THE STRUCTURE OF BENZIMIDAZOLE-3-OXIDE-1-OXYL RADICALS IN A TOLUENE MATRIX : A COMBINED ADVANCED ELECTRON PARAMAGNETIC RESONANCE SPECTROSCOPY AND QUANTUM MECHANICS CALCULATION STUDY By Yo-Yuan Cheng A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Chemistry 2011 ABSTRACT THE STRUCTURE OF BENZIMIDAZOLE-3-OXIDE-1-OXYL RADICALS IN A TOLUENE MATRIX : A COMBINED ADVANCED ELECTRON PARAMAGNETIC RESONANCE SPECTROSCOPY AND QUANTUM MECHANICS CALCULATION STUDY By Yo-Yuan Cheng The present thesis reports the results of a systematic computational and experimental study devoted to a better understanding of magneto-structural relationships in BNNs. From a methodological point of view, the results derived by Barone's PBE0/N07D/PCM model for structural and magnetic properties, which are accurate enough to allow for quantitative studies, are in excellent accord with the information derived from ESEEM and ENDOR and the potential energy surface by UHF-reference QCISD/6-31G*/PCM. We were thus able to unravel the role of different factors (both structural and electronic) in tuning the magnetic properties of nitrogen free radicals. ACKNOWLEDGMENTS I am very grateful to my advisor, Professor John McCracken, for giving me the opportunity to come to USA and to study at the Michigan State University, for his kind and patient supervision, valuable guidance and encouragement during the total time period. I wish to express my sincere gratitude to Dr. James Jackson, who gave many helpful advice and useful suggestions to DFT calculation of the project. I thank my guidance committee including Professor David Weliky, and Professor Katharine Hunt for their valuable guidance. I would also thank following authors who discuss with me through emails. William Ames Emiliano Stendardo David Sherrill Andy Cooksy iii TABLE OF CONTENTS List of Tables .....................................................................................................v List of Figures ...................................................................................................vi 1. Introduction .........................................................................................1 2. Materials and Methods.........................................................................5 2.1 Computational Details………………………………................…………...........5 2.2 DFT Hyperfine Tensor Calculation…………………………………..................5 2.3 Molecular Frame and Euler angles………………………………….................5 2.4 Sample Preparation………………………………………………….......................8 2.5 Easyspin Simulation………………………………………………….......................9 2.6 ESEEM Spectroscopy……………………………………………….......................10 2.7 Advanced EPR Instrument…………………………………………....................10 2.8 ENDOR………………………………………………………………............................11 3. Theoretical Background: EPR.…………………………………………….................13 4. Results and Discussion……………………………………………………...................20 5. Potential Energy Surface of BNN radical #1 and BNN radical #2……....…68 6. Conclusion……………….....................……………………………………………………86 7. Bibliography.......................................................................................88 iv LIST OF TABLES 3.1 g tensors calculated by PBE0 functional with different basis sets and experimental results .................................................................................17 4.1 Nitrogen parameter table obtained from Gaussian03 (PBE0/EPR-II/PCM) with different phenyl ring dihedral angles (degree, D)..............................31 4.2 Nitrogen parameter table obtained from Gaussian03 (PBE0/EPR-III/PCM) with different phenyl ring dihedral angles (degree, D)..............................35 4.3 Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D)..............................39 4.4 Nitrogen parameter table obtained from Gaussian03 (PBE0/TZVP/PCM) with different phenyl ring dihedral angles (degree, D)..............................43 4.5 Nitrogen parameter table obtained from Gaussian03 (PBE0/6-31G*/PCM) with different phenyl ring dihedral angles (degree, D)..............................47 4.6 14 N ESEEM results, BNN radical #1............................................................49 4.7 Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D)..............................58 4.8 Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D)..............................70 4.9 Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D)..............................78 v LIST OF FIGURES 2.1 Molecular principal axes (X, Y, Z) and the orientation (x, y, z) of each interaction frame (g, A, or Q) ....................................................................6 2.2 PBIDO (BNN radical #1)..............................................................................9 2.3 The three-pulse sequence........................................................................10 4.1 The optimized geometry of BNN radical #1..............................................18 4.2 CW-EPR spectrum of BNN radical #1 at ambient temperature................20 4.3 Energy levels of a system with one unpaired electron and two identically coupled nuclei with I = 1..........................................................................21 4.4 Field-Swept, echo-detected EPR spectrum at W-band of BNN radical #1 in D-toluene at 20 K.....................................................................................22 4.5 Summary of room-temperature X-band CW-EPR spectrum and frozen solution W-band field-swept EPR of BNN radical #1...............................24 4.6 Time domain and frequency domain ESEEM of the BNN radical #1.............................................................................................................25 4.7 Molecular axis system of BNN radical #1 in Gaussian03..........................28 4.8 Easyspin simulations by the parameters obtained from PBE0/EPR-II/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K..............................33 4.9 Easyspin simulations with the parameters obtained from PBE0/EPR-III/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K..............................37 vi 4.10 Easyspin simulations by the parameters obtained from PBE0/N07D/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K..............................41 4.11 Easyspin simulations by the parameters obtained from PBE0/TZVP/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K..............................45 4.12 Easyspin simulations by the parameters obtained from PBE0/6-31G*/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K..............................50 