 14, 283.9 K, 39.8 mM 15, 283.9 K, 31.8 mM 16, 283.9 K, 4.0 mM 17, 291.8 K, 397.5 mM 18, 291.8 K, 318.0 mM 19, 291.8 K, 238.5 mM 20, 291.8 K, 159.0 mM 21, 291.8 K, 79.5 mM 22, 291.8 K, 39.8 mM 23, 291.8 K, 31.8 mM 24, 291.8 K, 4.0 mM 25, 299.6 K, 397.5 mM 26, 299.6 K, 318.0 mM 27, 299.6 K, 238.5 mM 28, 299.6 K, 159.0 mM 29, 299.6 K, 79.5 mM 30, 299.6 K, 39.8 mM 31, 299.6 K, 31.8 mM 32, 299.6 K, 4.0 mM 120 1’ in benzene (NH) [Exp. 3] 01, 280.3 K, 135.6 mM 02, 280.3 K, 108.5 mM 03, 280.3 K, 81.4 mM 04, 280.3 K, 54.3 mM 05, 280.3 K, 27.1 mM 06, 280.3 K, 13.6 mM 07, 280.3 K, 2.7 mM 08, 280.3 K, 1.1 mM 09, 280.3 K, 542.5 (cid:80)M 10, 280.3 K, 135.6 (cid:80)M 11, 280.3 K, 54.3 (cid:80)M 12, 291.6 K, 135.6 mM 13, 291.6 K, 108.5 mM 14, 291.6 K, 81.4 mM 15, 291.6 K, 54.3 mM 16, 291.6 K, 27.1 mM 17, 291.6 K, 13.6 mM 18, 291.6 K, 2.7 mM 19, 291.6 K, 1.1 mM 20, 291.6 K, 542.5 (cid:80)M 21, 291.6 K, 135.6 (cid:80)M 22, 291.6 K, 54.3 (cid:80)M 23, 301.5 K, 135.6 (cid:80)M 24, 301.5 K, 108.5 mM 25, 301.5 K, 81.4 mM 26, 301.5 K, 54.3 mM 27, 301.5 K, 27.1 mM 28, 301.5 K, 13.6 mM 29, 301.5 K, 2.7 mM 30, 301.5 K, 1.1 mM 31, 301.5 K, 542.5 (cid:80)M 32, 301.5 K, 135.6 (cid:80)M 33, 301.5 K, 54.3 (cid:80)M 34, 310.9 K, 135.6 mM 35, 310.9 K, 108.5 mM 36, 310.9 K, 81.4 mM 37, 310.9 K, 54.3 mM 38, 310.9 K, 27.1 mM 39, 310.9 K, 13.6 mM 40, 310.9 K, 2.7 mM 41, 310.9 K, 1.1 mM 42, 310.9 K, 542.5 (cid:80)M 43, 310.9 K, 135.6 (cid:80)M 44, 310.9 K, 54.3 (cid:80)M 121 1’ in benzene (NH) [Exp. 1] 01, 280.2 K, 129.0 mM 02, 280.2 K, 103.2 mM 03, 280.2 K, 77.4 mM 04, 280.2 K, 51.6 mM 05, 280.2 K, 25.8 mM 06, 280.2 K, 12.9 mM 07, 280.2 K, 2.6 mM 08, 280.2 K, 1.0 mM 09, 280.2 K, 516.2 (cid:80)M 10, 280.2 K, 129.0 (cid:80)M 11, 291.7 K, 129.0 mM 12, 291.7 K, 103.2 mM 13, 291.7 K, 77.4 mM 14, 291.7 K, 51.6 mM 15, 291.7 K, 25.8 mM 16, 291.7 K, 12.9 mM 17, 291.7 K, 2.6 mM 18, 291.7 K, 1.0 mM 19, 291.7 K, 516.2 (cid:80)M 20, 291.7 K, 129.0 (cid:80)M 21, 301.5 K, 129.0 mM 22, 301.5 K, 103.2 mM 23, 301.5 K, 77.4 mM 24, 301.5 K, 51.6 mM 25, 301.5 K, 25.8 mM 26, 301.5 K, 12.9 mM 27, 301.5 K, 2.6 mM 28, 301.5 K, 1.0 mM 29, 301.5 K, 516.2 (cid:80)M 30, 301.5 K, 129.0 (cid:80)M 31, 311.0 K, 129.0 mM 32, 311.0 K, 103.2 mM 33, 311.0 K, 77.4 mM 34, 311.0 K, 51.6 mM 35, 311.0 K, 25.8 mM 36, 311.0 K, 12.9 mM 37, 311.0 K, 2.6 mM 38, 311.0 K, 1.0 mM 39, 311.0 K, 516.2 (cid:80)M 40, 311.0 K, 129.0 (cid:80)M 122 1’ in benzene (NH) [Exp. 2] 01, 280.3 K, 134.6 mM 02, 280.3 K, 107.7 mM 03, 280.3 K, 80.8 mM 04, 280.3 K, 53.9 mM 05, 280.3 K, 26.9 mM 06, 280.3 K, 13.5 mM 07, 280.3 K, 2.7 mM 08, 280.3 K, 1.1 mM 09, 280.3 K, 538.6 (cid:80)M 10, 280.3 K, 134.6 (cid:80)M 11, 280.3 K, 53.9 (cid:80)M 12, 291.7 K, 134.6 mM 13, 291.7 K, 107.7 mM 14, 291.7 K, 80.8 mM 15, 291.7 K, 53.9 mM 16, 291.7 K, 26.9 mM 17, 291.7 K, 13.5 mM 18, 291.7 K, 2.7 mM 19, 291.7 K, 1.1 mM 20, 291.7 K, 538.6 (cid:80)M 21, 291.7 K, 134.6 (cid:80)M 22, 291.7 K, 53.9 (cid:80)M 23, 301.5 K, 134.6 mM 24, 301.5 K, 107.7 mM 25, 301.5 K, 80.8 mM 26, 301.5 K, 53.9 mM 27, 301.5 K, 26.9 mM 28, 301.5 K, 13.5 mM 29, 301.5 K, 2.7 mM 30, 301.5 K, 1.1 mM 31, 301.5 K, 538.6 (cid:80)M 32, 301.5 K, 134.6 (cid:80)M 33, 301.5 K, 53.9 (cid:80)M 34, 311.1 K, 134.6 mM 35, 311.1 K, 107.7 mM 36, 311.1 K, 80.8 mM 37, 311.1 K, 53.9 mM 38, 311.1 K, 26.9 mM 39, 311.1 K, 13.5 mM 40, 311.1 K, 2.7 mM 41, 311.1 K, 1.1 mM 42, 311.1 K, 538.6 (cid:80)M 43, 311.1 K, 134.6 (cid:80)M 44, 311.1 K, 53.9 (cid:80)M 123 2 in benzene (NH) [Exp. 1] 01, 279.8 K, 42.0 mM 02, 279.8 K, 33.6 mM 03, 279.8 K, 25.2 mM 04, 279.8 K, 16.8 mM 05, 279.8 K, 8.4 mM 06, 279.8 K, 4.2 mM 07, 279.8 K, 839.4 (cid:80)M 08, 279.8 K, 335.7 (cid:80)M 09, 279.8 K, 167.9 (cid:80)M 10, 279.8 K, 83.9 (cid:80)M 11, 279.8 K, 42.0 (cid:80)M 12, 291.7 K, 42.0 mM 13, 291.7 K, 33.6 mM 14, 291.7 K, 25.2 mM 15, 291.7 K, 16.8 mM 16, 291.7 K, 8.4 mM 17, 291.7 K, 4.2 mM 18, 291.7 K, 839.4 (cid:80)M 19, 291.7 K, 335.7 (cid:80)M 20, 291.7 K, 167.9 (cid:80)M 21, 291.7 K, 83.9 (cid:80)M 22, 291.7 K, 42.0 (cid:80)M 23, 301.5 K, 42.0 mM 24, 301.5 K, 33.6 mM 25, 301.5 K, 25.2 mM 26, 301.5 K, 16.8 mM 27, 301.5 K, 8.4 mM 28, 301.5 K, 4.2 mM 29, 301.5 K, 839.4 (cid:80)M 30, 301.5 K, 335.7 (cid:80)M 31, 301.5 K, 167.9 (cid:80)M 32, 301.5 K, 83.9 (cid:80)M 33, 301.5 K, 42.0 (cid:80)M 34, 310.9 K, 42.0 mM 35, 310.9 K, 33.6 mM 36, 310.9 K, 25.2 mM 37, 310.9 K, 16.8 mM 38, 310.9 K, 8.4 mM 39, 310.9 K, 4.2 mM 40, 310.9 K, 839.4 (cid:80)M 41, 310.9 K, 335.7 (cid:80)M 42, 310.9 K, 167.9 (cid:80)M 43, 310.9 K, 83.9 (cid:80)M 44, 310.9 K, 42.0 (cid:80)M 124 2 in benzene (NH) [Exp. 2] 01, 280.26 K, 39.5 mM 02, 280.26 K, 31.6 mM 03, 280.26 K, 23.7 mM 04, 280.26 K, 15.8 mM 05, 280.26 K, 7.9 mM 06, 280.26 K, 3.9 mM 07, 280.26 K, 789.9 (cid:80)M 08, 280.26 K, 316.0 (cid:80)M 09, 280.26 K, 158.0 (cid:80)M 10, 280.26 K, 79.0 (cid:80)M 11, 280.26 K, 55.3 (cid:80)M 12, 291.7 K, 39.5 mM 13, 291.7 K, 31.6 mM 14, 291.7 K, 23.7 mM 15, 291.7 K, 15.8 mM 16, 291.7 K, 7.9 mM 17, 291.7 K, 3.9 mM 18, 291.7 K, 789.9 (cid:80)M 19, 291.7 K, 316.0 (cid:80)M 20, 291.7 K, 158.0 (cid:80)M 21, 291.7 K, 79.0 (cid:80)M 22, 291.7 K, 55.3 (cid:80)M 23, 301.5 K, 39.5 mM 24, 301.5 K, 31.6 mM 25, 301.5 K, 23.7 mM 26, 301.5 K, 15.8 mM 27, 301.5 K, 7.9 mM 28, 301.5 K, 3.9 mM 29, 301.5 K, 789.9 (cid:80)M 30, 301.5 K, 316.0 (cid:80)M 31, 301.5 K, 158.0 (cid:80)M 32, 301.5 K, 79.0 (cid:80)M 33, 301.5 K, 55.3 (cid:80)M 34, 311.1 K, 39.5 mM 35, 311.1 K, 31.6 mM 36, 311.1 K, 23.7 mM 37, 311.1 K, 15.8 mM 38, 311.1 K, 7.9 mM 39, 311.1 K, 3.9 mM 40, 311.1 K, 789.9 (cid:80)M 41, 311.1 K, 316.0 (cid:80)M 42, 311.1 K, 158.0 (cid:80)M 43, 311.1 K, 79.0 uM 44, 311.1 K, 55.3 uM 125 2 in benzene (NH) [Exp. 3] 01, 280.0 K, 40.3 mM 02, 280.0 K, 32.3 mM 03, 280.0 K, 24.2 mM 04, 280.0 K, 16.1 mM 05, 280.0 K, 8.1 mM 06, 280.0 K, 4.0 mM 07, 280.0 K, 806.4 (cid:80)M 08, 280.0 K, 322.6 (cid:80)M 09, 280.0 K, 161.3 (cid:80)M 10, 280.0 K, 80.6 (cid:80)M 11, 291.7 K, 40.3 mM 12, 291.7 K, 32.3 mM 13, 291.7 K, 24.2 mM 14, 291.7 K, 16.1 mM 15, 291.7 K, 8.1 mM 16, 291.7 K, 4.0 mM 17, 291.7 K, 806.4 (cid:80)M 18, 291.7 K, 322.6 (cid:80)M 19, 291.7 K, 161.3 (cid:80)M 20, 291.7 K, 80.6 (cid:80)M 21, 301.5 K, 40.3 mM 22, 301.5 K, 32.3 mM 23, 301.5 K, 24.2 mM 24, 301.5 K, 16.1 mM 25, 301.5 K, 8.1 mM 26, 301.5 K, 4.0 mM 27, 301.5 K, 806.4 (cid:80)M 28, 301.5 K, 322.6 (cid:80)M 29, 301.5 K, 161.3 (cid:80)M 30, 301.5 K, 80.6 (cid:80)M 31, 310.9 K, 40.3 mM 32, 310.9 K, 32.3 mM 33, 310.9 K, 24.2 mM 34, 310.9 K, 16.1 mM 35, 310.9 K, 8.1 mM 36, 310.9 K, 4.0 mM 37, 310.9 K, 806.4 (cid:80)M 38, 310.9 K, 322.6 (cid:80)M 39, 310.9 K, 161.3 (cid:80)M 40, 310.9 K, 80.6 (cid:80)M 126 2 in acetonitrile (NH) 01, 283.0 K, 201.1 mM 02, 283.0 K, 160.9 mM 03, 283.0 K, 120.7 mM 04, 283.0 K, 80.5 mM 05, 283.0 K, 40.2 mM 06, 283.0 K, 20.1 mM 07, 283.0 K, 5.0 mM 08, 283.0 K, 1.0 mM 09, 283.0 K, 502.8 (cid:80)M 10, 292.6 K, 201.1 mM 11, 292.6 K, 160.9 mM 12, 292.6 K, 120.7 mM 13, 292.6 K, 80.5 mM 14, 292.6 K, 40.2 mM 15, 292.6 K, 20.1 mM 16, 292.6 K, 5.0 mM 17, 292.6 K, 1.0 mM 18, 292.6 K, 502.8 (cid:80)M 19, 302.2 K, 201.1 mM 20, 302.2 K, 160.9 mM 21, 302.2 K, 120.7 mM 22, 302.2 K, 80.5 mM 23, 302.2 K, 40.2 mM 24, 302.2 K, 20.1 mM 25, 302.2 K, 5.0 mM 26, 302.2 K, 1.0 mM 27, 302.2 K, 502.8 (cid:80)M 28, 311.6 K, 201.1 mM 29, 311.6 K, 160.9 mM 30, 311.6 K, 120.7 mM 31, 311.6 K, 80.5 mM 32, 311.6 K, 40.2 mM 33, 311.6 K, 20.1 mM 34, 311.6 K, 5.0 mM 35, 311.6 K, 1.0 mM 36, 311.6 K, 502.8 (cid:80)M 127 2 in chloroform (NH) [exp. 1] 01, 276.9 K, 331.7 mM 02, 276.9 K, 265.4 mM 03, 276.9 K, 199.0 mM 04, 276.9 K, 132.7 mM 05, 276.9 K, 66.3 mM 06, 276.9 K, 33.2 mM 07, 276.9 K, 8.3mM 08, 276.9 K, 3.3 mM 09, 276.9 K, 1.7 mM 10, 276.9 K, 829.3 (cid:80)M 11, 276.9 K, 414.6 (cid:80)M 12, 286.7 K, 331.7 mM 13, 286.7 K, 265.4 mM 14, 286.7 K, 199.0 mM 15, 286.7 K, 132.7 mM 16, 286.7 K, 66.3 mM 17, 286.7 K, 33.2 mM 18, 286.7 K, 8.3mM 19, 286.7 K, 3.3 mM 20, 286.7 K, 1.7 mM 21, 286.7 K, 829.3 (cid:80)M 22, 286.7 K, 414.6 (cid:80)M 23, 296.4 K, 331.7 mM 24, 296.4 K, 265.4 mM 25, 296.4 K, 199.0 mM 26, 296.4 K, 132.7 mM 27, 296.4 K, 66.3 mM 28, 296.4 K, 33.2 mM 29, 296.4 K, 8.3 mM 30, 296.4 K, 3.3 mM 31, 296.4 K, 1.7 mM 32, 296.4 K, 829.3 (cid:80)M 33, 296.4 K, 414.6 (cid:80)M 34, 303.6 K, 331.7 mM 35, 303.6 K, 265.4 mM 36, 303.6 K, 199.0 mM 37, 303.6 K, 132.7 mM 38, 303.6 K, 66.3 mM 39, 303.6 K, 33.2 mM 40, 303.6 K, 8.3 mM 41, 303.6 K, 3.3 mM 42, 303.6 K, 1.7 mM 43, 303.6 K, 829.3 (cid:80)M 44, 303.6 K, 414.6 (cid:80)M 128 2 in chloroform (NH) [exp. 2] 01, 276.2 K, 464.6 mM 02, 276.2 K, 371.7 mM 03, 276.2 K, 278.8 mM 04, 276.2 K, 185.8 mM 05, 276.2 K, 92.9 mM 06, 276.2 K, 46.5 mM 07, 276.2 K, 11.6 mM 08, 276.2 K, 4.6 mM 09, 276.2 K, 580.7 (cid:80)M 10, 285.9 K, 464.6 mM 11, 285.9 K, 371.7 mM 12, 285.9 K, 278.8 mM 13, 285.9 K, 185.8 mM 14, 285.9 K, 92.9 mM 15, 285.9 K, 46.5 mM 16, 285.9 K, 11.6mM 17, 285.9 K, 4.6 mM 18, 285.9 K, 580.7 (cid:80)M 19, 295.7 K, 464.6 mM 20, 295.7 K, 371.7 mM 21, 295.7 K, 278.8 mM 22, 295.7 K, 185.8 mM 23, 295.7 K, 92.9 mM 24, 295.7 K, 46.5 mM 25, 295.7 K, 11.6mM 26, 295.7 K, 4.6 mM 27, 295.7 K, 580.7 (cid:80)M 28, 303.4 K, 464.6 mM 29, 303.4 K, 371.7 mM 30, 303.4 K, 278.8 mM 31, 303.4 K, 185.8 mM 32, 303.4 K, 92.9 mM 33, 303.4 K, 46.5 mM 34, 303.4 K, 11.6 mM 35, 303.4 K, 4.6 mM 36, 303.4 K, 580.7 (cid:80)M 129 2 in dichloromethane (NH) 01, 276.1 K, 370.7 mM 02, 276.1 K, 296.5 mM 03, 276.1 K, 222.4 mM 04, 276.1 K, 148.3 mM 05, 276.1 K, 74.1 mM 06, 276.1 K, 37.1 mM 07, 276.1 K, 18.5 mM 08, 276.1 K, 3.7 mM 09, 284.0 K, 370.7 mM 10, 284.0 K, 296.5 mM 11, 284.0 K, 222.4 mM 12, 284.0 K, 148.3 mM 13, 284.0 K, 74.1 mM 14, 284.0 K, 37.1 mM 15, 284.0 K, 18.5 mM 16, 284.0 K, 3.7 mM 17, 291.7 K, 370.7 mM 18, 291.7 K, 296.5 mM 19, 291.7 K, 222.4 mM 20, 291.7 K, 148.3 mM 21, 291.7 K, 74.1 mM 22, 291.7 K, 37.1 mM 23, 291.7 K, 18.5 mM 24, 291.7 K, 3.7 mM 25, 299.5 K, 370.7 mM 26, 299.5 K, 296.5 mM 27, 299.5 K, 222.4 mM 28, 299.5 K, 148.3 mM 29, 299.5 K, 74.1 mM 30, 299.5 K, 37.1 mM 31, 299.5 K, 18.5 mM 32, 299.5 K, 3.7 mM 130 2’ in chloroform (NH) 01, 277.0 K, 318.5 mM 02, 277.0 K, 254.8 mM 03, 277.0 K, 191.1 mM 04, 277.0 K, 127.4 mM 05, 277.0 K, 63.7 mM 06, 277.0 K, 31.8 mM 07, 277.0 K, 8.0 mM 08, 277.0 K, 3.2 mM 09, 277.0 K, 1.6 mM 10, 286.8 K, 318.5 mM 11, 286.8 K, 254.8 mM 12, 286.8 K, 191.1 mM 13, 286.8 K, 127.4 mM 14, 286.8 K, 63.7 mM 15, 286.8 K, 31.8 mM 16, 286.8 K, 8.0 mM 17, 286.8 K, 3.2 mM 18, 286.8 K, 1.6 mM 19, 296.5 K, 318.5 mM 20, 296.5 K, 254.8 mM 21, 296.5 K, 191.1 mM 22, 296.5 K, 127.4 mM 23, 296.5 K, 63.7 mM 24, 296.5 K, 31.8 mM 25, 296.5 K, 8.0 mM 26, 296.5 K, 3.2 mM 27, 296.5 K, 1.6 mM 28, 303.8 K, 318.5 mM 29, 303.8 K, 254.8 mM 30, 303.8 K, 191.1 mM 31, 303.8 K, 127.4 mM 32, 303.8 K, 63.7 mM 33, 303.8 K, 31.8 mM 34, 303.8 K, 8.0 mM 35, 303.8 K, 3.2 mM 36, 303.8 K, 1.6 mM 131 2’ in benzene (NH) [Exp. 1] 01, 280.2 K, 50.4 mM 02, 280.2 K, 40.3 mM 03, 280.2 K, 30.2 mM 04, 280.2 K, 20.2 mM 05, 280.2 K, 10.1 mM 06, 280.2 K, 5.0 mM 07, 280.2 K, 1.0 mM 08, 280.2 K, 403.1 (cid:80)M 09, 280.2 K, 201.5 (cid:80)M 10, 280.2 K, 100.8 (cid:80)M 11, 280.2 K, 70.5 (cid:80)M 12, 291.6 K, 50.4 mM 13, 291.6 K, 40.3 mM 14, 291.6 K, 30.2 mM 15, 291.6 K, 20.2 mM 16, 291.6 K, 10.1 mM 17, 291.6 K, 5.0 mM 18, 291.6 K, 1.0 mM 19, 291.6 K, 403.1 (cid:80)M 20, 291.6 K, 201.5 (cid:80)M 21, 291.6 K, 100.8 (cid:80)M 22, 291.6 K, 70.5 (cid:80)M 23, 301.3 K, 50.4 mM 24, 301.3 K, 40.3 mM 25, 301.3 K, 30.2 mM 26, 301.3 K, 20.2 mM 27, 301.3 K, 10.1 mM 28, 301.3 K, 5.0 mM 29, 301.3 K, 1.0 mM 30, 301.3 K, 403.1 (cid:80)M 31, 301.3 K, 201.5 (cid:80)M 32, 301.3 K, 100.8 (cid:80)M 33, 301.3 K, 70.5 (cid:80)M 34, 310.1 K, 50.4 mM 35, 310.1 K, 40.3 mM 36, 310.1 K, 30.2 mM 37, 310.1 K, 20.2 mM 38, 310.1 K, 10.1 mM 39, 310.1 K, 5.0 mM 40, 310.1 K, 1.0 mM 41, 310.1 K, 403.1 (cid:80)M 42, 310.1 K, 201.5 (cid:80)M 43, 310.1 K, 100.8 (cid:80)M 44, 310.1 K, 70.5 (cid:80)M 132 2’ in benzene (NH) [Exp. 3] 01, 280.2 K, 47.2 mM 02, 280.2 K, 37.8 mM 03, 280.2 K, 28.3 mM 04, 280.2 K, 18.9 mM 05, 280.2 K, 9.4 mM 06, 280.2 K, 4.7 mM 07, 280.2 K, 944.7 (cid:80)M 08, 280.2 K, 377.9 (cid:80)M 09, 280.2 K, 188.9 (cid:80)M 10, 291.4 K, 47.2 mM 11, 291.4 K, 37.8 mM 12, 291.4 K, 28.3 mM 13, 291.4 K, 18.9 mM 14, 291.4 K, 9.4 mM 15, 291.4 K, 4.7 mM 16, 291.4 K, 944.7 (cid:80)M 17, 291.4 K, 377.9 (cid:80)M 18, 291.4 K, 188.9 (cid:80)M 19, 301.5 K, 47.2 mM 20, 301.5 K, 37.8 mM 21, 301.5 K, 28.3 mM 22, 301.5 K, 18.9 mM 23, 301.5 K, 9.4 mM 24, 301.5 K, 4.7 mM 25, 301.5 K, 944.7 (cid:80)M 26, 301.5 K, 377.9 (cid:80)M 27, 301.5 K, 188.9 (cid:80)M 28, 310.7 K, 47.2 mM 29, 310.7 K, 37.8 mM 30, 310.7 K, 28.3 mM 31, 310.7 K, 18.9 mM 32, 310.7 K, 9.4 mM 33, 310.7 K, 4.7 mM 34, 310.7 K, 944.7 (cid:80)M 35, 310.7 K, 377.9 (cid:80)M 36, 310.7 K, 188.9 (cid:80)M 133 2’ in dichloromethane (NH) 01, 276.2 K, 236.6 mM 02, 276.2 K, 189.3 mM 03, 276.2 K, 142.0 mM 04, 276.2 K, 94.6 mM 05, 276.2 K, 47.3 mM 06, 276.2 K, 23.7 mM 07, 276.2 K, 5.9 mM 08, 276.2 K, 2.4 mM 09, 276.2 K, 1.2 mM 10, 276.2 K, 295.8 (cid:80)M 11, 283.9 K, 236.6 mM 12, 283.9 K, 189.3 mM 13, 283.9 K, 142.0 mM 14, 283.9 K, 94.6 mM 15, 283.9 K, 47.3 mM 16, 283.9 K, 23.7 mM 17, 283.9 K, 5.9 mM 18, 283.9 K, 2.4 mM 19, 283.9 K, 1.2 mM 20, 283.9 K, 295.8 (cid:80)M 21, 291.8 K, 236.6 mM 22, 291.8 K, 189.3 mM 23, 291.8 K, 142.0 mM 24, 291.8 K, 94.6 mM 25, 291.8 K, 47.3 mM 26, 291.8 K, 23.7 mM 27, 291.8 K, 5.9 mM 28, 291.8 K, 2.4 mM 29, 291.8 K, 1.2 mM 30, 291.8 K, 295.8 (cid:80)M 31, 299.5 K, 236.6 mM 32, 299.5 K, 189.3 mM 33, 299.5 K, 142.0 mM 34, 299.5 K, 94.6 mM 35, 299.5 K, 23.7 mM 36, 299.5 K, 47.3 mM 37, 299.5 K, 5.9 mM 38, 299.5 K, 2.4 mM 39, 299.5 K, 1.2 mM 40, 299.5 K, 295.8 (cid:80)M 134 2’ in acetonitrile (NH) 01, 279.2 K, 83.2 mM 02, 279.2 K, 66.6 mM 03, 279.2 K, 49.9 mM 04, 279.2 K, 33.3 mM 05, 279.2 K, 16.6 mM 06, 279.2 K, 8.3 mM 07, 279.2 K, 4.2 mM 08, 279.2 K, 1.7 mM 09, 288.8 K, 83.2 mM 10, 288.8 K, 66.6 mM 11, 288.8 K, 49.9 mM 12, 288.8 K, 33.3 mM 13, 288.8 K, 16.6 mM 14, 288.8 K, 8.3 mM 15, 288.8 K, 4.2 mM 16, 288.8 K, 1.7 mM 17, 298.7 K, 83.2 mM 18, 298.7 K, 66.6 mM 19, 298.7 K, 49.9 mM 20, 298.7 K, 33.3 mM 21, 298.7 K, 16.6 mM 22, 298.7 K, 8.3 mM 23, 298.7 K, 4.2 mM 24, 298.7 K, 1.7 mM 25, 308.43 K, 83.2 mM 26, 308.43 K, 66.6 mM 27, 308.43 K, 49.9 mM 28, 308.43 K, 33.3 mM 29, 308.43 K, 16.6 mM 30, 308.43 K, 8.3 mM 31, 308.43 K, 4.2 mM 32, 308.43 K, 1.7 mM 135 2’ in benzene (NH) [Exp. 2] 01, 280.0 K, 50.7 mM 02, 280.0 K, 40.6 mM 03, 280.0 K, 30.4 mM 04, 280.0 K, 20.3 mM 05, 280.0 K, 10.1 mM 06, 280.0 K, 5.1 mM 07, 280.0 K, 1.0 mM 08, 280.0 K, 405.9 (cid:80)M 09, 280.0 K, 203.0 (cid:80)M 10, 280.0 K, 101.5 (cid:80)M 11, 291.7 K, 50.7 mM 12, 291.7 K, 40.6 mM 13, 291.7 K, 30.4 mM 14, 291.7 K, 20.3 mM 15, 291.7 K, 10.1 mM 16, 291.7 K, 5.1 mM 17, 291.7 K, 1.0 mM 18, 291.7 K, 405.9 (cid:80)M 19, 291.7 K, 203.0 (cid:80)M 20, 291.7 K, 101.5 (cid:80)M 21, 301.5 K, 50.7 mM 22, 301.5 K, 40.6 mM 23, 301.5 K, 30.4 mM 24, 301.5 K, 20.3 mM 25, 301.5 K, 10.1 mM 26, 301.5 K, 5.1 mM 27, 301.5 K, 1.0 mM 28, 301.5 K, 405.9 (cid:80)M 29, 301.5 K, 203.0 (cid:80)M 30, 301.5 K, 101.5 (cid:80)M 31, 310.9 K, 50.7 mM 32, 310.9 K, 40.6 mM 33, 310.9 K, 30.4 mM 34, 310.9 K, 20.3 mM 35, 310.9 K, 10.1 mM 36, 310.9 K, 5.1 mM 37, 310.9 K, 1.0 mM 38, 310.9 K, 405.9 (cid:80)M 39, 310.9 K, 203.0 (cid:80)M 40, 310.9 K, 101.5 (cid:80)M 136 IM in acetonitrile (NH) 01, 276.2 K, 825.4 mM 02, 276.2 K, 660.3 mM 03, 276.2 K, 495.2 mM 04, 276.2 K, 330.2 mM 05, 276.2 K, 165.1 mM 06, 276.2 K, 82.5 mM 07, 276.2 K, 20.6 mM 08, 276.2 K, 4.1 mM 09, 285.9 K, 825.4 mM 10, 285.9 K, 660.3 mM 11, 285.9 K, 495.2 mM 12, 285.9 K, 330.2 mM 13, 285.9 K, 165.1 mM 14, 285.9 K, 82.5 mM 15, 285.9 K, 20.6 mM 16, 285.9 K, 4.1 mM 17, 295.7 K, 825.4 mM 18, 295.7 K, 660.3 mM 19, 295.7 K, 495.2 mM 20, 295.7 K, 330.2 mM 21, 295.7 K, 165.1 mM 22, 295.7 K, 82.5 mM 23, 295.7 K, 20.6 mM 24, 295.7 K, 4.1 mM 25, 303.4 K, 825.4 mM 26, 303.4 K, 660.3 mM 27, 303.4 K, 495.2 mM 28, 303.4 K, 330.2 mM 29, 303.4 K, 165.1 mM 30, 303.4 K, 82.5 mM 31, 303.4 K, 20.6 mM 32, 303.4 K, 4.1 mM 137 IM in benzene (NH) 01, 276.1 K, 249.1 mM 02, 276.1 K, 199.3 mM 03, 276.1 K, 149.5 mM 04, 276.1 K, 99.6 mM 05, 276.1 K, 49.8 mM 06, 276.1 K, 24.9 mM 07, 276.1 K, 6.2 mM 08, 276.1 K, 2.5 mM 09, 276.1 K, 1.2 mM 10, 276.1 K, 311.4 (cid:80)M 11, 285.9 K, 249.1 mM 12, 285.9 K, 199.3 mM 13, 285.9 K, 149.5 mM 14, 285.9 K, 99.6 mM 15, 285.9 K, 49.8 mM 16, 285.9 K, 24.9 mM 17, 285.9 K, 6.2 mM 18, 285.9 K, 2.5 mM 19, 285.9 K, 1.2 mM 20, 285.9 K, 311.4 (cid:80)M 21, 295.6 K, 249.1 mM 22, 295.6 K, 199.3 mM 23, 295.6 K, 149.5 mM 24, 295.6 K, 99.6 mM 25, 295.6 K, 49.8 mM 26, 295.6 K, 24.9 mM 27, 295.6 K, 6.2 mM 28, 295.6 K, 2.5 mM 29, 295.6 K, 1.2 mM 30, 295.6 K, 311.4 (cid:80)M 31, 305.3 K, 249.1 mM 32, 305.3 K, 199.3 mM 33, 305.3 K, 149.5 mM 34, 305.3 K, 99.6 mM 35, 305.3 K, 49.8 mM 36, 305.3 K, 24.9 mM 37, 305.3 K, 6.2 mM 38, 305.3 K, 2.5 mM 39, 305.3 K, 1.2 mM 40, 305.3 K, 311.4 (cid:80)M 138 IM in chloroform (NH) 01, 276.1 K, 618.6 mM 02, 276.1 K, 494.9 mM 03, 276.1 K, 371.2 mM 04, 276.1 K, 247.4 mM 05, 276.1 K, 123.7 mM 06, 276.1 K, 61.9 mM 07, 276.1 K, 15.5 mM 08, 276.1 K, 6.2 mM 09, 276.1 K, 3.1 mM 10, 276.1 K, 773.3 (cid:80)M 11, 283.9 K, 618.6 mM 12, 283.9 K, 494.9 mM 13, 283.9 K, 371.2 mM 14, 283.9 K, 247.4 mM 15, 283.9 K, 123.7 mM 16, 283.9 K, 61.9 mM 17, 283.9 K, 15.5 mM 18, 283.9 K, 6.2 mM 19, 283.9 K, 3.1 mM 20, 283.9 K, 773.3 (cid:80)M 21, 291.8 K, 618.6 mM 22, 291.8 K, 494.9 mM 23, 291.8 K, 371.2 mM 24, 291.8 K, 247.4 mM 25, 291.8 K, 123.7 mM 26, 291.8 K, 61.9 mM 27, 291.8 K, 15.5 mM 28, 291.8 K, 6.2 mM 29, 291.8 K, 3.1 mM 30, 291.8 K, 773.3 (cid:80)M 31, 299.6 K, 618.6 mM 32, 299.6 K, 494.9 mM 33, 299.6 K, 371.2 mM 34, 299.6 K, 247.4 mM 35, 299.6 K, 123.7 mM 36, 299.6 K, 61.9 mM 37, 299.6 K, 15.5 mM 38, 299.6 K, 6.2 mM 39, 299.6 K, 3.1 mM 40, 299.6 K, 773.3 (cid:80)M 139 IM in dichloromethane (NH) 01, 276.2 K, 666.2 mM 02, 276.2 K, 533.0 mM 03, 276.2 K, 399.7 mM 04, 276.2 K, 266.5 mM 05, 276.2 K, 133.2 mM 06, 276.2 K, 66.6 mM 07, 276.2 K, 16.7 mM 08, 276.2 K, 6.7 mM 09, 283.9 K, 666.2 mM 10, 283.9 K, 533.0 mM 11, 283.9 K, 399.7 mM 12, 283.9 K, 266.5 mM 13, 283.9 K, 133.2 mM 14, 283.9 K, 66.6 mM 15, 283.9 K, 16.7 mM 16, 283.9 K, 6.7 mM 17, 291.7 K, 666.2 mM 18, 291.7 K, 533.0 mM 19, 291.7 K, 399.7 mM 20, 291.7 K, 266.5 mM 21, 291.7 K, 133.2 mM 22, 291.7 K, 66.6 mM 23, 291.7 K, 16.7 mM 24, 291.7 K, 6.7 mM 25, 299.5 K, 666.2 mM 26, 299.5 K, 533.0 mM 27, 299.5 K, 399.7 mM 28, 299.5 K, 266.5 mM 29, 299.5 K, 133.2 mM 30, 299.5 K, 66.6 mM 31, 299.5 K, 16.7 mM 32, 299.5 K, 6.7 mM 140 APPENDIX D: NMR and IR spectra of compounds 1, 1’, 2 and 2’ 141 1H NMR spectrum of 1 in CDCl3 3.23 6.13 6.13 6.13 6.14 6.26 6.27 6.27 7.26 CDCl3 = J , t ( 7 2 6 . , ) H 1 , s ( 2 1 . 1 1 δ ) d - m r o f o r o l h C , z H M 0 0 5 ( R M N H 1 . ) H 3 , s ( 3 2 3 . , ) H 1 , m ( 2 1 6 . – 7 1 . 6 , ) 11.12 O H 1 , z H 6 . 2 N C 3 H H N 142 2 - 1 - 0 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1 3 1 4 1 3.00 0.97 0.97 0.97 13C NMR spectrum of 1 in CDCl3 29.99 77.16 CDCl3 108.41 112.52 155.26 . 9 9 . 9 2 , 1 9 . 6 7 , 6 1 . 7 7 , 2 4 . 7 7 , 1 4 . 8 0 1 , . 2 5 2 1 1 , . 6 2 5 5 1 δ ) 3 l c d c , z H M 6 2 1 ( R M N C 3 1 O N C 3 H H N 143 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 1H NMR spectrum of 1’ in CDCl3 2.61 3.24 6.02 7.26 CDCl3 , ) H 1 , s ( 2 0 . 6 δ ) d - m r o f o r o l h C , z H M 0 0 5 ( R M N H 1 . ) H 3 , s ( 1 6 . 2 , ) H 4 , s ( 4 2 . 3 H N O N C 3 H 144 2 - 1 - 0 1 2 3 4 5 3.01 4.00 0.96 6 7 8 9 0 1 1 1 2 1 3 1 4 1 13C NMR spectrum of 1’ in CDCl3 30.43 37.87 47.36 77.16 CDCl3 . 3 4 0 3 . , 7 8 7 3 . , 6 3 . 7 4 , 4 6 . 3 6 1 δ ) 3 l c d c , z H M 6 2 1 ( R M N C 3 1 163.64 H N O N C 3 H 145 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 1H NMR spectrum of 2 in CDCl3 3.92 3.92 3.93 3.93 3.95 3.96 3.96 3.97 4.84 6.54 6.54 6.64 7.26 CDCl3 . ) H 6 , m ( 9 7 . 3 – 6 1 4 . , ) H 2 , s ( 4 8 4 . , ) H 2 , z H 6 1 . = J , d ( 4 5 . 6 , ) H 1 , s ( 4 6 . 6 δ ) d - m r o f o r o l h C , z H M 0 0 5 ( R M N H 1 H N N N 146 4.00 1.00 0.98 0.98 2 - 1 - 0 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1 3 1 4 1 13C NMR spectrum of 2 in CDCl3 43.52 48.19 77.16 CDCl3 110.62 129.59 158.67 . 2 5 . 3 4 , 9 1 . 8 4 , 2 6 . 0 1 1 , 9 5 . 9 2 1 , 7 6 . 8 5 1 δ ) 3 l c d c , z H M 6 2 1 ( R M N C 3 1 H N N N 147 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 1H NMR spectrum of 2’ in CDCl3 2.99 3.01 3.02 3.74 3.76 3.77 6.77 7.26 CDCl3 . 0 7 = J , t ( 6 7 3 . , ) H 1 , s ( 7 7 6 . δ ) d - m r o f o r o l h C , z H M 0 0 5 ( R M N H 1 . ) H 4 , z H 0 . 7 = J , t ( 1 0 . 3 , ) H 4 , z H H N N N 148 2 - 1 - 0 1 2 4.00 3 4.00 0.76 4 5 6 7 8 9 0 1 1 1 2 1 3 1 4 1 13C NMR spectrum of 2’ in CDCl3 49.53 52.70 77.16 CDCl3 . 