4.13 Frequency domain ESEEM data of the BNN radical # 2............................53 4.14 Molecular axis system of BNN radical #2 in Gaussian03...........................54 4.15 Easyspin simulations by the parameters obtained from PBE0/N07D/PCM calculation of different pyridyl dihedral angles on BNN radical #2 and ESEEM spectrum obtained from Bruker E680 at 10 K...............................61 4.16 Easyspin simulation by PBE0/N07D/PCM parameters and BNN radical #1 ENDOR spectrum at magnetic field = 3351.3 mT.......................................66 4.17 Easyspin ENDOR simulation of the 47 degree phenyl dihedral angle of BNN radical #1 with PBE0/N07D/PCM parameters............................................68 4.18 BNN radical #1 ENDOR spectrum at magnetic fields 3342.3 mT and 3358.2 mT................................................................................................................74 4.19 Easyspin simulation with PBE0/N07D/PCM parameters and BNN #2 ENDOR spectra at magnetic field = 3352.9 mT............................................75 4.20 Easyspin ENDOR simulation of the 47 degree pyridyl dihedral angle of BNN radical #2 with PBE0/N07D/PCM parameters.............................................77 4.21 BNN radical #2 ENDOR spectrum and Easyspin ENDOR simulation at magnetic fields 3359.9 mT (a) and 3348.4 mT (b).......................................83 vii 5.1 UHF reference QCISD potential energy surface of BNN radical #1 and BNN radical #2...................................................................................................85 viii Chapter 1 Introduction Free radicals containing the nitrogen nucleus are present in many processes of chemical, physical, and biological interest. Much of the scientific interest in nitroxide radicals stems from their prominent role as spin labels in biology, biochemistry, biophysics, and nanotechnology to monitor the structure and the motion of macromolecular systems[1, 2]. Indeed, labeling of specific sites by nitroxide probes allows effective structural and dynamic analyses by means of Electron Paramagnetic Resonance (EPR) and Electron-Nuclear Double Resonance (ENDOR) spectroscopy, thanks to the sensitivity of their magnetic parameters (e.g. gyromagnetic and electron-nuclear hyperfine tensors) to interactions with the surrounding molecules and to the polarity of the local environment[3]. Advanced EPR spectroscopy provides rich information consisting essentially of the electron-nuclear hyperfine coupling (AN) and gyromagnetic (g) tensors. However, interpretation of these experiments in structural terms strongly benefits from quantum mechanical (QM) calculations able to dissect 1 the overall observables in terms of the interplay of several subtle effects. The computation of nuclear hyperfine tensors by QM methods has a long history, which has finally led to the development of cost-effective and reliable approaches[4-6] [5, 7-14] [15] [16], whereas quantitative calculations of g-tensors for large molecules by the machinery of non-empirical quantum chemistry, have become possible only recently[17] [18]. Free radicals are generally short-lived, highly reactive species, usually characterized experimentally by their magnetic properties only. Thus a successful theoretical approach must be able to provide at the same time reliable structural and magnetic properties. In the past few years, methods based on the unrestricted Kohn-Sham (UKS) approach to density functional theory (DFT) have revolutionized this field, since they couple a remarkable reliability with a very favorable scaling with the number of basis functions, which has become essentially linear in the latest implementations[4, 19]. Furthermore, spin contamination is usually negligible due to a reasonable balance between exchange and correlation contributions. The electron-nuclear hyperfine coupling (AN) can be factored into both an isotropic (spherically symmetric) and an anisotropic (dipolar) term, T(aniso). The isotropic term (aiso), so called isotropic hyperfine coupling constant (hfcc), depends on the unpaired 2 electron spin density at the coupled nucleus, making this property very sensitive to the level of the calculation, specifically to the electron correlation, the one-electron basis set, and the use of an adequate molecular geometry. In previous papers[20-24], P. Calle and co-workers investigated the reliability of the density functional theory (DFT) methodology to compute hfccs of different nuclei of a large number of both organic and inorganic radicals in their ground states. The main conclusion was that the best overall results are obtained when the B3LYP[25, 26] functional is combined with either TZVP[27] or EPR-III[28, 29] basis sets, yielding highly accurate values of hfccs of nuclei belonging to the first three rows of the periodic table. An exception was found for 14N nuclei in which the smaller and less computationally demanding 6-31G* [30, 31] basis set yields hfcc values closer to the experimental ones, probably due to the fact that it has six d functions instead of the five d functions of the TZVP and EPR-III basis sets, providing an additional s function to complete the s space. Recently, Barone and co-workers developed a new polarized split-valence basis set for the calculation of hfccs of second- and third-row atoms, the so-called N07D[32, 33], by adding a reduced number of polarization and diffuse functions to the 6-31G basis set. To get accurate values of hfccs and 3 retain, or even improve, the good performance of the parent 6-31G* basis set for other properties dominated by valence orbitals, the new set was tailored by optimizing the core-valence s functions and reoptimizing polarization and diffuse p functions. Such a basis set was made specifically for both the B3LYP and the parameter-free PBE0[34] functionals. Here, we adopted Barone’s tailored N07D basis set for aromatic systems to evaluate the role of spin delocalization on the geometry and the magnetic parameters by means of DFT computation and advanced EPR spectroscopy. While many studies have been devoted to the comparison between experimental and computed EPR properties of “non-conjugated nitroxides”[7] [5, 35-38], only a few of them deal with aromatic systems[39] [40]. This is quite surprising in view of the remarkable thermal and chemical stability of aromatic nitroxides, in which the –NO spin density is delocalized over the aromatic ring system. 4 Chapter 2 Materials and Methods 1. Computational details A good molecular geometry is a mandatory starting point for evaluating the electronic structure. For our study, we used PBE0/N07D/PCM optimized geometries for radicals and compared them with X-ray structures taken from the Cambridge Crystallographic Data Center[41]. 2. DFT hyperfine tensor calculation All quantum mechanical computations were performed with the Gaussian 03 codes[42]. Based on the work of Barone[32], we selected a parameter-free model that was introduced in 1999 (referred to as PBE0)[34]. The redundant set of six d functions has to be employed for the N07D basis set, since it has been developed with this feature[32, 33]. Thus, most of the computations were performed at the PBE0/N07D/PCM level, including full geometry optimizations. The QM calculations were performed in toluene solvent by using the so called polarizable continuum model (PCM) which is a very effective tool for taking into account bulk solvent effects[37, 43]. 3. Molecular frame and Euler angles 5 All calculations were performed by Gaussian03 in the molecular principal axes (X, Y, Z) defined by the green axes in figure 2.1. Figure 2.1: Molecular principal axes (X, Y, Z) and the orientation (x, y, z) of each interaction frame (g, A, or Q) For interpretation of the references to color in this and all other figures, the reader is referred to the electronic version of this thesis. It is customary to specify the orientation of each magnetic interaction with respect to the principal axis system of the g tensor in an EPR study of frozen solution samples. For our EPR spectral simulations, we set the g principal axis frame identical to the molecular principal axes with an identity rotational matrix for g.  2.012  g   2.007     2.002    6 1 0 0  g. pa  0 1 0    0 0 1    Therefore, the orientation (x, y, z) of all of the magnetic interactions were expressed relative to the molecular principal axes. For each interaction (g, A, Q), a 3x3 orthogonal rotation matrix "eigenvalues" or principal values  R11 R   R21   R31  R12 R22 R32 R13  R23  and 3  R33   v   1  v  were obtained from Gaussian03. The  2 v   3 set of three Euler angles was determined from the following equations:  R 32   R 31      tan 1    R 31   R 33 cos      tan 1    R 23   R13      tan 1   By noting that R can be expressed as the product of three non-commutative rotations  ,  ,  about the z, the (new) y and the (new) z axes, respectively: 7 (1) R=R ( )  R (  )  R ( ) z y z  cos  sin  0  cos  0  sin   cos  sin  0         sin  cos  0  0 1 0   sin  cos  0   0 0 1  sin  1 cos   0 0 1     sin  cos  sin   cos  cos   cos  cos  cos   sin  sin      cos  cos  cos   sin  sin   sin  cos  sin   cos  cos   cos  sin  sin  sin    sin  cos    sin  sin    cos   (2) The Euler rotations in Eq. (2) are defined in a right-handed coordinate system, where a positive angle corresponds to an anticlockwise rotation about the respective axis as viewed looking towards the origin. 4. Sample preparation Organic radical materials containing unpaired electron spins exhibit technologically useful properties, such as electrical conductivity or ferromagnetism. The goal is to create an assembly of organic molecules or macromolecules made up from only light elements (C, H, O, S, etc.) and possessing properties similar to those of pure metals to enable spin alignment. Phenylbenzoimidazole-1-yl N,N’-dioxide (PBIDO)(figure 2.2) is the only benzoimidazole nitroxide radical whose magnetic properties have been reported and it is the only benzoimidazole whose structure has been determined by x-ray crystallography[44]. PBIDO dimerizes and exhibits strong antiferromagnetic coupling. The magnetic properties of these stable radicals, which can be building blocks for new advanced magnetic materials, need to be 8 explored. Figure 2.2: PBIDO (BNN radical #1) We received benzimidazole-3-oxide-1-oxyl radicals (BNNs) (Figure 2.2) from our collaborator, Professor Burak Esat, Department of Chemistry, Fatih University, Turkey. The compounds were dissolved in reagent-grade toluene to a final concentration of 45 mM. A 10-fold molar excess of powdered PbO2 was then added and the mixture was vortexed for 10 minutes to poise the molecule in its radical form. The resulting solution was centrifuged at high speed to remove excess PbO2. The radical solution has a yellowish color. A second BNN radical species, where pyridyl replaces the phenyl ring of BNN radical #1 was also studied and labeled as BNN radical #2. 5. Easyspin simulation Easyspin is a computational package for spectral simulation and analysis in ESEEM and ENDOR[45]. It is based on Matlab, a commercial technical computation software package. 9 6. ESEEM spectroscopy Electron Spin Echo Envelope Modulation (ESEEM) spectroscopy became very popular for studying hyperfine and nuclear quadrupole couplings. The application of ESEEM for the measurement of small hyperfine and nuclear quadrupole interactions is described in a number of reviews[46-48]. In this work we used the most widely applied experiment based on the three-pulse, stimulated echo sequence (figure 2.3). ESEEM is one of the few techniques for providing local structure information. In three-pulse ESEEM, an echo envelop modulation is observed when the time delay T between the second and third pulses of a simulated echo sequence is incremented. Figure 2.3: In the three-pulse sequence, two pulses separated by time τ are applied, followed by a third pulse after time T, and the stimulated-echo is observed at time τ after the third pulse. The echo envelope is obtained as T is incremented. 7. Advanced EPR instrument ESEEM and ENDOR data were collected on a Bruker E-680x EPR spectrometer operating at X-(9 GHz) and W-(95 GHz) bands. X-band 10 experiments used a model EN 4118X-MD4 probe that contained a 4 mm dielectric resonator. An Oxford model CF-935 liquid helium cryostat and ITC-503 temperature controller were used to maintain sample temperatures at 10 K for ESEEM and 20 K for ENDOR studies. X-band ESEEM data were collected using a stimulated echo (90o--90o-T-90o-echo) sequence as detailed above. A four step phase cycling scheme was used to eliminate distortions from 2-pulse echoes and correct DC-offsets from the baseline. ESEEM frequency spectra were obtained from time domain data using a procedure that involved removal of the "DC+decay" portion of the data, followed by application of a Hamming window function and then, Fourier Transformation (FFT). The spectra are then obtained by taking the absolute value of the FFT output. 