3 5 9 4 . , 0 7 . 2 5 , 4 5 . 1 7 1 δ ) 3 l c d c , z H M 6 2 1 ( R M N C 3 1 171.54 H N N N 149 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 1H NMR spectrum of 5S in DMSO-d6 2.50 DMSO-d6 2.62 3.86 2.90 4.00 . ) H 1 , s ( 6 0 2 . , ) H 2 , s ( 0 3 . 3 , ) H 1 , s ( 5 3 . 9 9.91 2.01 δ ) 6 d - O S M D , z H M 0 0 5 ( R M N H 1 - I + H N N H S C 3 H 150 2 - 1 - 0 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1 3 1 13C NMR spectrum of 5S in DMSO-d6 13.84 39.52 DMSO-d6 45.21 170.30 . 4 8 . 3 1 , 1 2 . 5 4 , 0 3 . 0 7 1 δ ) o s m d , z H M 6 2 1 ( R M N C - I + H N N H S C 3 H 3 1 151 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 1D and 2D spectra used for the assignment of aromatic hydrogens of compounds 1 and 2 1H NMR spectrum of 1 in C6D6 -0.00 TMS 4 2.67 5.36 5.37 5.37 5.37 5.76 5.77 5.77 . ) H 3 , s ( 7 6 . 2 , ) H 1 , z H 1 . 2 , 8 . 2 = J , d d ( 7 3 . 5 , ) H 1 , z H 6 . 2 = J , t ( 7 7 . 5 , ) H 1 , s ( 3 2 2 3 5 3 . 5 5 7 . 5 3.00 0.80 0.81 O H 1 N 5 2 N 3 4 C 3 H 4 0 2 1 . δ ) 6 d - e n e z n e B , z H M 0 0 5 ( R M N H 12.04 1 0.99 1 152 1 - 0 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1 3 1 4 1 13C NMR spectrum of 1 in C6D6 29.24 4 108.20 111.90 2 3 128.06 C6D6 . 4 2 9 2 . , 0 2 . 8 0 1 , 0 9 . 1 1 1 , 1 0 . 6 5 1 δ ) 6 d - e n e z n e b , z H M 6 2 1 ( R M N C 3 1 156.01 5 O H N 5 2 N 3 4 C 3 H 153 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 HSQC spectrum of 1 in C6D6 1 2 3 4 {2.67,28.92} 4 CH3 4 O N 3 5 2 N H 1 {5.77,107.99} {5.37,111.61} 2 3 {7.16,128.06}C6D6 HSQC 4 2 3 5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 154 HMBC spectrum of 1 in C6D6 HMBC 4 2 3 5 1 2 3 4 CH3 4 O N 3 5 2 N H 1 {5.76,111.81} {7.16,128.06}C6D6 {5.37,108.15} {2.67,111.88} {5.36,156.02} {2.67,156.01} {5.77,156.01} -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 155 Stacked NOE spectra of 1 in C6D6 irradiated CH3 4 O N 3 5 2 N H 1 2 3 irradiated 4 5.5 5.0 4.5 4.0 3.5 3.0 2.5 156 1H NMR spectrum of 2 in C6D6 -0.00 TMS 5 4 5 8 . 2 5 0 . 3 4 3 2 1 2.87 2.88 2.89 2.89 2.91 5 3.04 3.06 3.06 3.07 6.19 6.19 6.29 6.29 6.96 6.97 . ) H 3 , m ( 2 7 2 . – 6 9 . 2 , ) H 4 , z H 9 . 6 , . 0 9 = J , d d ( 6 0 3 . , ) H 1 . , z H 6 1 = J , d ( 9 1 . 6 H 2 4 N 5 6 N N 1 3 157 , ) H 2 , m ( 5 2 . 6 – 4 3 . 6 , ) H 1 , z H 6 . 1 = J , d ( 6 9 . 6 δ ) 6 d - e n e z n e B , z H M 0 0 5 ( R M N H 1 2.00 1.98 0.63 0.86 0.59 1 - 0 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1 3 1 4 1 13C NMR spectrum of 2 in C6D6 43.20 48.16 4 5 110.27 128.06 C6D6 130.51 3 1 . 0 2 . 3 4 , 6 1 . 8 4 , 7 2 . 0 1 1 , 1 5 . 0 3 1 , . 6 7 9 5 1 δ ) 6 d 6 c , z H M 6 2 1 ( R M N C 3 1 159.76 6 H 2 4 N 5 6 N N 1 3 158 0 0 2 0 4 0 6 0 8 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 0 0 2 0 2 2 HSQC spectrum of 2 in C6D6 1 2 3 4 5 {3.04,47.89} {2.89,42.91} H 2 4 5 N N 6 1 N 3 {6.19,109.98} {6.97,130.21} 4 5 3 1 6 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 159 Stacked NOE spectra of 2 in C6D6 H 2 4 5 N N 6 1 N 3 1 3 2 irradiated irradiated 5 4 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 160 IR Spectra of compounds 1 and 2 Compound 1: Compound 2: 161 APPENDIX E: Wavefunction-based energies 162 Wavefunction-based energies for all species are presented in the appendix. DF-HF/aQZ values are the total electronic energies (density fitted) at the specified level; DF-MP2/aQZ values are the two-point extrapolated “MP2 correlation energies” (density fitted) at the specified level; CCSD(T)/aDZ values are the calculated total electronic energy (not density- fitted) at the specified level, CCSD(T)/CBS values are approximated CCSD(T) energies extrapolated to the complete basis set limit. The symmetries of species are shown in parentheses, if applicable. The table is divided into sections based on which figure the named structures belong in. For the redox systems, the hydrogenated species are specified using “- H2” at the end of the their names, and the formic acid bound compounds are specified by “:FA”. 163 The following code was used to extract the CCSD(T)/CBS energies from a directory that had Gaussian16 geometry output files in the current directory (./), DF-MP2/aQ5Z Molpro137,138 output files in the “./DF-MP2/done” subdirectory, and CCSD(T)/aDZ Molpro output files in the “aDZ_CCSD_T/done/” subdirectory: #!/bin/sh echo "File DF-HF/a5Z DF-MP2/aQ5Z CCSD(T)/aDZ CCSD(T)/CBS/(kcal/mol)" > CCSDT_CBS.csv for fname in *.log; do name=${fname%.*} data=$(tail -3 aDZ_CCSD_T/done/$name.out 2> /dev/null |sed '2,3d') CCSDT=$(echo $data | awk '{print $1}') MP2=$(echo $data | awk '{print $2}') HF=$(echo $data | awk '{print $3}') MP2_aQ5Z=$(grep "SETTING DF_MP2_CORR_AQ5Z_M" DF-MP2/done/$name.out 2> /dev/null | awk '{print $4}') HF_a5Z=$(tail -3 DF-MP2/done/$name.out 2> /dev/null |sed '2,3d' | awk '{print $2}' ) if [ -n "$CCSDT" ] && [ -n "$MP2_aQ5Z" ]; then cbs=$(echo "627.509*($HF_a5Z + $MP2_aQ5Z + $CCSDT - $MP2)" | bc) fi [ -z "$CCSDT" ] && CCSDT="---" && cbs="---" [ -z "$MP2" ] && MP2="---" && cbs="---" [ -z "$HF" ] && HF="---" && cbs="---" [ -z "$MP2_aQ5Z" ] && MP2_aQ5Z="---" && cbs="---" [ -z "$HF_a5Z" ] && HF_a5Z="---" && cbs="---" echo "$name $HF_a5Z $MP2_aQ5Z $CCSDT $cbs" >> CCSDT_CBS.csv done cat CCSDT_CBS.csv | column -t sed -i 's| |,|g' CCSDT_CBS.csv 164 Example CCSD(T)/aDZ input file for Molpro (formic acid): geometry={ 5 FA.log Energy: -118470.4941797 O 1.17367 0.10891 -0.00000 O -1.04407 -0.44342 0.00000 C 0.00000 0.42556 -0.00000 H -0.38064 1.46061 -0.00000 H -0.65615 -1.33794 0.00000 } memory,2400,m basis=aVDZ hf HF_ADZ_M=energy mp2 MP2_ADZ_M=energy ccsd(t) CCSD_T_ADZ_M=energy DELTA = CCSD_T_ADZ_M - MP2_ADZ_M show,DELTA 165 Example DF-MP2/aQ5Z input file for Molpro (formic acid): geometry={ 5 FA.log Energy: -118470.4941797 O 1.17367 0.10891 -0.00000 O -1.04407 -0.44342 0.00000 C 0.00000 0.42556 -0.00000 H -0.38064 1.46061 -0.00000 H -0.65615 -1.33794 0.00000 } memory,2400,m BASIS=aVDZ DF-HF,DF_BASIS=aVDZ/JKFIT DF_HF_ADZ_M=energy DF-MP2,DF_BASIS=aVDZ/MP2FIT DF_MP2_ADZ_M=energy DF_MP2_CORR_ADZ_M=(DF_MP2_ADZ_M - DF_HF_ADZ_M) BASIS=aVTZ DF-HF,DF_BASIS=aVTZ/JKFIT DF_HF_ATZ_M=energy DF-MP2,DF_BASIS=aVTZ/MP2FIT DF_MP2_ATZ_M=energy DF_MP2_CORR_ATZ_M=(DF_MP2_ATZ_M - DF_HF_ATZ_M) BASIS=aVQZ DF-HF,DF_BASIS=aVQZ/JKFIT DF_HF_AQZ_M=energy DF-MP2,DF_BASIS=aVQZ/MP2FIT DF_MP2_AQZ_M=energy DF_MP2_CORR_AQZ_M=(DF_MP2_AQZ_M - DF_HF_AQZ_M) GTHRESH,THROVL=1.00D-9 BASIS=aV5Z DF-HF,DF_BASIS=aV5Z/JKFIT DF_HF_A5Z_M=energy DF-MP2,DF_BASIS=aV5Z/MP2FIT DF_MP2_A5Z_M=energy DF_MP2_CORR_A5Z_M=(DF_MP2_A5Z_M - DF_HF_A5Z_M) DF_MP2_CORR_ADTZ_M = ((27 * DF_MP2_CORR_aTZ_M) - (8 * DF_MP2_CORR_aDZ_M))/19 DF_MP2_ADTZ_M = DF_MP2_CORR_ADTZ_M + DF_HF_ATZ_M 166 DF_MP2_CORR_ATQZ_M = ((64 * DF_MP2_CORR_aQZ_M) - (27 * DF_MP2_CORR_aTZ_M))/37 DF_MP2_ATQZ_M = DF_MP2_CORR_ATQZ_M + DF_HF_AQZ_M DF_MP2_CORR_AQ5Z_M = ((125 * DF_MP2_CORR_a5Z_M) - (64 * DF_MP2_CORR_aQZ_M))/61 DF_MP2_AQ5Z_M = DF_MP2_CORR_AQ5Z_M + DF_HF_A5Z_M show,DF_MP2_ADTZ_M show,DF_MP2_ATQZ_M show,DF_MP2_AQ5Z_M 167 Energies of the structures for the main AMHB case in Figures I-5 to I-8 DF-MP2/aQ5Z CCSD(T)/aDZ CCSD(T)/CBS DF-HF/a5Z (a.u) -299.832448 -599.6851583 -301.0167305 -602.049544 -602.049418 -319.6603015 -639.3419929 -641.7216002 -641.7215321 -320.8518087 -642.3187447 -1284.656011 -1287.021655 -1287.021617 -643.503011 -599.575739 -599.5764303 -299.7848202 -601.9366708 -601.9367001 -300.9623507 -639.1978489 -319.5923714 -320.7701895 -641.5532279 -641.5532219 -641.5530149 -641.5530181 -320.7683902 -642.2995114 -1284.616293 -1286.975364 -1286.975311 -643.4801478 -559.959781 -559.9605655 -279.9737399 -562.3026734 -562.302701 -281.1447868 -599.6268368 -599.6268812 -299.8066536 -300.9857816 -601.9853038 -601.9853205 -601.9853519 -601.9854326 -300.9856599 -1244.941148 -1244.941163 -622.4651953 -623.6390123 -1247.289869 -1247.289867 (a.u) -1.24936507 -2.51207132 -1.27288822 -2.55504901 -2.55509392 -1.27932864 -2.56911508 -2.6159716 -2.61600044 -1.30394142 -1.219865 -2.45252837 -2.50067745 -2.50073281 -1.24538408 -2.52632162 -2.52563735 -1.24702766 -2.56505541 -2.56506823 -1.27654466 -2.58084518 -1.27957856 -1.30901944 -2.62932188 -2.6293234 -2.62962658 -2.62962489 -1.30859578 -1.21686903 -2.45386143 -2.49948661 -2.49952168 -1.24357489 -2.45504016 -2.45449653 -1.22289028 -2.5006276 -2.50076544 -1.2447543 -2.50883664 -2.50880481 -1.24954215 -1.27417056 -2.56003645 -2.5600193 -2.55973707 -2.55998908 -1.27456875 -2.39553118 -2.395501 -1.19255927 -1.21738416 -2.44788776 -2.44788891 (a.u) -300.7481821 -601.5315286 -301.9596451 -603.9468021 -603.9466734 -320.5794488 -641.1925899 -643.6234896 -643.6234333 -321.7976807 -643.2039551 -1286.440211 -1288.86303 -1288.863079 -644.4177855 -601.4386773 -601.4390471 -300.7041933 -603.852725 -603.8527681 -301.9135506 -641.0672456 -320.5182185 -321.7276326 -643.4792946 -643.4792965 -643.4793782 -643.479378 -321.7253257 -643.1806455 -1286.398341 -1288.815633 -1288.81566 -644.3934189 -561.8064213 -561.8065949 -280.8917333 -564.2056673 -564.2058235 -282.090536 -601.4740125 -601.4741065 -300.7247067 -301.9317204 -603.8896909 -603.889695 -603.8893022 -603.8898898 -301.9320807 -1246.722872 -1246.722949 -623.3499945 -624.5548889 -1249.135677 -1249.135677 (kcal/mol) -188971.2323 -377962.8869 -189736.4059 -379488.8103 -379488.7423 -201430.1431 -402879.9692 -404415.6176 -404415.5801 -202199.5802 -403869.2189 -807757.3607 -809285.8658 -809285.8771 -404634.9709 -377903.6912 -377903.8741 -188942.3328 -379427.371 -379427.3966 -189706.3192 -402799.5931 -201390.1982 -202153.975 -404322.6879 -404322.6863 -404322.7243 -404322.7251 -202152.6483 -403856.2939 -807734.2958 -809258.2046 -809258.1963 -404620.6555 -353005.0346 -353005.2882 -176495.8547 -354521.3281 -354521.4192 -177253.4595 -377927.2579 -377927.2641 -188956.4894 -189719.1392 -379453.3735 -379453.3758 -379453.2201 -379453.4695 -189719.2758 -782805.8504 -782805.8357 -391396.4522 -392156.4622 -784327.6011 -784327.6004 cpd. 1a (C2v) 1a' (C2) 1a dimer (C2h) 1a' dimer (C2) 1a' dimer (Ci) 1b dimer (C2h) 1b' dimer (C2) 1b' dimer (Ci) 1b (Cs) 1b' 1c (Cs) 1c' 1c dimer (C2h) 1c' dimer (C2) 1c' dimer (Ci) 2a dimer (C2) 2a dimer (Ci) 2a' dimer (C2) 2a' dimer (Ci) 2b dimer (C2h) 2a 2a' 2b 2b' [1] 2b' dimer (C2) [1] 2b' dimer (C2) 2b' dimer (Ci) [1] 2b' dimer (Ci) 2b' 2c 2c' 2c dimer (C2h) 2c' dimer (C2) 2c' dimer (Ci) 3a dimer (C2) 3a dimer (Ci) 3a' dimer (C2) 3a' dimer (Ci) 3b dimer (C2) 3b dimer (Ci) 3a' 3a 3b 3b' [1] 3b' dimer (C2) [1] 3b' dimer (C2) 3b' dimer (Ci) [1] 3b' dimer (Ci) 3c dimer (C2) 3c dimer (Ci) 3b' 3c 3c' [1] 3c' dimer (C2) [1] 3c' dimer (C2) 168 Energies of the structures for the main AMHB cases in Figures I-5 to I-8 (cont’d) DF-MP2/aQ5Z CCSD(T)/aDZ CCSD(T)/CBS (a.u) -1249.135892 -1249.135892 -624.5561494 -561.7600546 -561.76045 -280.872362 -564.139689 -564.1391964 -282.059204 -601.3896215 -601.3898117 -300.684893 -301.8794936 -603.7819249 -603.7819236 -603.7819824 -603.7819823 -301.8794902 -1246.709161 -1246.709315 -623.3449405 -624.5428171 -1249.108635 -1249.109325 -1249.108692 -1249.109392 -624.5432165 -338.7268169 -677.4814207 -679.9255397 -679.9255345 -679.9255407 -679.9255406 -339.9478799 -358.570739 -717.1697118 -719.6155108 -719.6155118 -359.7918445 -681.184147 -1362.397339 -1364.831827 -1364.831829 -682.4000485 -338.7419187 -677.5067141 -339.9666354 -679.9562559 -679.9562548 -358.5995488 -717.2214201 -359.8283774 -719.6804382 -681.2053354 (kcal/mol) -784327.7067 -784327.7057 -392157.1343 -352975.5168 -352975.9007 -176483.5199 -354478.0762 -354477.7881 -177232.9371 -377871.6539 -377871.7164 -188930.0232 -189684.5496 -379382.5823 -379382.5818 -379382.5585 -379382.5573 -189684.5512 -782801.6239 -782801.6528 -391395.46 -392149.9044 -784313.1005 -784313.39 -784313.068 -784313.4254 -392150.1108 -212829.414 -425674.793 -427219.5603 -427219.5541 -427219.5575 -427219.5575 -213601.1692 -225296.2295 -450608.7812 -452154.5346 -452154.5347 -226068.0226 -427726.8077 -855470.2684 -857008.5261 -857008.5283 -428495.1663 -212839.2526 -425691.2425 -213613.5978 -427240.0088 -427240.006 -225314.6375 -450641.7763 -226091.643 -452196.621 -427740.2312 cpd. 3c' 3c' dimer (Ci) [1] 3c' dimer (Ci) 4a dimer (C2) 4a dimer (Ci) 4a' dimer (C2) 4a' dimer (Ci) 4b dimer (C2) 4b dimer (Ci) 4a' 4a 4b 4b' [1] 4b' dimer (C2) [1] 4b' dimer (C2) 4b' dimer (Ci) [1] 4b' dimer (Ci) 4c dimer (C2) 4c dimer (Ci) 4b' 4c 4c' [1] 4c' dimer (C2) [1] 4c' dimer (C2) 4c' dimer (Ci) [1] 4c' dimer (Ci) 4c' 5a (Cs) 5a dimer (C2h) 5a' dimer (C2)_C1 5a' dimer (C2) 5a' dimer (Ci)_C1 5a' dimer (Ci) 5a' 5b (Cs) 5b dimer (C2h) 5b' dimer (C2) 5b' dimer (Ci) 5b' 5c (Cs) 5c dimer (C2h) 5c' dimer (C2) 5c' dimer (Ci) 5c' 6a (Cs) 6a' 6a dimer (C2h) 6a' dimer (C2) 6a' dimer (Ci) 6b dimer (C2h) 6b' dimer (C2h) 6b (C2v) 6b' (C2v) 6c (Cs) DF-HF/a5Z (a.u) -1247.29007 -1247.290065 -623.6397267 -559.9030376 -559.9038405 -279.948716 -562.2186284 -562.2182279 -281.1043282 -599.5213348 -599.5214208 -299.754534 -300.9185656 -601.8507968 -601.850794 -601.8506779 -601.8506692 -300.918578 -1244.931001 -1244.930994 -622.4608337 -623.6274378 -1247.266842 -1247.266874 -1247.266746 -1247.266903 -623.6275261 -337.6812385 -675.3788149 -677.760215 -677.7601984 -677.760201 -677.7602019 -338.8719849 -357.5255426 -715.0690572 -717.4474094 -717.4474113 -358.7146109 -680.1705273 -1360.358914 -1362.727137 -1362.727139 -681.3548878 -337.7015359 -675.4133547 -338.8961842 -677.8029968 -677.8029888 -357.5599612 -715.131351 -358.7582231 -717.5288431 -680.1977379 (a.u) -2.44775494 -2.44775867 -1.21776693 -2.46676874 -2.46646775 -1.22934588 -2.51166597 -2.51163535 -1.25057197 -2.52271558 -2.52273166 -1.25844087 -1.28272791 -2.57435002 -2.57435339 -2.5744455 -2.57445237 -1.28272152 -2.39971615 -2.3997711 -1.19600709 -1.21648372 -2.44392539 -2.44428202 -2.44390521 -2.44428194 -1.21679088 -1.4065704 -2.82188242 -2.88561946 -2.88562483 -2.88562793 -2.88562725 -1.43723477 -1.43668033 -2.88077114 -2.94974257 -2.94974081 -1.46924096 -1.3760872 -2.76022996 -2.82701809 -2.82701879 -1.40768469 -1.40253589 -2.81490363 -1.43404447 -2.87758514 -2.87759078 -1.4317008 -2.87152289 -1.46420513 -2.93697234 -1.37011576 169 Energies of the structures for the main AMHB cases in Figures I-5 to I-8 (cont’d) DF-MP2/aQ5Z CCSD(T)/aDZ CCSD(T)/CBS (a.u) -2.75012508 -1.40065894 -2.81080759 -1.37306597 -2.7610224 -2.8298886 -2.8298885 -1.4084834 -1.40266605 -2.82091003 -2.89238294 -1.43945113 -1.34195136 -2.70111973 -2.77234806 -2.77234444 -1.3791661 -1.37291703 -2.75831081 -2.81918323 -2.81918393 -1.40307833 -1.40143194 -2.81677851 -1.4329658 -2.87903367 -1.34046815 -2.69560652 -1.36894468 -2.75200196 (a.u) -1362.433726 -682.429896 -1364.88298 -318.8661613 -637.7619436 -640.2050049 -640.2050056 -320.0909168 -338.7146345 -677.4600272 -679.909839 -339.9430023 -661.327294 -1322.687075 -1325.124987 -1325.124989 -662.5507178 -318.8784942 -637.7868921 -640.2364409 -640.2364376 -320.1038207 -338.7294508 -677.4983396 -339.9621784 -679.9615314 -661.3353167 -1322.712404 -662.562158 -1325.166016 (kcal/mol) -855493.2113 -428514.4292 -857041.6882 -200352.3597 -400721.6628 -402265.9496 -402265.9495 -201126.3818 -212822.1596 -425661.9909 -427210.5157 -213598.4854 -415252.3459 -830523.1416 -832063.7405 -832063.7435 -416025.2904 -200360.2197 -400737.6705 -402286.3048 -402286.3054 -201134.9573 -212831.6775 -425686.3694 -213611.0581 -427243.7079 -415257.3891 -830538.9061 -416032.9355 -832089.8919 DF-HF/a5Z (a.u) -1360.405725 -681.3929678 -1362.796663 -317.8245251 -635.6624271 -638.0386673 -638.0386666 -319.0145976 -337.6735434 -675.3611736 -677.7423679 -338.8663862 -660.3178984 -1320.649741 -1323.01857 -1323.018574 -661.5050004 -317.8378639 -635.6916364 -638.0825183 -638.0825154 -319.0341643 -337.6904596 -675.4048676 -338.8935895 -677.8094579 -660.3279831 -1320.680992 -661.5271963 -1323.0799 cpd. 6c' (Cs) 7a (Cs) 6c dimer (C2h) 6c' dimer (C2h) 7a dimer (C2h) 7a' dimer (C2) 7a' dimer (Ci) 7b dimer (C2h) 7b' dimer (C2h) 7a' 7b (Cs) 7b' 7c (Cs) 7c dimer (C2h) 7c' dimer (C2) 7c' dimer (Ci) 7c' 8a 8a' 8a dimer (C2h) 8a' dimer (C2) 8a' dimer (Ci) 8b (Cs) 8b' (Cs) 8c (Cs) 8c' (Cs) 8b dimer (C2h) 8b' dimer (C2h) 8c dimer (C2h) 8c' dimer (C2h) 170 cpd. 9 (Cs) 10 11 9 dimer (C2h) 10 dimer (C2) 10 dimer (Ci) 11 dimer (C2) 11 dimer (Ci) 12 dimer (C2) 12 dimer (Ci) 12 Energies of the structure for the AMHB case study in Figure I-10 DF-MP2/aQ5Z CCSD(T)/aDZ DF-HF/a5Z (a.u) -355.7027398 -711.4256407 -356.8679428 -713.754775 -713.7549317 -356.8834637 -713.7800417 -713.780695 -358.0573836 -716.1306709 -716.1304132 (a.u) -1.55668884 -3.131799 -1.576723 -3.17312756 -3.1729724 -1.57942871 -3.17304979 -3.17209429 -1.60268975 -3.21920925 -3.21939837 (a.u) -356.874087 -713.7876858 -358.0678758 -716.1733532 -716.1734777 -358.0832706 -716.1961342 -716.1956881 -359.2861315 -718.6033596 -718.6030909 CCSD(T)/CBS (kcal/mol) -224234.7747 -448492.0543 -224988.9224 -449999.4834 -449999.5378 -224998.2001 -450012.8939 -450012.7883 -225758.2854 -451534.3314 -451534.2311 171 13 dimer 13' dimer 13'' dimer 14 dimer 14' dimer 14'' dimer 15 dimer 15' dimer 15'' dimer 13 13' 13'' 14 14' 14'' 15 15' 15'' Energies of the structures for the fused rings in Figure 12 DF-MP2/aQ5Z CCSD(T)/aDZ DF-HF/a5Z (a.u) -948.8070042 -474.3895175 -951.1401735 -475.559067 -951.137489 -475.5579203 -948.8563775 -474.4188472 -951.139054 -475.5584618 -951.1377559 -475.5582475 -948.8555022 -474.4186015 -951.138329 -475.5578982 -951.1346375 -475.5560914 (a.u) -4.13180154 -2.05817079 -4.18095861 -2.08331416 -4.18151208 -2.08327427 -4.11812359 -2.05245742 -4.18516881 -2.08561762 -4.18586352 -2.08555362 -4.11858376 -2.05117752 -4.18492582 -2.08409325 -4.18657193 -2.08480694 (a.u) --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- CCSD(T)/CBS (kcal/mol) --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- 172 cpd. 1 1' 1y 1x 1z (Cs) 1 dimer (C2h) 1' dimer (C2) 1' dimer (Ci) 1x dimer (C2) 1x dimer (Ci) 1y dimer (C2) 1y dimer (Ci) 1z dimer (C2h) 2 dimer (C2) 2 dimer (Ci) 2' dimer (C2) 2' dimer (Ci) 2x dimer (C2) 2x dimer (Ci) 2y dimer (C2) 2y dimer (Ci) 2z dimer (C2) 2z dimer (Ci) 2x 2 2' 2y 2z Energies of the structures for Hybridization vs AMHB in Figure I-18 (a.u) CCSD(T)/aDZ -679.93541184 -339.94997571 -682.34992915 -682.34976998 -341.16123427 -758.33400267 -758.33396021 -379.15196639 -758.33776576 -758.33765113 -379.15501415 -834.32905164 -417.14917160 -716.19613421 -716.19568807 -358.08327056 -718.60335960 -718.60309089 -359.28613151 -794.59160233 -794.59151194 -397.27844990 -794.58582645 -794.58568330 -397.27686794 -870.57993548 -870.57985739 -435.27242091 (kcal/mol) CCSD(T)/CBS -427231.87750 -213605.73788 -428757.14985 -428757.07518 -214370.69011 -476496.05399 -476496.03434 -238239.56944 -476498.92407 -476498.90171 -238241.44610 -524241.70092 -262112.28792 -450012.89386 -450012.78826 -224998.20007 -451534.33144 -451534.23110 -225758.28540 -499275.53573 -499275.50652 -249627.90569 -499272.48856 -499272.45192 -249627.10029 -547016.98642 -547016.94083 -273498.53764 (a.u) DF-HF/a5Z -677.77540313 -338.87785110 -680.13827916 -680.13815120 -340.06152125 -755.87689744 -755.87690335 -377.93036012 -755.88063589 -755.88063541 -377.93220565 -831.61806225 -415.80089362 -713.78004172 -713.78069503 -356.88346369 -716.13067085 -716.13041319 -358.05738357 -791.87521525 -791.87522087 -395.92829942 -791.86991180 -791.86975027 -395.92656687 -867.61261553 -867.61248704 -433.79700540 (a.u) DF-MP2/aQ5Z -2.90080507 -1.44343803 -2.94347318 -2.94351287 -1.46688351 -3.26154981 -3.26151781 -1.62548236 -3.26343939 -3.26343938 -1.62720212 -3.58981478 -1.78964045 -3.17304979 -3.17209429 -1.57942871 -3.21920925 -3.21939837 -1.60268975 -3.53497689 -3.53494563 -1.76032625 -3.53542570 -3.53560816 -1.76082872 -3.85951196 -3.85960817 -1.92240565 173 Energies of the structures for the RAHB cases in Figure I-20 DF-MP2/aQ5Z CCSD(T)/aDZ (a.u) -1.20508534 -2.42254765 -2.42255752 -1.20487476 -2.42254782 -2.42251430 -1.17368485 -2.35826355 -2.35796503 -1.17349423 -2.35740303 -2.35749936 -1.17262218 -2.35686637 -2.35686758 -1.23682218 -2.49166072 -2.49165854 -1.20623025 -2.42733072 -1.20560447 -2.42644714 -1.20504254 -2.42751212 (a.u) -266.06902938 -532.16174110 -532.16147312 -266.06862419 -532.16174310 -532.16190189 -264.84090254 -529.69917488 -529.69899968 -264.85012300 -529.72374648 -529.72396678 -264.84758672 -529.72097080 -529.72097107 -285.91408322 -571.86558879 -571.86559512 -284.68369942 -569.39618998 -284.69512538 -569.42798867 -284.69168748 -569.42198472 CCSD(T)/CBS (kcal/mol) -167188.12341 -334390.00889 -334389.85457 -167187.90691 -334390.00774 -334390.07838 -166411.68355 -332832.86635 -332832.79280 -166417.76188 -332849.28243 -332849.35855 -166416.25909 -332847.55804 -332847.55742 -179655.59797 -359333.34022 -359333.33998 -178877.77958 -357772.20058 -178885.20317 -357792.83229 -178883.06402 -357789.05941 DF-HF/a5Z (a.u) -265.13813394 -530.28744479 -530.28724165 -265.13796719 -530.28744081 -530.28751061 -263.94049754 -527.88630703 -527.88644225 -263.95130335 -527.91503085 -527.91502350 -263.94924588 -527.91229461 -527.91229214 -284.98023806 -569.98017201 -569.98017501 -283.77951520 -567.57232537 -283.79316520 -567.60838937 -283.78962941 -567.60051784 cpd. An1 An1 dimer ((C2)) An1 dimer (Ci) An1 [1] An4 An2 An3 An1 dimer (C2) [1] An1 dimer (Ci) [1] An2 dimer (C2) An2 dimer (Ci) An3 dimer (C2) An3 dimer (Ci) An4 dimer (C2) An4 dimer (Ci) Im1 dimer (C2) Im1 dimer (Ci) Im2 dimer (C2h) Im3 dimer (C2h) Im4 dimer (C2h) Im2 Im3 Im4 Im1 174 1F cpd. 1A:FA 1A-H2:FA 1A-H2 1A 1B:FA 1B-H2:FA 1B-H2 1B 1C:FA 1C-H2:FA 1C-H2 1C 1D:FA 1D-H2:FA 1D-H2 1D 1E:FA 1E-H2:FA 1E-H2 1E 1F:FA 1F-H2:FA 1F-H2 1G:FA 1G-H2:FA 1G-H2 1G 1H:FA 1H-H2:FA 1H-H2 1H 1I:FA 1I-H2:FA 1I-H2 1J:FA 1J-H2:FA 1J-H2 1K:FA 1K-H2:FA 1K-H2 1K 1L:FA 1L-H2:FA 1L-H2 1M:FA 1M-H2:FA 1M-H2 1M 1N:FA 1N-H2:FA 1N-H2 1L 1J 1I DF-HF/a5Z (a.u) -811.86618309 -813.06764830 -624.18805068 -622.99163528 -811.86766202 -813.06516629 -624.18606312 -622.99411115 -811.92203832 -813.06351232 -624.18589954 -623.05162532 -811.87551412 -813.06076823 -624.18001703 -622.99820985 -811.89315024 -813.06008206 -624.18033938 -623.01626462 -811.89282739 -813.06467092 -624.18626634 -623.02223148 -811.88548652 -813.05993994 -624.17981540 -623.00869374 -811.89790024 -813.06333421 -624.18491853 -623.02725482 -811.87068517 -813.09400923 -624.21948707 -622.99210295 -811.88174834 -813.08915021 -624.21437470 -623.00387368 -811.86034320 -813.09039383 -624.21392406 -622.98590120 -811.89783450 -813.09013261 -624.21606270 -623.02725187 -811.87690457 -813.08781999 -624.21149550 -623.00008500 -811.89284947 -813.08996155 -624.21576762 (a.u) -3.28304168 -3.33770007 -2.60710724 -2.55494417 -3.28384051 -3.33902443 -2.60853819 -2.55558731 -3.28040312 -3.33762954 -2.60621643 -2.55232067 -3.28502902 -3.33566660 -2.60458791 -2.55497765 -3.28007016 -3.33348587 -2.60227867 -2.55018132 -3.27629674 -3.33362457 -2.60202681 -2.54813807 -3.27931548 -3.33451070 -2.60321291 -2.55007572 -3.27411838 -3.33220373 -2.60022297 -2.54620031 -3.28307436 -3.33270698 -2.60281132 -2.55368405 -3.28331868 -3.33166597 -2.60184465 -2.55357474 -3.27874303 -3.32700361 -2.59666223 -2.55039104 -3.27441712 -3.32466252 -2.59405919 -2.54620023 -3.28617995 -3.32789096 -2.59758572 -2.55592516 -3.27640819 -3.32531799 -2.59479615 Energies of the structures for the redox systems in Figure I-21 DF-MP2/aQ5Z CCSD(T)/aDZ (a.u) -814.26210801 -815.50028113 -626.11021733 -624.87824469 -814.26391382 -815.49910362 -626.10959557 -624.88087676 -814.30864401 -815.49598075 -626.10710339 -624.92890475 -814.27160523 -815.49218901 -626.10080148 -624.88400848 -814.28492174 -815.49047977 -626.09994794 -624.89782829 -814.28312268 -815.49351729 -626.10376118 -624.90315164 -814.27722553 -815.49088389 -626.09998608 -624.89057830 -814.28617043 -815.49127114 -626.10131839 -624.90630076 -814.26630154 -815.52179125 -626.13648043 -624.87779564 -814.27685073 -815.51674897 -626.13127286 -624.88882354 -814.25572811 -815.51317712 -626.12580692 -624.87156346 -814.28643577 -815.51038706 -626.12487768 -624.90630240 -814.27424685 -815.51165497 -626.12445732 -624.88684077 -814.28334778 -815.51091723 -626.12537678 CCSD(T)/CBS (kcal/mol) -511611.54702 -512398.52756 -393398.67040 -392615.53098 -511612.68232 -512397.76923 -393398.26877 -392617.19196 -511641.15668 -512395.94976 -393396.87422 -392647.76340 -511617.39859 -512393.21265 -393392.40490 -392619.03366 -511625.90779 -512391.98880 -393391.74666 -392627.84807 -511624.99970 -512394.20987 -393394.48897 -392631.44283 -511621.04509 -512392.42573 -393391.93207 -392623.27121 -511626.95300 -512392.83123 -393392.97078 -392633.46452 -511613.98509 -512412.29442 -393415.53727 -392615.06127 -511620.67692 -512408.87356 -393411.99623 -392622.07044 -511607.42453 -512406.75213 -393408.56133 -392611.26240 -511627.05677 -512404.98108 -393408.05868 -392633.46365 -511618.97242 -512405.66000 -393407.59044 -392620.78606 -511625.07486 -512405.21865 -393408.26767 175 Energies of the structures for the redox systems in Figure I-21 (cont’d) DF-MP2/aQ5Z CCSD(T)/aDZ (a.u) -624.90315343 -814.28081609 -815.51934826 -626.13230898 -624.89600415 -814.26004763 -815.51564804 -626.12912688 -624.87440177 -814.26565370 -815.51512634 -626.12778271 -624.88113826 -814.27737791 -815.50851314 -626.12017735 -624.88798694 -814.28503066 -815.50378180 -626.11952881 -624.90238768 -814.26000001 -815.50878471 -626.12057318 -624.87580397 -814.26909956 -815.50638431 -626.12227730 -624.88622578 -189.35617046 -1.16486912 CCSD(T)/CBS (kcal/mol) -392631.44294 -511623.30500 -512410.79753 -393412.99903 -392626.87940 -511610.15931 -512408.40958 -393410.93394 -392613.18684 -511613.73517 -512408.14754 -393410.15815 -392617.46745 -511621.06669 -512403.73378 -393405.03694 -392621.72765 -511625.94561 -512400.57022 -393404.46038 -392630.83012 -511610.13005 -512404.00158 -393405.38739 -392614.06118 -511615.70658 -512402.38812 -393406.39467 -392620.45735 -118979.60464 -738.13271 1P cpd. 1N 1O:FA 1O-H2:FA 1O-H2 1O 1P:FA 1P-H2:FA 1P-H2 1Q:FA 1Q-H2:FA 1Q-H2 1Q 1R:FA 1R-H2:FA 1R-H2 1R 1S:FA 1S-H2:FA 1S-H2 1S 1T:FA 1T-H2:FA 1T-H2 1U:FA 1U-H2:FA 1U-H2 1T 1U H2 FA (formic acid) DF-HF/a5Z (a.u) -623.02223239 -811.88827587 -813.09570462 -624.22002574 -623.01417072 -811.86178466 -813.09077455 -624.21582799 -622.98783130 -811.87054758 -813.09107332 -624.21546135 -622.99708141 -811.88369610 -813.08534147 -624.20875810 -623.00485806 -811.89170662 -813.08030134 -624.20776139 -623.01971890 -811.86585862 -813.08610715 -624.20975820 -622.99235288 -811.87062985 -813.08315765 -624.21103043 -622.99856791 -188.85623790 -1.13333857 (a.u) -2.54813555 -3.28371053 -3.32832648 -2.59777511 -2.55416321 -3.28370848 -3.32931687 -2.59852817 -2.55293773 -3.28068758 -3.32853973 -2.59748494 -2.55083601 -3.28106808 -3.32659026 -2.59532507 -2.55114581 -3.28166611 -3.32666885 -2.59557055 -2.55175444 -3.27819422 -3.32657652 -2.59515021 -2.54888686 -3.28744193 -3.32702062 -2.59561218 -2.55734416 -0.72047604 -0.03429902 176 cpd. Flavin Flavin-H2 Flavin:FA Flavin-H2:FA Flavin:FA [2] Flavin-H2:FA [2] FA (formic acid) H2 Energies of the structures for the flavin case in Figure I-22 DF-MP2/aQ5Z CCSD(T)/aDZ DF-HF/a5Z (a.u) -789.08189262 -790.25727546 -977.95469469 -979.12866832 -977.95225562 -979.13008002 -188.85624878 -1.13333686 (a.u) -3.32531923 -3.35901174 -4.05350101 -4.08797460 -4.05390936 -4.08801201 -0.72046662 -0.03429923 (a.u) -791.55931102 -792.76088999 -980.94140714 -982.14241829 -980.93961334 -982.14383970 -189.35617236 -1.16486966 CCSD(T)/CBS (kcal/mol) -497346.39130 -498109.86912 -616341.25163 -617104.41145 -616340.11124 -617105.26172 -118979.60668 -738.13210 177 CCSD(T)/CBS (kcal/mol) -213605.74002 -213605.73870 -427231.87661 -427231.87938 -427231.87847 -214370.69122 -428757.15015 -428757.07531 -224998.19985 -450012.89394 -450012.78829 -225758.28546 -451534.33164 -451534.23121 -263773.69211 -527565.17058 -179666.75116 -359349.81330 -359349.82211 Gas-phase references for DFT method evaluation in Table II-2 DF-MP2/aQ5Z CCSD(T)/aDZ DF-HF/a5Z (a.u) -338.87785831 -338.87785283 -677.77541637 -677.77541379 -677.77540841 -340.06152715 -680.13828087 -680.13815180 -356.88346293 -713.78004220 -713.78069548 -358.05738394 -716.13067195 -716.13041342 -418.49976816 -837.01950532 -285.00267390 -570.02053756 -570.02052101 (a.u) -1.44343752 -1.44343571 -2.90078920 -2.90079875 -2.90080308 -1.46687997 -2.94347183 -2.94351255 -1.57942919 -3.17304927 -3.17209433 -1.60268953 -3.21920831 -3.21939844 -1.75484204 -3.51749366 -1.23336713 -2.47751571 -2.47754720 (a.u) -339.94997234 -339.94997767 -679.93541288 -679.93541066 -679.93541027 -341.16123370 -682.34992928 -682.34976991 -358.08327050 -716.19613438 -716.19568763 -359.28613145 -718.60335976 -718.60309077 -419.80271227 -839.63550465 -285.93159430 -571.89149807 -571.89152938 cpd. 1 (Cs) 1 (C1) 2 (C1) 1' (C1) 1 dimer (C2h) 1 dimer (C2) 1 dimer (Ci)) 1' dimer (C2) 1' dimer (Ci)) 2 dimer (C2) 2 dimer (Ci)) 2' dimer (C2) 2' dimer (Ci)) BA dimer (C2h) IM dimer (C2) IM dimer (Ci)) IM (C1) 2' (C1) BA (benzoic acid) (Cs) 178 APPENDIX F: Calculated NICS values 179 NICS(0) and NICS(1)zz values for all species are presented in this appendix. To avoid arbitrary choice of the face of the ring for placing the NICS(1)zz probe in cases where the ring was not completely flat, NICS(1)zz was averaged after calculations of its values on both faces at no extra computational cost. The “NICS(1)zz” on each face is denoted as “NICS(1)zz [1]” and “NICS(1)zz [2]”, and their average is denoted as “NICS(1)zz [avg]”. In fused ring systems, the ring involved in H-bonding was considered as “ring I”, and the other ring was named “ring II”. For the flavin case, with three rings, the farthest ring from the H-bonding ring was named “ring III”. The symmetries of species are shown in parentheses, if applicable. The table is divided into sections based on which figure the named structures belong. For the redox systems, the hydrogenated species are specified using “-H2” at the end of the their names and the Formic acid bound compounds are specified by “:FA”. 180 The code used for extracting NICS values from Gaussian16 output files in the current directory: #!/bin/sh echo "File NICS(0) NICS(1)zz[1] NICS(1)zz[2] NICS(1)zz[avg]" > nics.csv for gout in *.log; do nics0_raw=$(grep "Bq Isotropic =" $gout -A 4 | awk 'NR==1' | awk '{print $8}') nics1a_raw=$(grep "Bq Isotropic =" $gout -A 4 | awk 'NR==9' | awk '{print $6}') nics1b_raw=$(grep "Bq Isotropic =" $gout -A 4 | awk 'NR==14' | awk '{print $6}') nics0=$(echo " $nics0_raw * -1" | bc) nics1a=$(echo " $nics1a_raw * -1" | bc) nics1b=$(echo " $nics1b_raw * -1" | bc) nics1=$(echo "scale=4; $nics1a/2 + $nics1b/2" | bc) echo "${gout%.