8. ENDOR W-band ENDOR spectra were collected using a Davies ENDOR pulse sequence with the following parameters; microwave frequency, 9.71 GHz; microware pulse power, 5 mW; microwave pulse length, 320 ns; sample temperature, 20 K; τ-value, 1000 ns; rf (radiowave frequency) pulse width, 800 ns; rf pulse power, 200 W; Spectra were obtained by measuring the amplitude of the free induction decay (FID) of the radical as function of the applied rf 11 pulse frequency. 12 Chapter 3 Theoretical background: EPR Electron paramagnetic resonance spectroscopy (EPR) is a technique that probes the electronic nature of a paramagnetic species by characterizing the interaction of that species with an applied magnetic field. This method can provide detailed information about the unpaired electron spin density distribution within a paramagnetic species through the measurement of electron-nuclear hyperfine couplings. The magnetic interactions of the systems can be accounted for using a spin Hamiltonian (equation 3), which phenomenologically accounts for all magnetic interactions in the system of interest H   S  g  B  n I  g n  B  S  A  I  I  Q  I (3) The first term, the electronic Zeeman Hamiltonian, accounts for the interaction between the electron spin and the external magnetic field; B is the applied external magnetic field, g is the g-tensor, and  is the electronic Bohr magneton. In general, g can be written as three principal values gx, gy, gz, and three Euler angles (  ,  ,  ) which describe the orientation of the g 13 principal axes frame relative to the molecular principal axes. For our spectra simulations, the g principal axis frame was considered coincident with the molecular principal axes and all other interaction frames ( A and Q ) are referred to the molecular principal axes as well. The hyperfine structure seen in room-temperature CW-EPR experiments arises from electron-nuclear hyperfine coupling (hfc), the third term of equation 3. The magnitude of this interaction is gauged by the hfc tensor, A , which collapses to the isotropic hyperfine coupling constant, aiso, in dynamically averaged (i.e. isotropic) conditions (e. g. measured at room temperature). However, hyperfine interactions seen in frozen solution EPR, ESEEM and ENDOR are contributed from both the isotropic hyperfine, aiso, and anisotropic hyperfine interactions, Taniso. The Hamiltonian is represented by H HF  S  A I (4) , which comprises one of the most important sources of information in EPR spectroscopy. The hyperfine tensor A can be written as the sum of the isotropic or Fermi contact part and anisotropic part: A  a iso1  T aniso with 14 (5) 2  g g    (0) 2 . a  iso 3 0 e N e N 0  0 (0) 2 is interpreted as the unpaired electron spin density at the nucleus. The anisotropic part can be interpreted in terms of point dipole-dipole interactions and can be written as T aniso  1 0 0  1 0  4 g e g N  e  N 3 0 1 0   r   0 0 2    T    T   2T     (6) where  is the distance between the unpaired electron and the interacting nucleus. ESEEM spectroscopy is a good method to determine these couplings. The nuclear Zeeman Interaction 15 The coupling of a nuclear spin I to the external field B is described by the nuclear Zeeman interaction H NZ    N g N B  I (7) The (isotropic) nuclear g factor, gN, is an inherent property of a nucleus. For protons the nuclear Zeeman interaction is only 1/658 of the electron Zeeman interaction, for all other nuclei it is even less. Nuclear quadrupole Interaction Nuclei with spin I  1 are distinguished by a non-spherical distribution of protons giving rise to a nuclear electric quadrupole moment Q. The general form of the spin Hamiltonian is HQ  I  Q  I (8) Q is traceless and can be described by:  Q  x Q 0   0  0 Q y 0 The g Tensor Calculation 16  0   0   Q  z (9) EPR has played a central role in identifying and characterizing radicals. In this paper, we can learn the calculated g-value of BNN radicals. The gyromagnetic tensor[49] can be written : g  ge I  g RM  gG  gOZ SOC where ge is the free-electron value (ge) 2.0023193 and I is an identity matrix. Computation of the relativistic mass (RM) and gauge (G) corrections is quite straightforward because they are first-order contributions[50]. The last term arises from the coupling of the orbital Zeeman (OZ) and the spin-orbit coupling (SOC) operator. The OZ contribution is computed using the gauge-including atomic orbital (GIAO) approach[51], where for light atoms, the two electron SOC operator can be reliably approximated by a one electron operator involving adjusted effective nuclear charges[28]. Upon complete averaging by rotational motions, only the isotropic part of the g tensor survives, which is given by giso = 1/3Tr(g). Of course, the corresponding shift from the free electron value is ∆giso = giso – ge. All the results will be given as g-tensor values. PBE0 gx gy gz EPR-II 6-31G* TZVP N07D EPR-III Exp. 2.013 2.013 2.014 2.013 2.013 2.011 2.007 2.007 2.007 2.007 2.007 2.006 2.002 2.002 2.002 2.002 2.002 2.002 Table 3.1: g tensors calculated by PBE0 functional with different basis sets and experimental results 17 Chapter 4 Results and Discussion A prerequisite to electronic structure calculations is the determination of the optimized geometry of the molecules to be studied. Figure 4.1 shows the optimized geometry of BNN radical #1 that was obtained by PBE0/N07D/PCM. The XRD structure of Cambridge Database is also provided for comparison[41]. These two structures have identical bond length patterns. PBE0/N07D/PCM Figure 4.1: A comparison of the optimized geometry of BNN radical #1 with the XRD structure[41] Unit: Å 18 continued figure XRD structure Figure 4.1: A comparison of the optimized geometry of BNN radical #1 with the XRD structure[41] Unit: Å A continuous wave (CW)–EPR spectrum of BNN radical #1 in toluene is shown in figure 4.2 (red trace). The spectrum shows five absorption peaks with a 1:2:3:2:1 intensity patterns indicative of hyperfine complying to two equivalent 14N nuclei. Because these data were collected at room temperature, only the isotropic portion of the 14N hyperfine couplings is obtained. The 14N isotropic hyperfine coupling (aiso) is 11.2 MHz. The EPR spectrum is centered at an average g-value of 2.006. 19 '' d /dH (a.u.) 3350 Magnetic Field, G 3400 Figure 4.2: CW-EPR spectrum of BNN radical #1 taken at ambient temperature. Condition used to collect the these data were: Microwave frequency: 9.44 GHz. Time constant: 20ms. Conversion time: 80 ms. Modulation frequency: 100 KHz. Modulation amplitude: 1G. The isotropic hyperfine coupling for the nitrogen atoms of the NO groups can be measured directly from the EPR spectrum of figure 4.2 using the strategy described in the energy level diagram of figure 4.3. The diagram shows the origin of the five EPR transitions resolved in our measurements. The intensity pattern is a consequence of the degeneracy of the hyperfine energy levels. 