*} $nics0 $nics1a $nics1b $nics1" >> nics.csv done cat nics.csv | column -t sed -i 's| |,|g' nics.csv 181 Example NICS input file for Gaussian16: # nmr=giao gen nosymm mpwpw91 This is a comment line. 0 1 O 2.46555400 -0.00000000 -0.00000000 N 0.36074400 1.09014000 -0.00000000 N 0.36074400 -1.09014000 0.00000000 C -0.97593600 0.68527000 -0.00000000 C -0.97593600 -0.68527000 -0.00000000 C 1.23038400 -0.00000000 -0.00000000 H 0.70669400 2.04064000 -0.00000000 H 0.70669400 -2.04064000 0.00000000 H -1.80551600 1.38528000 -0.00000000 H -1.80551600 -1.38528000 -0.00000000 bq 0.00000000 0.00000000 0.00000000 bq 0.00000000 0.00000000 1.00000000 bq 0.00000000 0.00000000 -1.00000000 O H N C 0 6-311++G(3df,3pd) **** 182 2a 3c 4a 2b 2c 3a 3b cpd. 1a (C2v) 1b (Cs) 1c (Cs) 1a dimer (C2h) 1b dimer (C2h) 1c dimer (C2h) 2a dimer (C2) 2a dimer (Ci) 2b dimer (C2h) 2c dimer (C2h) 3a dimer (C2) 3a dimer (Ci) 3b dimer (C2) 3b dimer (Ci) 3c dimer (C2) 3c dimer (Ci) 4a dimer (C2) 4a dimer (Ci) 4b dimer (C2) 4b dimer (Ci) 4c dimer (C2) 4c dimer (Ci) 5a dimer (C2h) 5b dimer (C2h) 5c dimer (C2h) 6a dimer (C2h) 6b dimer (C2h) 6c dimer (C2h) 7a dimer (C2h) 7b dimer (C2h) 7c dimer (C2h) 8a dimer (C2h) 8b dimer (C2h) 8c dimer (C2h) 5a (Cs) 5b (Cs) 5c (Cs) 6a (Cs) 6b (C2v) 6c (Cs) 7a (Cs) 7b (Cs) 7c (Cs) 8b (Cs) 8c (Cs) 4b 4c 8a NICS(0) -25.3221 -23.2633 -27.4987 -25.9574 -29.1508 -27.5345 -23.6321 -18.4351 -18.5625 -24.6175 -19.8805 -19.1221 -16.9614 -9.6613 -12.7358 -13.2597 -15.2836 -17.9751 -17.9912 -16.0074 -19.0985 -19.0968 -8.3504 -9.5270 -9.9176 -12.2128 -13.5093 -13.5296 -10.2972 -11.1600 -11.1649 -28.3943 -29.8807 -24.5804 -27.2502 -24.0058 -27.5684 -28.7793 -28.7834 -30.8265 -31.2348 -27.3301 -28.1249 -34.1613 -33.8665 -39.0621 -37.9094 -41.3565 -38.4509 -25.1258 -25.9216 -29.7228 -30.0552 -29.1740 -27.7666 -15.0420 -17.0960 -12.5100 -14.0729 -12.0275 -13.7494 -12.5416 -19.1302 -19.0828 -11.7602 -16.1784 -13.5330 -16.1620 -26.5917 -24.6245 -24.1810 -21.4652 -19.4091 -19.3526 -22.0304 -19.3305 -19.3157 -27.2163 -26.0313 -25.6014 -23.2381 -21.7088 -21.5541 -24.7611 -22.7620 -22.6302 2.6965 3.8509 6.1100 7.6389 4.1206 6.2059 -3.7599 -3.4012 -0.6794 0.0372 -2.9479 -2.2927 10.7246 9.2360 15.5995 13.1353 19.6025 15.3109 -3.6774 -3.7261 0.5930 -0.1696 -1.2013 -1.9457 NICS values for the four cases of AMHB in Figures I-5 to I-8 NICS(1)zz [1] NICS(1)zz [2] NICS(1)zz [avg] -15.0420 -17.0960 -12.5100 -14.0729 -12.0275 -13.7494 -12.7829 -18.6532 -18.4517 -10.8795 -16.1784 -13.5282 -16.1620 -26.8984 -24.5039 -24.2526 -21.1983 -19.3623 -19.4225 -21.5200 -19.3756 -19.4351 -27.2015 -25.7398 -25.7921 -23.2875 -21.5691 -21.7410 -24.5850 -22.6592 -22.8117 2.6965 3.8509 6.1100 7.6389 4.1206 6.2059 -3.7599 -3.4012 -0.6794 0.0372 -2.9479 -2.2927 10.7246 9.2360 15.5995 13.1353 19.6025 15.3109 -3.5824 -3.7261 0.5930 -0.1696 -1.2013 -1.9457 -15.0420 -17.0960 -12.5100 -14.0729 -12.0275 -13.7494 -12.6623 -18.8917 -18.7673 -11.3199 -16.1784 -13.5306 -16.1620 -26.7451 -24.5642 -24.2168 -21.3318 -19.3857 -19.3876 -21.7752 -19.3531 -19.3754 -27.2089 -25.8856 -25.6968 -23.2628 -21.6390 -21.6476 -24.6731 -22.7106 -22.7210 2.6965 3.8509 6.1100 7.6389 4.1206 6.2059 -3.7599 -3.4012 -0.6794 0.0372 -2.9479 -2.2927 10.7246 9.2360 15.5995 13.1353 19.6025 15.3109 -3.6299 -3.7261 0.5930 -0.1696 -1.2013 -1.9457 183 cpd. 9 (Cs) [ring I] 9 (Cs) [ring II] 9 dimer (C2h) [ring I] 9 dimer (C2h) [ring II] 10 10 dimer (C2) 10 dimer (Ci) 11 dimer (C2) 11 dimer (Ci) 11 NICS(0) -16.4712 -15.4878 -7.7871 -10.2526 -29.6438 -27.0103 -27.0832 -13.8733 -15.6099 -16.0699 -22.6335 -23.4836 -30.3510 -27.9754 -8.9333 -11.5620 -11.5082 -23.8597 -21.8891 -21.4433 NICS values for the case study in Figure I-10 NICS(1)zz [1] NICS(1)zz [2] -22.6335 -23.4836 -30.3510 -27.9754 -9.5831 -12.6744 -12.6336 -23.0941 -22.0145 -21.5664 NICS(1)zz [avg] -22.6335 -23.4836 -30.3510 -27.9754 -9.2582 -12.1182 -12.0709 -23.4769 -21.9518 -21.5049 184 cpd. 13 [ring I] 13 [ring II] 13 dimer [ring I] 13 dimer [ring II] 13' 13'' 13' dimer 13'' dimer 14 [ring I] 14 [ring II] 14 dimer [ring I] 14 dimer [ring II] 14' 14'' 14' dimer 14'' dimer 15 [ring I] 15 [ring II] 15 dimer [ring I] 15 dimer [ring II] 15' 15'' 15' dimer 15'' dimer NICS values for the fused rings in Figure I-12 NICS(1)zz [1] NICS(1)zz [2] -14.9718 -18.3134 -14.0180 -18.0441 -8.7720 -10.6261 -8.3394 -10.9710 -8.3881 -11.1508 -26.2968 -26.2369 -9.0845 -11.2612 -9.6620 -12.1514 -8.1397 -10.9006 -24.7713 -25.1814 -9.1794 -11.6962 -8.8522 -11.2467 NICS(1)zz [avg] -14.9718 -18.3134 -14.0180 -18.0440 -8.4579 -10.9702 -8.3421 -10.9783 -8.3880 -11.1508 -26.2968 -26.2368 -8.9613 -11.3903 -9.4869 -11.9460 -8.1396 -10.9006 -24.7712 -25.1814 -8.8549 -11.4002 -8.8120 -11.3683 NICS(0) -9.2153 -6.7532 -5.3612 -2.6724 -13.5527 -11.8505 -11.5286 -9.6177 -12.8723 -11.1953 -5.9773 -5.6686 -13.4711 -11.9102 -12.6342 -10.7572 -14.7782 -12.5067 -3.9241 -4.3776 -12.8530 -10.5383 -11.0463 -9.1417 -14.9718 -18.3134 -14.0180 -18.0441 -8.1439 -11.3145 -8.3448 -10.9856 -8.3881 -11.1508 -26.2968 -26.2369 -8.8383 -11.5195 -9.3119 -11.7407 -8.1397 -10.9006 -24.7713 -25.1814 -8.5305 -11.1043 -8.7719 -11.4900 185 cpd. NICS values for the redox systems in Figure I-20 NICS(1)zz [1] NICS(1)zz [2] 5.5648 -3.7078 6.3103 -3.0683 -17.8766 -13.4616 -19.9900 -16.3935 3.3945 -0.0867 3.6018 0.4900 -18.4821 -13.8950 -20.6838 -16.6205 5.5904 -24.1280 6.1756 -23.9200 -16.9714 -12.8757 -18.6321 -16.8764 -6.7539 6.6499 -9.1046 7.9208 -13.2577 -13.1671 -16.6993 -16.5935 -8.2297 3.7772 -10.9178 4.4628 -13.7492 -11.1163 -17.3543 -14.3069 1.0033 3.7096 1.4858 4.2236 -11.4262 -13.0186 -14.0190 -16.1937 -5.9111 4.7897 -8.1188 NICS(1)zz [avg] 5.5648 -3.7078 6.3102 -3.0682 -17.8766 -13.4616 -19.9900 -16.3934 3.3944 -0.0866 3.6018 0.4900 -18.4820 -13.8950 -20.6838 -16.6204 5.5904 -24.1280 6.1756 -23.9200 -16.9714 -12.8756 -18.6320 -16.8764 -6.7538 6.6498 -9.1046 7.9208 -13.2576 -13.1670 -16.6992 -16.5934 -8.2296 3.7772 -10.9178 4.4628 -13.7492 -11.1162 -17.3542 -14.3068 1.0032 3.7096 1.4858 4.2236 -11.4262 -13.0186 -14.0190 -16.1936 -5.9110 4.7896 -8.1188 1A [ring I] 1A [ring II] 1A:FA [ring I] 1A:FA [ring II] 1A-H2 [ring I] 1A-H2 [ring II] 1A-H2:FA [ring I] 1A-H2:FA [ring II] 1B [ring I] 1B [ring II] 1B:FA [ring I] 1B:FA [ring II] 1B-H2 [ring I] 1B-H2 [ring II] 1B-H2:FA [ring I] 1B-H2:FA [ring II] 1C [ring I] 1C [ring II] 1C:FA [ring I] 1C:FA [ring II] 1C-H2 [ring I] 1C-H2 [ring II] 1C-H2:FA [ring I] 1C-H2:FA [ring II] 1D [ring I] 1D [ring II] 1D:FA [ring I] 1D:FA [ring II] 1D-H2 [ring I] 1D-H2 [ring II] 1D-H2:FA [ring I] 1D-H2:FA [ring II] 1E [ring I] 1E [ring II] 1E:FA [ring I] 1E:FA [ring II] 1E-H2 [ring I] 1E-H2 [ring II] 1E-H2:FA [ring I] 1E-H2:FA [ring II] 1F [ring I] 1F [ring II] 1F:FA [ring I] 1F:FA [ring II] 1F-H2 [ring I] 1F-H2 [ring II] 1F-H2:FA [ring I] 1F-H2:FA [ring II] 1G [ring I] 1G [ring II] 1G:FA [ring I] NICS(0) -22.0703 -16.1816 -23.7034 -16.6617 -8.8965 -7.9184 -7.1452 -6.1670 -20.6435 -17.9179 -21.7974 -18.5429 -7.4796 -7.3826 -5.7661 -5.8210 -25.5448 -3.1417 -27.1939 -3.0388 -9.6202 -6.4896 -8.0501 -3.9654 -13.1462 -16.8412 -11.1770 -17.7483 -11.1856 -6.7412 -8.7869 -4.8956 -13.3780 -27.0482 -11.3804 -27.8508 -9.9742 -9.3637 -7.5019 -7.6035 -18.8506 -20.9527 -19.1998 -21.4346 -12.7409 -8.8304 -10.8469 -6.8437 -15.3350 -17.8488 -13.6633 5.5648 -3.7078 6.3103 -3.0683 -17.8766 -13.4616 -19.9900 -16.3935 3.3945 -0.0867 3.6018 0.4900 -18.4821 -13.8950 -20.6838 -16.6205 5.5904 -24.1280 6.1756 -23.9200 -16.9714 -12.8757 -18.6321 -16.8764 -6.7539 6.6499 -9.1046 7.9208 -13.2577 -13.1671 -16.6993 -16.5935 -8.2297 3.7772 -10.9178 4.4628 -13.7492 -11.1163 -17.3543 -14.3069 1.0033 3.7096 1.4858 4.2236 -11.4262 -13.0186 -14.0190 -16.1937 -5.9111 4.7897 -8.1188 186 NICS values for the redox systems in Figure I-20 (cont’d) NICS(1)zz [2] NICS(1)zz [1] cpd. NICS(0) -18.2541 -8.4441 -7.7247 -5.9641 -5.5475 -19.9265 -19.6795 -20.3538 -19.8561 -11.0673 -9.6685 -8.9993 -7.2129 -12.2112 -17.8875 -10.9809 -18.7629 -12.8923 -1.6646 -10.6191 -1.5661 -11.0223 -28.9323 -9.2311 -29.0645 -13.9942 -2.5190 -11.8233 -2.4726 -21.1834 -20.3840 -22.0148 -21.1735 -13.4269 -4.2612 -11.1109 -4.0717 -19.9269 -19.6796 -20.7374 -19.7758 -13.3535 -1.6156 -11.4425 -1.7522 -12.0636 -20.0076 -10.1110 -19.7339 -14.8548 -1.4256 5.8155 -14.6484 -12.5234 -18.0909 -16.0817 2.0932 -1.8054 2.6493 -1.4298 -12.3981 -11.9355 -15.0172 -15.5246 -6.1004 7.5817 -8.6723 7.8634 -8.8707 -23.1691 -11.7324 -23.6720 -7.5254 5.3570 -10.5925 5.5231 -8.1776 -21.7100 -11.0977 -22.1888 5.9895 11.5024 7.3009 13.1282 -8.6351 -22.1850 -11.8135 -22.4913 2.0931 -1.8044 2.4038 -1.6755 -7.7658 -22.7282 -10.3484 -22.7716 -6.8052 11.4940 -9.4558 11.5565 -7.6612 -22.7646 5.8155 -14.6484 -12.5234 -18.0910 -16.0817 2.0932 -1.8054 2.6493 -1.4298 -12.3981 -11.9355 -15.0172 -15.5246 -6.1004 7.5817 -8.6723 7.8634 -8.8707 -23.1691 -11.7324 -23.6720 -7.5254 5.3570 -10.5925 5.5231 -8.1776 -21.7100 -11.0977 -22.1888 5.9895 11.5024 7.3009 13.1282 -8.6351 -22.1850 -11.8135 -22.4913 2.0931 -1.8044 2.4038 -1.6755 -7.7658 -22.7282 -10.3484 -22.7716 -6.8052 11.4940 -9.4558 11.5565 -7.6612 -22.7646 NICS(1)zz [avg] 5.8154 -14.6484 -12.5234 -18.0909 -16.0816 2.0932 -1.8054 2.6492 -1.4298 -12.3980 -11.9354 -15.0172 -15.5246 -6.1004 7.5816 -8.6722 7.8634 -8.8706 -23.1690 -11.7324 -23.6720 -7.5254 5.3570 -10.5924 5.5230 -8.1776 -21.7100 -11.0976 -22.1888 5.9894 11.5024 7.3008 13.1282 -8.6350 -22.1850 -11.8134 -22.4912 2.0930 -1.8044 2.4038 -1.6754 -7.7658 -22.7282 -10.3484 -22.7716 -6.8052 11.4940 -9.4558 11.5564 -7.6612 -22.7646 1G:FA [ring II] 1G-H2 [ring I] 1G-H2 [ring II] 1G-H2:FA [ring I] 1G-H2:FA [ring II] 1H [ring I] 1H [ring II] 1H:FA [ring I] 1H:FA [ring II] 1H-H2 [ring I] 1H-H2 [ring II] 1H-H2:FA [ring I] 1H-H2:FA [ring II] 1I [ring I] 1I [ring II] 1I:FA [ring I] 1I:FA [ring II] 1I-H2 [ring I] 1I-H2 [ring II] 1I-H2:FA [ring I] 1I-H2:FA [ring II] 1J [ring I] 1J [ring II] 1J:FA [ring I] 1J:FA [ring II] 1J-H2 [ring I] 1J-H2 [ring II] 1J-H2:FA [ring I] 1J-H2:FA [ring II] 1K [ring I] 1K [ring II] 1K:FA [ring I] 1K:FA [ring II] 1K-H2 [ring I] 1K-H2 [ring II] 1K-H2:FA [ring I] 1K-H2:FA [ring II] 1L [ring I] 1L [ring II] 1L:FA [ring I] 1L:FA [ring II] 1L-H2 [ring I] 1L-H2 [ring II] 1L-H2:FA [ring I] 1L-H2:FA [ring II] 1M [ring I] 1M [ring II] 1M:FA [ring I] 1M:FA [ring II] 1M-H2 [ring I] 1M-H2 [ring II] 187 NICS values for the redox systems in Figure I-20 (cont’d) NICS(1)zz [2] NICS(1)zz [1] cpd. -10.8524 -23.1836 1.0036 3.7096 1.1813 3.6285 -7.0398 -22.7900 -9.6538 -22.8921 9.5119 -18.1754 10.9806 -17.7130 -9.8411 -25.5487 -12.2358 -25.9800 1.5260 11.1064 1.4525 11.7146 -10.2321 -22.7917 -12.7961 -23.3105 2.8150 2.8795 3.0149 