20 Figure 4.3: Energy levels of a system with one unpaired electron and two identically coupled nuclei with I = 1. At a sufficiently high fixed magnetic field B = 3363 G, the thin line would be the transition corresponding to hν = gβeB in the absence of hyperfine interactions, A. Five absorption peaks can be obtained according to allowed EPR transitions, and the difference of the energy levels is 5.6 MHz. Figure 4.4 shows an electron spin echo detected EPR spectrum of BNN radical #1 at 94.1 GHz. The data were collected at 20 K with the sample dissolved in deuterated toluene. The high magnetic field required for this experiment led to resolution of the radical's g tensor principal values at the magnetic field positions marked with arrows. The measured g values are gx = 21 2.011, gy = 2.006, and gz = 2.002. Because the high field g-value is near the free electron g value, it is assigned to the direction along the 2pπ or 2pz orbital on the nitrogen of the NO groups. These data also show 14N hyperfine splitting associated with the gz = 2.002 feature of the spectrum and thus, provides a direct measurement of the z-component for the 14N hyperfine coupling, Az = 35.6 MHz. The gx and gy features of the spectrum are narrow indicating that the 14N hyperfine couplings in the plane of the molecule are small. microwave frequency : 94.10243 GHz 1 ESE Intensity 33426G 33514 G 33583 G 0 33400 33500 33600 33700 Field (G) Figure 4.4: Field-Swept, echo-detected EPR spectrum at W-band (microwave frequency: 94.1 GHz) of 180mM BNN radical #1 in D-toluene at 20 K. Because the 14 sample is a frozen solution, the anisotropies in the electronic Zeeman and N hyperfine interaction are revealed. The measured g-value are gx = 2.011, gy = 2.006, and gz = 2.002. The five absorption pattern centered at gz =2.002 shows the intensity 14 pattern, 1:2:3:2:1, and can be assigned to the N’s of the 2 N-O groups. The 22 anisotropic hyperfine interaction at gz (Az) is 35.6 MHz. The pulse sequence is ns, t  320 ns, and   1000 ns.  2      echo , with t   2  160 Taken together, the X-band solution spectrum and the W-band frozen solution spectrum provide sufficient information to estimate the principal values of the 14N hyperfine tensors for BNN radical #1. If we take the coupling to be the sum of a scalar, isotropic component and a traceless anisotropic portion of axial symmetry, thus Ax = Ay = aiso - T while Az = aiso + 2T. Placing the measured aiso and Az values into the latter expression, an estimated value of T = 12.2 MHz is obtained. If the nitronyl nitrogen hyperfine coupling is axial, then Ax = Ay = -1.0 MHz. This small value is in agreement with the lack of 14N-hyperfine splitting for the two lower field g features of the W-band spectrum (figure 4.4). 23 Figure 4.5: From room-temperature X-band CW-EPR spectrum of BNN radical #1, we can get the isotropic hyperfine couplings (aiso), which are 11.2 MHz. From W-band frozen solution field swept at 20 K, we can get Az = 35.6 MHz. Ax and Ay are approximately -1.0 MHz. ESEEM spectroscopy at X-band offers the best chance to measure weak 14N hyperfine couplings like those predicted for Ax and Ay of BNN radical #1. Figure 4.6 shows X-band 3-pulse ESEEM data collected for the radical at 3456 G, g = 2.006. The ESEEM spectrum shows a broad peak centered at 2.6 MHz with a shoulder at 1.6 MHz and a broad, less intense peak at 4.5 MHz. ESEEM spectra similar to these have been reported for the semiquinone catalytic intermediate of copper amine oxidases[52]. For that system, the nitrogen nucleus that gave rise to the ESEEM was also from a heterocyclic π-radical 24 where the perpendicular hyperfine component was found to be at low frequency. Amplitude (a. u.) (a) 0.04 0.00 -0.04 0 Time (ns) 4000 Figure 4.6: Figure (a) shows time domain ESEEM data of the BNN radical #1. Figure (b) shows the Fourier transformations of the respective time domain traces to (a). Spectrometer conditions: magnetic field strength, 3465 G; microwave frequency, 9.729 GHz; microwave pulse power, 54 dBm; sample temperature, 10.0 K; τ value, (a) and (b) 136 ns; starting T value, (a) and (b) 40 ns; time increment, 8 ns. 25 Amplitude (a.u.) continued figure (b) Peaks at (MHz) 0.98 1.59 2.56 1 0 0 10 20 Frequency (MHz) Figure 4.6: Figure (a) shows time domain ESEEM data of the BNN radical #1. Figure (b) shows the Fourier transformations of the respective time domain traces to (a). Spectrometer conditions: magnetic field strength, 3465 G; microwave frequency, 9.729 GHz; microwave pulse power, 54 dBm; sample temperature, 10.0 K; τ value, (a) and (b) 136 ns; starting T value, (a) and (b) 40 ns; time increment, 8 ns. 14N hyperfine coupling analysis To analyze the 14N ESEEM spectrum shown in figure 4.6, we need the following parameters : gn, the 14N nuclear g-value; Ax, Ay, Az, the three 14N electron-nuclear hyperfine coupling principal values; Apa ,Apa  ,Apa  , the three Euler angles that describe the orientation of the electron-nuclear hyperfine principal axis relative to molecular 26 principal axes; Qx, Qy, Qz, the three nuclear quadrupole interaction principal values;   , the three Euler angles describing the orientation of Q  ,Q  ,Q    pa pa pa  the nuclear quadrupole principal axes relative to molecular principal axes. To facilitate the analysis, we performed DFT calculations on BNN radical #1. Our goal was to gain theoretical predictions of the perpendicular 14N hyperfine couplings, Ax, Ay, and the parameters that describe the 14N nuclear quadrupole interaction. The orientations of the principal axis system of these interactions are also needed for ESEEM simulations, and supplied by the DFT calculations. As mentioned above, our spectral simulations were done with the program, Easyspin. Fortunately, the common axis systems to which all magnetic interactions are placed for calculation in Easyspin, is the molecular axis system. Parameters calculated with Gaussian03 are also referenced to the molecular axis system. This allowed us to use the Gaussian03 parameters directly in our simulations. Gaussian03 input setup Gaussian03 calculations were performed using the optimized geometry for BNN radical #1 showed in figure 4.1 and the molecular axis system depicted in figure 4.7. The basis sets used with the PBE0 functional were EPR-II, EPR-III, N07D, TZVP, and 6-31G*. Solvent effects were modeled with 27 PCM. For each basis set, we calculated the hyperfine coupling principal values, the Euler angles describing the orientation of the hyperfine coupling (principal) axes relative to the molecular (principal) axes, the nuclear quadrupole coupling principal values, and the Euler angles of nuclear quadrupole (principal) axes relative to molecular (principal) axes. During the course of the study, we found that the dihedral angle that describes the orientation of the phenyl ring relative to the plane of the benzoimidazole group (figure 4.7), has a modest affect on the nitrogen coupling for the NO groups, while these conformational effects were too small to influence the 14N-ESEEM, they did affect the 1H couplings of the phenyl ring measured by ENDOR and discussed later in this thesis. Figure 4.7: Different dihedral angles of the phenyl ring of BNN radical #1 are calculated in Gaussian03 by PBE0/EPR-II (or EPR-III, N07D, TZVP, and 6-31G*)/PCM. 28 Table 4.1-4.5 on the following pages show the results of our DFT calculations using the different basis sets listed above with the PBE0 functional. Two sets of 14N hyperfine and nuclear quadrupole interaction parameters are given, one for each of the NO nitrogens. The electron-nuclear hyperfine couplings are given in MHz and the Euler angles are in radians. Each of these tables is followed by a set of corresponding 14N-ESEEM simulations. The simulations are displayed in red and provided as a function of the dihedral angle describing the phenyl group orientations (figure 4.7). Overall, the most satisfactory simulations as judged by the predicted ESEEM frequencies and relative amplitudes resulted from parameters dervived from use of the EPR-III (figure 4.9) and N07D (figure 4.10) basis sets. At first glance, the N07D parameters appear to do a worse job than those of the EPR-III basis set because they predicted a frequency component at 0.5 MHz that is not observed in our experiments (figure 4.10b-black trace vs. red trace). However, part of the processing of ESEEM data calls for the removal of the function background decay and this always distorts the low frequency portion of the spectrum if the modulated part of the data is strongly damped. The time domain 14N ESEEM data shown in figure 4.6a show that the 14N modulation is weak in that the initial modulation amplitude is only about 8 % of 29 the signal strength and that these amplitudes are < 1% after the pulse spacing T > 1second. No attempt was made to model signal damping in our simulations and this could easily account for the discrepancy observed at low frequency for the simulations derived from the N07D basis set. The simulated 14N ESEEM parameters for these two basis sets at a phenyl ring dihedral angle of 40-45o are given in table 4.6. The Euler angles associated with orienting the principal axis systems of the nuclear quadrupole interactions with respect to the molecular axes show that the directions of the strongest interaction for both NO nitrogens is aligned with the molecular z-axis or the 2pπ orbital. The interplay between the α and γ angles is such that the Qx component is turned ±15.5o from the molecular frame x-axis bringing it in line with the NO bond directions for each interaction. The Euler angles associated with the electron-nuclear hyperfine principal axis system show that its z-axis is also aligned with the 2pπ orbital on the NO nitrogens coincident with the molecular z-axis. In the plane of molecule, the x-axis of the hyperfine tensor is rotated ± 90o from the molecular frame to the NO groups. 30 EPRII 0D 42D 45D 90D aiso(MHz) 9.69 9.60 9.59 9.32 aiso1 9.69 9.60 9.59 9.33 Txx(MHz) -11.72 -11.44 -11.41 -11.22 Tyy -10.69 -10.42 -10.40 -10.18 Tzz 22.41 21.86 21.81 21.40 Txx1 -11.72 -11.44 -11.41 -11.22 Tyy1 -10.69 -10.42 -10.40 -10.18 Tzz1 22.41 21.86 21.81 21.40 Qxx(a.u.) -0.42 -0.40 -0.40 -0.39 Qyy -0.07 -0.06 -0.06 -0.05 Qzz 0.49 0.47 0.46 0.44 Qxx1 -0.42 -0.40 -0.40 -0.39 Qyy1 -0.07 -0.06 -0.06 -0.05 Qzz1 0.49 0.47 0.46 0.44 A.paα (rad) 1.57 0.28 0.28 0.28 Table 4.1: Nitrogen parameter table obtained from Gaussian03 (PBE0/EPR-II/PCM) with different phenyl ring dihedral angles (degree, D) Note : Quadrupole hyperfine couplings in MH were obtained by multiplying the EFG in a. u. by the nuclear electric 14 quadrupole moment (in b) times 234.9647 and divided by 2I(2I-1)[53]. Q ( N) : 31 Q Q 2 xx yy 0.02044 b. e Qq = EFG * 0.02044*234.9647 in MHz ;  Q zz continued table A.paβ 0.00 0.00 0.00 0.00 A.paγ 0.00 1.29 1.29 1.29 A.pa1α -1.57 -0.28 -0.28 -0.28 A.pa1β 0.00 0.00 0.00 0.00 A.pa1γ 0.00 -1.29 -1.29 -1.29 Q.paα(rad) 0.00 1.25 1.25 0.00 Q.paβ 0.00 0.03 -0.03 0.00 Q.paγ 0.00 -0.98 -0.98 0.00 Q.pa1α 0.00 -1.25 -1.25 0.00 Q.pa1β 0.00 0.03 -0.03 0.00 Q.pa1γ 0.00 0.98 0.98 0.00 Table 4.1: Nitrogen parameter table obtained from Gaussian03 (PBE0/EPR-II/PCM) with different phenyl ring dihedral angles (degree, D) Note : Quadrupole hyperfine couplings in MH were obtained by multiplying the EFG in a. u. by the nuclear electric quadrupole moment (in b) times 234.9647 and divided 2 by 2I(2I-1)[53]. Q (14N) : 0.02044 b. e Qq = EFG * 0.02044*234.9647 in MHz ;  Q Q xx yy Q zz 32 (a) 1 Normalized Exp@136ns 0D (EPR-II) 0 0 MHz 10 (b) 1 Normalized Exp@136ns 42D (EPR-II) 0 0 10 MHz Figure 4.8 (a-c): Easyspin simulations by the parameters obtained from PBE0/EPR-II /PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K figure continued 33 (c) 1 Normalized Exp@136ns 90D(EPR-II) 0 0 MHz 10 Figure 4.8 (a-c): Easyspin simulations by the parameters obtained from PBE0/EPR-II /PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 34 EPR-III 00D 40D 90D aiso(MHz) 10.01 9.91 9.69 aiso1 10.01 9.91 9.69 Txx(MHz) -12.33 -12.03 -11.81 Tyy -11.39 -11.11 -10.87 Tzz 23.72 23.15 22.68 Txx1 -12.33 -12.03 -11.81 Tyy1 -11.39 -11.11 -10.87 Tzz1 23.72 23.15 22.68 Qxx(a.u.) -0.38 -0.36 -0.35 Qyy -0.03 -0.02 -0.01 Qzz 0.41 0.39 0.35 Qxx1 -0.38 -0.36 -0.35 Qyy1 -0.03 -0.02 -0.01 Qzz1 0.41 0.39 0.35 A.paα (rad) 1.57 0.28 0.28 A.paβ 0.00 0.00 0.00 A.paγ 0.00 1.29 1.29 Table 4.2: Nitrogen parameter table obtained from Gaussian03 (PBE0/EPR-III/PCM) 35 with different phenyl ring dihedral angles (degree, D) continued table A.pa1α -1.57 -0.28 -0.28 A.pa1β 0.00 0.00 0.00 A.pa1γ 0.00 -1.29 -1.29 Q.Paα(rad) 0.00 1.25 0.00 Q.paβ 0.00 0.03 0.00 Q.paγ 0.00 -0.98 0.00 Q.pa1α 0.00 -1.25 0.00 Q.pa1β 0.00 0.03 0.00 Q.pa1γ 0.00 0.98 0.00 Table 4.2: Nitrogen parameter table obtained from Gaussian03 (PBE0/EPR-III/PCM) with