3.5343 -9.9538 -22.7084 -12.5012 -23.2339 -6.3335 10.3407 -8.6455 10.5117 -7.7352 -21.0146 -10.8282 -21.9963 -7.3744 7.9965 -9.8601 7.2869 -7.7062 -20.1983 -10.4790 -20.8043 3.7265 NICS(1)zz [avg] -10.8524 -23.1836 1.0036 3.7096 1.1812 3.6284 -7.0398 -22.7900 -9.6538 -22.8920 9.5118 -18.1754 10.9806 -17.7130 -9.8410 -25.5486 -12.2358 -25.9800 1.5260 11.1064 1.4524 11.7146 -10.2320 -22.7916 -12.7960 -23.3104 2.8150 2.8794 3.0148 3.5342 -9.9538 -22.7084 -12.5012 -23.2338 -6.3334 10.3406 -8.6454 10.5116 -7.7352 -21.0146 -10.8282 -21.9962 -7.3744 7.9964 -9.8600 7.2868 -7.7062 -20.1982 -10.4790 -20.8042 3.7264 1M-H2:FA [ring I] 1M-H2:FA [ring II] 1N [ring I] 1N [ring II] 1N:FA [ring I] 1N:FA [ring II] 1N-H2 [ring I] 1N-H2 [ring II] 1N-H2:FA [ring I] 1N-H2:FA [ring II] 1O [ring I] 1O [ring II] 1O:FA [ring I] 1O:FA [ring II] 1O-H2 [ring I] 1O-H2 [ring II] 1O-H2:FA [ring I] 1O-H2:FA [ring II] 1P [ring I] 1P [ring II] 1P:FA [ring I] 1P:FA [ring II] 1P-H2 [ring I] 1P-H2 [ring II] 1P-H2:FA [ring I] 1P-H2:FA [ring II] 1Q [ring I] 1Q [ring II] 1Q:FA [ring I] 1Q:FA [ring II] 1Q-H2 [ring I] 1Q-H2 [ring II] 1Q-H2:FA [ring I] 1Q-H2:FA [ring II] 1R [ring I] 1R [ring II] 1R:FA [ring I] 1R:FA [ring II] 1R-H2 [ring I] 1R-H2 [ring II] 1R-H2:FA [ring I] 1R-H2:FA [ring II] 1S [ring I] 1S [ring II] 1S:FA [ring I] 1S:FA [ring II] 1S-H2 [ring I] 1S-H2 [ring II] 1S-H2:FA [ring I] 1S-H2:FA [ring II] 1T [ring I] NICS(0) -12.7185 -1.0153 -18.8508 -20.9520 -19.6608 -21.2115 -14.6864 -1.1963 -12.9266 -1.3853 -17.3325 -4.0831 -19.3306 -4.5099 -15.1882 -4.2141 -12.9059 -4.7560 -22.2825 -24.2215 -23.3315 -24.9905 -15.6243 -0.6553 -13.4305 -1.0890 -23.0745 -23.1363 -24.2501 -23.7070 -15.9113 -1.6881 -13.7595 -1.6402 -15.9078 -20.1806 -14.0969 -19.9524 -14.2084 -2.4202 -11.7689 -1.6284 -15.4667 -30.7135 -13.3240 -30.1211 -15.0052 -3.4372 -12.5932 -3.0360 -23.2912 -10.8524 -23.1836 1.0036 3.7096 1.1813 3.6285 -7.0398 -22.7900 -9.6538 -22.8921 9.5119 -18.1754 10.9806 -17.7130 -9.8411 -25.5487 -12.2358 -25.9800 1.5260 11.1064 1.4525 11.7146 -10.2321 -22.7917 -12.7961 -23.3105 2.8150 2.8795 3.0149 3.5343 -9.9538 -22.7084 -12.5012 -23.2339 -6.3335 10.3407 -8.6455 10.5117 -7.7352 -21.0146 -10.8282 -21.9963 -7.3744 7.9965 -9.8601 7.2869 -7.7062 -20.1983 -10.4790 -20.8043 3.7265 188 1T [ring II] 1T:FA [ring I] 1T:FA [ring II] 1T-H2 [ring I] 1T-H2 [ring II] 1T-H2:FA [ring I] 1T-H2:FA [ring II] 1U [ring I] 1U [ring II] 1U:FA [ring I] 1U:FA [ring II] 1U-H2 [ring I] 1U-H2 [ring II] 1U-H2:FA [ring I] 1U-H2:FA [ring II] 10.5248 4.7972 12.0934 -7.8732 -20.6548 -10.9700 -21.4612 -6.5957 15.6840 -8.9704 13.9676 -7.0817 -21.7625 -9.7055 -22.4626 NICS(1)zz [avg] 10.5248 4.7972 12.0934 -7.8732 -20.6548 -10.9700 -21.4612 -6.5956 15.6840 -8.9704 13.9676 -7.0816 -21.7624 -9.7054 -22.4626 NICS values for the redox systems in Figure I-20 (cont’d) NICS(1)zz [2] NICS(1)zz [1] cpd. NICS(0) -21.3442 -23.5063 -21.9598 -14.1931 -5.2989 -11.7794 -5.0252 -14.6400 -22.6971 -12.7615 -21.6600 -16.0243 -2.4025 -13.5768 -2.1362 10.5248 4.7972 12.0934 -7.8732 -20.6548 -10.9700 -21.4612 -6.5957 15.6840 -8.9704 13.9676 -7.0817 -21.7625 -9.7055 -22.4626 189 NICS values for the flavin case in Figure I-22 NICS(1)zz [1] NICS(1)zz [2] cpd. Flavin [ring I] Flavin [ring 2] Flavin [ring 3] Flavin:FA [ring I] Flavin:FA [ring 2] Flavin:FA [ring 3] Flavin:FA [2] [ring I] Flavin:FA [2] [ring 2] Flavin:FA [2] [ring 3] Flavin-H2 [ring I] Flavin-H2 [ring 2] Flavin-H2 [ring 3] Flavin-H2:FA [ring I] Flavin-H2:FA [ring 2] Flavin-H2:FA [ring 3] Flavin-H2:FA [2] [ring I] Flavin-H2:FA [2] [ring 2] Flavin-H2:FA [2] [ring 3] NICS(0) -18.2123 -21.7554 -3.3670 -16.8633 -21.0450 -3.9667 -18.3505 -22.8244 -2.8266 -34.5131 -18.6058 -2.8642 -34.5565 -18.6950 -2.9742 -34.7277 -18.6201 -2.8129 -7.2093 0.7828 -23.5947 -8.7288 0.7086 -24.0879 -6.8818 0.4949 -23.2572 12.5943 -1.8251 -20.3206 11.4364 -0.6893 -18.9620 13.3280 -1.8217 -20.5851 -7.2093 0.7828 -23.5947 -8.7288 0.7086 -24.0879 -6.8818 0.4949 -23.2572 11.5510 -0.3350 -18.4402 13.2445 -2.2535 -20.6499 11.6260 -0.3801 -18.9837 NICS(1)zz [avg] -7.2092 0.7828 -23.5946 -8.7288 0.7086 -24.0878 -6.8818 0.4948 -23.2572 12.0726 -1.0800 -19.3804 12.3404 -1.4713 -19.8059 12.4770 -1.1008 -19.7843 190 APPENDIX G: The Python code for insertion of NICS probes 191 import numpy, math, argparse, ast, sys import pybel, rdkit from rdkit import Chem from pprint import pprint from scipy.optimize import curve_fit from subprocess import Popen, PIPE, call ''' How to run this script: make sure there is Gaussian input file names "3c.com" exists in the directory and type: python nics.py -I 3c.com -R "1 2 3 4 5 6" ''' # parse arguments parser = argparse.ArgumentParser() parser.add_argument("-I", "--input", help="input file name: it can be either Gaussian16 input (*.com) or output (.log)") parser.add_argument("-R", "--rings", help="ring element indices starting from 1. Also, makes sure single quotes are included. e.g: '1 3 6 7 9'") parser.add_argument("-M", "--method", help="method: e.g mpwpw91") parser.add_argument("-B", "--basis", help="basis set: e.g 6-311+G(2d,p)") parser.add_argument("-C", "--charge", help="charge : e.g -1") parser.add_argument("-S", "--spin", help="basis set: e.g 2") args = parser.parse_args() input = args.input rings = args.rings method = args.method basis = args.basis charge = args.charge spin = args.spin # set default value for level of theory if not specified. if method == None: method = 'mpwpw91' if basis == None: basis = '6-311++G(3df,3pd)' if charge == None: charge = '0' if spin == None: spin = '1' 192 gaussian_card = '# nmr=giao gen nosymm ' + method charge_and_multiplicity = charge + ' ' + spin # dictionary of atoms atomlist = {'H' : 1,'He' : 2, \ 'Li':3,'Be':4,'B':5,'C':6,'N':7,'O':8,'F':9,'Ne':10, \ 'Na':11,'Mg':12,'Al':13,'Si':14,'P':15,'S':16,'Cl':17,'Ar':18,\ 'K':19,'Ca':20,'Ga':31,'Ge':32,'As':33,'Se':34,'Br':35,'Kr':36,\ 'Rb':37,'Sr':38,'In':49,'Sn':50,'Sb':51,'Te':52,'I':53,'Xe':54,\ 'Cs':55,'Ba':56,'Tl':81,'Pb':82,'Bi':83,'Po':84,'At':85,'Rn':86} ############################################################## ############### DEFINING FUNCTIONS ############################## ############################################################## # functions for getting geometries: def getGeometryGeneral(input): ''' this function tries to distinguish between a gaussian input and output and extract geometries from them. ''' if input.endswith('.log'): result = get_lines(input,'Standard orientation','Rotational constants (GHZ)',5,-1,'1 3 4 5') elif input.endswith('.com'): result = getGINgeometry(input) elif input.endswith('.mol2'): result = None elif input.endswith('.xyz'): result = None elif input.endswith('.mol'): result = None elif input.endswith('.sdf'): result = None elif input.endswith('.pdb'): result = None elif input.endswith('.xml'): result = None return result def getGINgeometry(input): ''' This function extracts the xyz coordinates from a xyz format Gaussian16 input file. it might work with Gaussian09 and Gaussian03 input files, too. At this point, the extention of the file does matter. ''' # open the file read it in and close it. 193 with open(input) as f: gin = f.readlines() # split each line into list to make a nested list. lines = [i.split() for i in gin] # convert the numbers in the list to floats if possible. final = [] for i in range(len(lines)): final0 = [] for j in range(len(lines[i])): b = lines[i][j] try: a = float(b) except ValueError: # print("error") a = b # print(type(a)) final0.append(a) final.append(final0) # check the lines tha have atomic coordinates and add them to the final list. lines = final geometry = [] for line in lines: if len(line) == 4 and type(line[1]) == float and type(line[2]) == float and type(line[3]) == float: return geometry def get_lines(g16,start_phrase,end_phrase,lines_after_start,lines_before_end,columns_matrix): ''' This function gets the line between two phrases and extracts the requested columns between them. Also, lines before and after the end and start phrase can be eliminated. start_phrase is where the point of interest begins. lines_after_atart is the number of lines to be eliminated after the start phrase. end phrase is the point where marks the point after which we are not interested in. lines_before_end is the number of lines that need to be eliminated before the end phrase columns_matrix is a string of integers separated by space which show the columns of interest starting from 0. ''' # Open the file and read it as a list by each line with open(g16) as f: gout = f.readlines() # Find the lines that have the geometries in between start_phrases = [] geometry.append(line) 194 for i, elem in enumerate(gout): if start_phrase in elem: start_phrases.append(i) end_phrases = [] for i, elem in enumerate(gout): if end_phrase in elem: end_phrases.append(i) # Get the last geometry in the file. start_line = start_phrases[-1] + lines_after_start end_line = end_phrases[-2] + lines_before_end # Sometime the frequencies cause confusion so correct for that. if (start_line > end_line): end_line = end_phrases[-1] + lines_before_end # Split each atom's properties and delete useless columns from the 2D list. lines = gout[start_line:end_line] lines = [i.split() for i in lines] columns_matrix0 = columns_matrix.split() columns = [int(i) for i in columns_matrix0] rows = list(range(0,(len(lines)))) final = [] for row in rows: final0 = [] for column in columns: b = lines[row][column] a = ast.literal_eval(b) final0.append(a) final.append(final0) #pprint(final) return final # functions for finding mean plane: def SortByAtomicNumber(unsorted): ''' This function sort a list of atoms by their atomic numbers. ''' for i, atom in enumerate(unsorted): a = unsorted[i][0] b = atomlist.get(a) atom.insert(0,b) sorted1 = sorted(unsorted, key=lambda x: x[0], reverse=True) for i, atom in enumerate(unsorted): atom.pop(0) # print2D(sorted1,False) return sorted1 195 def getAxis(geometry,column): ''' this function extracts a column of interest from a 2D nested list. ''' if column == 'X' or column == 'x': column = 1 elif column == 'Y' or column == 'y': column = 2 elif column == 'Z' or column == 'z': column = 3 axis = [] for i, row in enumerate(geometry): element = geometry[i][column] axis.append(element) # print(axis) return axis def getRings(geometry): ''' gets the ring elements