different phenyl ring dihedral angles (degree, D) 36 (a) 1 Normalized Exp@136ns 00D (EPR-III) 0 0 10 MHz (b) 1 Normalized Exp@136ns 40D (EPR-III) 0 0 MHz 10 Figure 4.9 (a-c): Easyspin simulations with the parameters obtained from PBE0/EPR-III/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 37 figure continued (c) 1 Normalized Exp@136ns 90D (EPR-III) 0 0 MHz 10 Figure 4.9 (a-c): Easyspin simulations with the parameters obtained from PBE0/EPR-III/PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 38 N07D 00D 45D 90D aiso(MHz) 11.79 11.60 11.35 aiso1 11.79 11.60 11.36 Txx(MHz) -11.30 -10.97 -10.80 Tyy -10.22 -9.90 -9.71 Tzz 21.51 20.88 20.51 Txx1 -11.30 -10.97 -10.80 Tyy1 -10.22 -9.90 -9.72 Tzz1 21.51 20.88 20.52 Qxx(a.u.) -0.37 -0.35 -0.33 Qyy -0.06 -0.05 -0.03 Qzz 0.43 0.39 0.37 Qxx1 -0.37 -0.35 -0.33 Qyy1 -0.06 -0.05 -0.03 Qzz1 0.43 0.39 0.37 Table 4.3: Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D) 39 continued table A.paα (rad) 1.57 0.28 0.28 A.paβ 0.00 0.00 0.00 A.paγ 0.00 1.29 1.29 A.pa1α -1.57 -0.28 -0.28 A.pa1β 0.00 0.00 0.00 A.pa1γ 0.00 -1.29 -1.29 Q.paα(rad) 0.00 1.25 1.25 Q.paβ 0.00 -0.03 0.03 Q.paγ 0.00 -0.98 -0.98 Q.pa1α 0.00 -1.25 1.25 Q.pa1β 0.00 -0.03 0.03 Q.pa1γ 0.00 0.98 -0.98 Table 4.3: Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D) 40 (a) 1 Normalized Exp@136ns 00D(N07D) 0 0 10 MHz (b) 1 Normalized Exp@136ns 45D (N07D) 0 0 MHz 10 Figure 4.10 (a-c): Easyspin simulations by the parameters obtained from PBE0/N07D/ PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 41 figure continued (c) 1 Normalized Exp@136ns 90D (N07D) 0 0 MHz 10 Figure 4.10 (a-c): Easyspin simulations by the parameters obtained from PBE0/N07D/ PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 42 TZVP 00D 42D 90D aiso(MHz) 8.88 8.79 8.56 aiso1 8.88 8.78 8.56 Txx(MHz) -11.94 -11.62 -11.38 Tyy -10.89 -10.58 -10.33 Tzz 22.84 22.20 21.71 Txx1 -11.94 -11.62 -11.39 Tyy1 -10.89 -10.58 -10.33 Tzz1 22.83 22.20 21.71 Qxx(a.u.) -0.39 -0.37 -0.36 Qyy -0.04 -0.03 -0.01 Qzz 0.43 0.40 0.37 Qxx1 -0.39 -0.37 -0.36 Qyy1 -0.04 -0.03 -0.01 Qzz1 0.43 0.40 0.37 Table 4.4: Nitrogen parameter table obtained from Gaussian03 (PBE0/TZVP/PCM) with different phenyl ring dihedral angles (degree, D) 43 continued table A.paα (rad) 1.57 0.28 0.28 A.paβ 0.00 0.00 0.00 A.paγ 0.00 1.29 1.29 A.pa1α -1.57 -0.28 -0.28 A.pa1β 0.00 0.00 0.00 A.pa1γ 0.00 -1.29 -1.29 Q.paα(rad) 0.00 1.25 0.00 Q.paβ 0.00 0.03 0.00 Q.paγ 0.00 -0.98 0.00 Q.pa1α 0.00 -1.25 0.00 Q.pa1β 0.00 0.03 0.00 Q.pa1γ 0.00 0.98 0.00 Table 4.4: Nitrogen parameter table obtained from Gaussian03 (PBE0/TZVP/PCM) with different phenyl ring dihedral angles (degree, D) 44 (a) 1 Normalized Exp@136ns 00D(TZVP) 0 0 MHz 10 (b) 1 Normalized Exp@136ns 42D(TZVP) 0 0 MHz 10 Figure 4.11(a-c): Easyspin simulations by the parameters obtained from PBE0/TZVP /PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 45 continued figure (c) 1 Normalized Exp@136ns 90D(TZVP) 0 0 MHz 10 Figure 4.11(a-c): Easyspin simulations by the parameters obtained from PBE0/TZVP /PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K 46 6-31G* 0D 42D 90D aiso(MHz) 11.83 11.57 11.15 aiso1 11.83 11.57 11.15 Txx(MHz) -10.92 -10.57 -10.30 Tyy -9.82 -9.48 -9.19 Tzz 20.74 20.06 19.49 Txx1 -10.92 -10.57 -10.30 Tyy1 -9.82 -9.48 -9.19 Tzz1 20.74 20.06 19.49 Qxx(a.u.) -0.36 -0.34 -0.33 Qyy -0.06 -0.05 -0.04 Qzz 0.43 0.40 0.37 Qxx1 -0.36 -0.34 -0.33 Qyy1 -0.06 -0.05 -0.04 Qzz1 0.43 0.40 0.37 Table 4.5: Nitrogen parameter table obtained from Gaussian03 (PBE0/6-31G*/PCM) with different phenyl ring dihedral angles (degree, D) 47 continued table A.paα (rad) 1.57 0.28 0.28 A.paβ 0.00 0.00 0.00 A.paγ 0.00 1.29 1.29 A.pa1α -1.57 -0.28 -0.28 A.pa1β 0.00 0.00 0.00 A.pa1γ 0.00 -1.29 -1.29 Q.paα(rad) 0.00 1.25 0.00 Q.paβ 0.00 0.03 0.00 Q.paγ 0.00 -0.98 0.00 Q.pa1α 0.00 -1.25 0.00 Q.pa1β 0.00 0.03 0.00 Q.pa1γ 0.00 0.98 0.00 Table 4.5: Nitrogen parameter table obtained from Gaussian03 (PBE0/6-31G*/PCM) with different phenyl ring dihedral angles (degree, D) 48 EPR-III N07D Dihedral angle 40 45 Az 33.1 32.5 Ay -1.20 1.70 Ax -2.12 0.63 Aiso 9.91 11.60 A.paα (rad) 0.28 0.28 A.paβ 0 0 A.paγ 1.29 1.29 Qxx(MHz) -0.86 -0.84 Qyy -0.05 -0.12 Qzz 0.94 0.94 Q.paα(rad) 1.25 1.25 Q.paβ 0.03 -0.03 Table 4.6: 14 N ESEEM results, BNN radical #1 49 (a) 1 Normalized Exp@136ns 0D(6-31G*) 0 0 10 MHz (b) 1 Normalized Exp@136ns 42D(6-31G*) 0 0 MHz 10 Figure 4.12 (a-c): Easyspin simulations by the parameters obtained from PBE0/6-31G*/PCM calculation of different phenyl dihedral angles on BNN radical #1 50 and ESEEM spectrum obtained from Bruker E680 at 10 K continued figure (c) 1 Normalized Exp@136ns 90D (6-31G*) 0 0 MHz 10 Figure 4.12 (a-c): Easyspin simulations by the parameters obtained from PBE0/6-31G* /PCM calculation of different phenyl dihedral angles on BNN radical #1 and ESEEM spectrum obtained from Bruker E680 at 10 K Conclusion: While the EPR-III and N07D basis sets both predict satisfactory 14N-ESEEM results, the N07D basis set gives a more precise value for the 14N isotropic hyperfine coupling when compared to our experimental result of 11.2 MHz. Therefore, we adopted this basis set for the analysis of BNN radical #2. PBE0/N07D/PCM computational model provides remarkably accurate magnetic properties at reasonable computational costs. The parameters 51 calculated by PBE0/N07D/PCM fit well with ESEEM peak frequencies. We choose PBE0/N07D/PCM method for analysis of the BNN radical #2 ESEEM and for the analysis of the W-band 1H-ENDOR spectra presented below. Gaussian03 calculations were performed using the optimized geometry for BNN radical #2 using the PBE0/N07D/PCM and the molecular axis system depicted in figure 4.13. The best basis set, N07D, used with the PBE0 functional was adopted. Solvent effects were modeled with PCM. Following the above protocol for BNN radical #1, we calculated the hyperfine coupling principal values, the Euler angles describing the orientation of the hyperfine coupling principal axis relative to the molecular axis system, the nuclear quadrupole coupling principal values, and the Euler angles of nuclear quadrupole principal axis relative to molecular axis system. In contrast to our work on BNN radical #1, we found that the dihedral angles of the pyridyl ring are most important for this radical because the most intense in the ESEEM spectrum at 3.2 MHz and a shoulder at 5.6 MHz are from the pyridyl nitrogen (figure 4.13). Our calculations show that the hyperfine coupling due to the pyridyl nitrogen are very sensitive to the pyridyl dihedral angle. This makes the simulation of the BNN radical #2 ESEEM spectrum dependent on the pyridyl dihedral angle. A 9 GHz ESEEM spectrum of BNN radical #2 is shown in figure 52 4.13. When compared to the corresponding data from BNN radical #1, two new features are observed, a dominant peak at 3.2 MHz and a broad feature with maximum peak intensity at 5.6 MHz. The shoulder at 1.5 MHz and peak near 2.5 MHz were observed previously for BNN radical #1 and are assigned to the NO nitrogens. From the analysis of the BNN radical #1, the 0.5 MHz peak is also assigned to the NO nitrogens. 