matrix using rdkit. both open Babel and rdkit need to be installed. ''' # write an xyz file of the original coordinates orig_stdout = sys.stdout number = len(geometry) sys.stdout = open('temp.xyz','wt') print(number) print('This is a comment line.') print2D(geometry,False) sys.stdout.close() sys.stdout=orig_stdout # convert the xyz file into a mol file to be opened by rdkit call(['obabel', 'temp.xyz', '-O', 'temp.mol'], stdout=PIPE, stderr=PIPE) # Popen(['obabel', '1.xyz', '-O', '1.mol'], stdout=PIPE, stderr=PIPE) m = Chem.MolFromMolFile('temp.mol') ssr = Chem.GetSymmSSSR(m) call(['rm', 'temp.xyz', 'temp.mol']) return ssr def getRingAxis(centered_geometry,ring_elements,column): ''' This function extracts partial columns of interest from a 2D nested list of geometry. ''' if column == 'X' or column == 'x': elif column == 'Y' or column == 'y': column = 1 196 column = 2 elif column == 'Z' or column == 'z': column = 3 ring_elements = ring_elements.split() ring_elements = [int(i) for i in ring_elements] ring_elements = [i - 1 for i in ring_elements] # print(ring_elements) axis = getAxis(centered_geometry,column) ring_axis = [] for row in ring_elements: element = centered_geometry[row][column] ring_axis.append(element) return ring_axis def centerRing(geometry,ring_elements,x_column,y_column,z_column): ring_elements = ring_elements.split() ring_elements = [int(i) for i in ring_elements] ring_elements = [i - 1 for i in ring_elements] # print(ring_elements) x = getAxis(geometry,x_column) y = getAxis(geometry,y_column) z = getAxis(geometry,z_column) x_ring = [] y_ring = [] z_ring = [] for row in ring_elements: element = geometry[row][1] x_ring.append(element) for row in ring_elements: element = geometry[row][2] y_ring.append(element) for row in ring_elements: element = geometry[row][3] z_ring.append(element) x_center = sum(x_ring)/len(x_ring) y_center = sum(y_ring)/len(y_ring) z_center = sum(z_ring)/len(z_ring) x_centered = [round(element - x_center,10) for element in x] y_centered = [round(element - y_center,10) for element in y] z_centered = [round(element - z_center,10) for element in z] centered_geometry = [] for i,element in enumerate(x_centered): atom = [] 197 e = geometry[i][0] atom.append(e) x = x_centered[i] atom.append(x) y = y_centered[i] atom.append(y) z = z_centered[i] atom.append(z) centered_geometry.append(atom) return centered_geometry def findMeanPlane(geometry,ring_elements): ''' Given a 2D nested list of xyz ccordinates (geometry) and a string containing the indices of the ring elements in th form of 'int int int int ...' (ring_elements, a string separated by spaces) finds the a, b, and c of a plane. The geometry does not need to be centered ''' # center the geometry and get the ring atom coordinates centered_geometry = centerRing(geometry,ring_elements,'x','y','z') x_ring = getRingAxis(centered_geometry,ring_elements,'x') y_ring = getRingAxis(centered_geometry,ring_elements,'y') z_ring = getRingAxis(centered_geometry,ring_elements,'z') # find the best fit def function(big_x,a,b): ''' this is a function for ring plane. ''' x,y = big_x return (a*x) + (b*y) p0 = 1, 1 best_vals, covar = curve_fit(function, (x_ring,y_ring), z_ring, p0) [a0,b0,c0] = [best_vals[0], best_vals[1], -1] # convert the mean plane vector to a unit vector length = (a0**2 + b0**2 + c0**2)**(0.5) [a,b,c] = [-a0/length, -b0/length, -c0/length] return (a,b,c) def insertNICS(geometry,ring_elements): ''' This function takes a 2D nested list of atomic coordinates, center them to the ring_elemens which is a string of integers separated by spaces, finds the mean plane, and rotates the molecule so the vector of 198 the mean plane is in the Z direction. It also add both NICS(1)zz and NICS(0) probes ''' atoms = getAxis(geometry,0) # get atoms column ''' This section was added later to fix the cases that have their rings already completely flat and in the XY plane. What it does, it only rotates the molecule to a random angle around the Y axis. In case problems raise, the value of the random variable can be changed. ''' RANDOM_PHI = 1.25 xx0 = getAxis(geometry,'x') yy0 = getAxis(geometry,'y') zz0 = getAxis(geometry,'z') [xx01,yy01,zz01] = PhiRot(xx0,yy0,zz0,RANDOM_PHI) # rotate the molecule around Y by A RANDOM phi randomly_rotated_geometry = [atoms,xx01,yy01,zz01] # randomly_rotated_geometry randomly_rotated_geometry = [list(i) for i in zip(*randomly_rotated_geometry)] # End of the patch up for random rotation of the system. -Tayeb on April 5, 2019 centered_geometry = centerRing(randomly_rotated_geometry,ring_elements,'x','y','z') # center the ring [a,b,c] = findMeanPlane(centered_geometry,ring_elements) [rho,tetha,phi] = car2sph(a,b,c) # convert the mean plane from cartesian to spherical coordinates xx = getAxis(centered_geometry,'x') yy = getAxis(centered_geometry,'y') zz = getAxis(centered_geometry,'z') centered = [atoms,xx,yy,zz] #print2D(centered,True) ################# ROTATE AROUND Z BY -THETA ################## [xx1,yy1,zz1] = TethaRot(xx,yy,zz,tetha) # rotate the molecule arounz Z by -tetha [aa1,bb1,cc1] = TethaRot(a,b,c,tetha) # rotate the plane vector arounz Z by -tetha [rho1,tetha1,phi1] = car2sph(aa1,bb1,cc1) # convert again the plane vector into spherical coordinates # print('rotated by tetha around z rho => tetha phi = ', rho1, tetha1, phi1) # tetha_around_z = [atoms,xx1,yy1,zz1] # print2D(tetha_around_z, True) ################## ROTATE AROUND Y BY -PHI ################### [xx2,yy2,zz2] = PhiRot(xx1,yy1,zz1,-phi1) # rotate the molecule around Y by phi 199 [aa2,bb2,cc2] = PhiRot(aa1,bb1,cc1,-phi1) # rotate the plane vector around Y by phi # print('rotated by tetha around y by phi => rho tetha phi = ', rho1, tetha1, phi1) # phi_around_y = [atoms,xx2,yy2,zz2] # print2D(phi_around_y, True) ################## ROTATE AROUND Y BY PHI #################### [xx3,yy3,zz3] = PhiRot(xx1,yy1,zz1,phi1) # rotate the molecule around Y by phi [aa3,bb3,cc3] = PhiRot(aa1,bb1,cc1,phi1) # rotate the plane vector around Y by phi # print('rotated by tetha around y by -phi => rho tetha phi = ', rho1, tetha1, phi1) # minus_phi_around_y = [atoms,xx3,yy3,zz3] # print2D(minus_phi_around_y, True) # find which courdinates to use if abs(cc2) > abs(cc3): [xx_final,yy_final,zz_final] = [xx2,yy2,zz2] else: [xx_final,yy_final,zz_final] = [xx3,yy3,zz3] xx_final = [ '%.8f' % elem for elem in xx_final ] yy_final = [ '%.8f' % elem for elem in yy_final ] zz_final = [ '%.8f' % elem for elem in zz_final ] xx_final = numpy.array(xx_final).tolist() yy_final = numpy.array(yy_final).tolist() zz_final = numpy.array(zz_final).tolist() # format the columns and get them ready for printing. xx_final = [i.rjust(14,' ') for i in xx_final] yy_final = [i.rjust(14,' ') for i in yy_final] zz_final = [i.rjust(14,' ') for i in zz_final] # add the nics probes and transpose the matrix nics_bq = [['bq',' 0.00000000',' 0.00000000',' 0.00000000'],\ ['bq',' 0.00000000',' 0.00000000',' 1.00000000'],\ ['bq',' 0.00000000',' 0.00000000',' -1.00000000']] nics = [atoms,xx_final,yy_final,zz_final] nics = [list(i) for i in zip(*nics)] nics.append(nics_bq[0]) nics.append(nics_bq[1]) nics.append(nics_bq[2]) return nics # functions for manipulating the coordinates: def car2sph(x,y,z): ''' This function converts Cartesian coordinates of a XYZ point to spherical coordinates. ''' rho = (x**2+y**2+z**2)**(0.5) tetha = -math.atan(y/x) phi = -math.atan(((x**2+y**2)**0.5)/z) return (rho, tetha, phi) 200 def TethaRot(x,y,z,tetha): ''' This function rotates coordinates of a single point or a set of points around the Z- AXIS by theta. ''' x0 = numpy.array(x) y0 = numpy.array(y) z0 = numpy.array(z) x1 = (x0*math.cos(tetha))-(y0*math.sin(tetha)) y1 = (x0*math.sin(tetha))+(y0*math.cos(tetha)) z1 = z0 return (x1,y1,z1) def PhiRot(x,y,z,phi): ''' This function rotates coordinates of a single point or a set of points around the Y- AXIS by phi. ''' x0 = numpy.array(x) y0 = numpy.array(y) z0 = numpy.array(z) x1 = (x0*math.cos(phi))+(z0*math.sin(phi)) y1 = y0 z1 = (z0*math.cos(phi))-(x0*math.sin(phi)) return (x1,y1,z1) # printing tool: def print2D(list_name,transpose): ''' This function prints a 2D list in a nice way with columns and everything lined up the list name is the name of the 2D list that you want to print. the transpose part is for whether you want to transpose the matrix before printing. if so type "True", otherwise type "False". ''' if transpose == True: mx = max((len(str(ele)) for sub in list_name for ele in sub)) for row in list_name: ############################################################# ################## END OF FUNCTIONS ############################ ############################################################# # import geometry from a Gaussian input or output. unsorted_geometry = getGeometryGeneral(input) list_name = [list(i) for i in zip(*list_name)] print(" ".join(["{:<{mx}}".format(ele,mx=mx) for ele in row])) 201 # check if ring atoms are requested manually. if rings == None: # if ring atoms are not specified, sort the atoms and find the rings. geometry = SortByAtomicNumber(unsorted_geometry) ssr = getRings(geometry) else: # otherwise, do not sort the geometry just convert the ring indices that were input to an appropriate nested list. geometry = unsorted_geometry ssr = rings.split() ssr = [int(x) for x in ssr] ssr = [x -1 for x in ssr] ssr = [ssr] # extract the atom names for the basis set. gaussian_atoms = " ".join(set(getAxis(unsorted_geometry,0))) + ' 0' # generate the input files for nics(1)zz for i in range(0,len(ssr)): # define the name of the files to be generated. file_name = str(input) file_name = file_name[0:-4] file_name = file_name + '_ring' + str(i + 1) + '.com' # print(file_name) ring_elements = list(ssr[i]) ring_elements = [i + 1 for i in ring_elements] ring_elements = " ".join(map(str, ring_elements)) # insert the NICS probe and write the file nics = insertNICS(geometry,ring_elements) orig_stdout = sys.stdout sys.stdout = open(file_name,'wt') print(gaussian_card) print() print('This is a comment line.') print() print(charge_and_multiplicity) print2D(nics,False) print() print(gaussian_atoms) print(basis) print('****') print() sys.stdout.close() sys.stdout=orig_stdout print(ring_elements) print2D(nics, False) 202 BIBLIOGRAPHY 203 BIBLIOGRAPHY (1) Smith, D. 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