1 Normalized Exp@100ns 0 0 MHz 10 Figure 4.13: This is a frequency domain ESEEM data of the BNN radical # 2. Spectrometer conditions: magnetic field strength: 3465 G; microwave frequency : 9.729 GHz; microwave pulse power : 25 dBm; sample temperature : 10.0 K; τ value : 100 ns; T value : 40 ns. We use 100 ns due to better resolutions of 5.6 MHz peak. 53 Figure 4.14: Different dihedral angles of the pyridyl ring of BNN radical #2 are calculated in Gaussian03 by PBE0/N07D/PCM. Table 4.7 shows the results of DFT calcualtions for BNN radical #2 using the PBE0 functional with N07D basis set and PCM approximation for solvent interactions. Hyperfine and nuclear quadrupole interaction parameters are listed for all three nitrogens of the radical. The predictions of the pyridyl nitrogen are given in green and it can be readily seen that the isotropic hyperfine coupling for the pyridyl nitrogen is most dependent on the dihedral angle describing the orientation of the group’s molecular plane relative to the BNN. At zero degrees, an Aiso value of -1.58 MHz is predicted and this value goes to zero as one varies the dihedral angle to 90o. The value of lAisol = 1.58 MHz is close to twice the 14N Larmor frequency at our experimental magnetic field strength of 346.5 mT. Such a coupling would give rise to intense ESEEM 54 as shown by the work of Mims[54] and Singel[55]. The ESEEM simulations that arise from the parameters provided in table 4.7 are shown in figure 4.15. The best simulation in terms of accounting for the observed hyperfine frequencies and relative peak amplitude is spectrum 7c , where the dihedral angle describing the relative orientation of the pyridyl ring is 47 degrees. The magnetic parameters for the three nitrogens that contribute to the ESEEM spectrum are given below. NO nitrogens Pyridyl N Az (MHz) 31.5 -0.09 Ay 1.41 -0.14 Ax 0.31 -2.26 Qz (MHz) 0.91 2.38 Qy -0.10 -0.79 Qx -0.82 -1.58 The hyperfine couplings for the NO nitrogens are very close to the values obtained from the DFT analysis of BNN radical #1. The Euler angles describing the orientations of the hyperfine axes relative to the molecular axis system show that the principle interactions, Az, is still along the 2pπ orbital of two nitrogen while the x and y axes are coincident with the molecular y and x 55 axes, respectively. Because the hyperfine tensor is nearly axial, the significance of the orientation of the Ax and Ay axes with respect to the molecular frame as provided by DFT is probably low. The hyperfine parameters for the pyridyl 14N show an axial tensor with scalar and dipolar constants of 0.83 and 0.70 MHz, respectively. The Euler angles indicate that the largest coupling, -2.26 MHz, is perpendicular to the pyridyl ring while one of the two minor componetns that are close to 0 MHz lies in the direction of the electron lone pair. The quadrupole coupling parameters for the pyridyl nitrogen yield e2qQ = 4.754 MHz and  = 0.333, These are similar to those found in NQR studies of condensed pyridyl of e2qQ = 4.584 MHz and  = 0.396[56]. In summary, of the ESEEM simultions shown in figure 4.15, the one using parameters derived from the 47o dihedral angle structure works best. This prediction best accounts for the frequencies of the peaks due to the NO and pyridyl nitrogens and is lacking only in the predicted relative amplitude of the NO peaks, at 1.5 and 2.5 MHz, and the dominant pyridyl peaks at 3.2 and 5.6 MHz. Figure 4.15a shows the predicted ESEEM spectrum if 10 orientations of the pyridyl ring, from 0o to 90o, are included in the calculations. While aspects of the simulation agree with the experimental data, it fails to predict the feature 56 at 5.6 MHz. 57 N07D 00D 47D 90D aiso(MHz) 11.23 11.07 10.99 aiso1 11.23 11.07 10.99 aiso2 -1.58 -0.83 -0.05 Txx(MHz) -11.03 -10.76 -10.66 Tyy -9.92 -9.66 -9.56 Tzz 20.95 20.42 20.22 Txx1 -11.03 -10.76 -10.66 Tyy1 -9.92 -9.66 -9.56 Tzz1 20.95 20.42 20.22 Txx2 -2.69 -1.43 -0.11 Tyy2 1.33 0.69 0.02 Tzz2 1.36 0.74 0.09 Table 4.7: Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D). The green fonts are the nitrogen of the pyridyl. 58 continued table Qxx(a.u.) -0.36 -0.34 -0.33 Qyy -0.04 -0.04 -0.03 Qzz 0.40 0.38 0.36 Qxx1 -0.36 -0.34 -0.33 Qyy1 -0.04 -0.04 -0.03 Qzz1 0.40 0.38 0.36 Qxx2 -0.66 -0.66 -0.67 Qyy2 -0.33 -0.33 -0.32 Qzz2 0.99 0.99 1.00 A.paα (rad) 1.25 1.25 1.25 A.paβ 0.00 0.00 0.00 A.paγ 0.32 0.32 0.32 A.pa1α -1.25 -1.25 -1.25 A.pa1β 0.00 0.00 0.00 A.pa1γ -0.32 -0.32 -0.32 Table 4.7: Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D). The green fonts are the nitrogen of the pyridyl. 59 continued table A.pa2α 0.00 0.79 1.57 A.pa2β 1.57 1.57 1.57 A.pa2γ -1.57 -1.57 -1.57 Q.paα(rad) 0.00 -1.11 0.00 Q.paβ 0.00 0.02 0.00 Q.paγ 0.00 0.79 0.00 Q.pa1α 0.00 1.11 0.00 Q.pa1β 0.00 0.02 0.00 Q.pa1γ 0.00 -0.79 0.00 Q.pa2α 0.00 0.83 1.57 Q.pa2β 1.57 1.57 1.57 Q.pa2γ -1.57 -1.57 -1.57 Table 4.7: Nitrogen parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D). The green fonts are the nitrogen of the pyridyl. 60 (a) 100ns Sum and Normalized of all angles Normalized 1 0 0 MHz 10 (b) 100ns 00D Normalized 1 0 0 MHz 10 Figure 4.15 (a-d): Easyspin simulations by the parameters obtained from PBE0/N07D /PCM calculation of different pyridyl dihedral angles on BNN radical #2 and ESEEM spectrum obtained from Bruker E680 at 10 K 61 figure continued (c) 1 Normalized 100ns 47D 0 0 MHz 10 (d) 100ns 90D Normalized 1 0 0 MHz 10 Figure 4.15 (a-d): Easyspin simulations by the parameters obtained from PBE0/N07D /PCM calculation of different pyridyl dihedral angles on BNN radical #2 and ESEEM spectrum obtained from Bruker E680 at 10 K 62 W-band ENDOR spectroscopy To further characterize the electronic structure of these two radicals and gain additional evidence for the dominance of the "47 degree" conformation predicted by 14N ESEEM/DFT analysis, we measured their 1H-ENDOR spectra in frozen solutions. These experiments were done at 94 GHz, where the anisotropy in the g tensor provides orientation dependent coupling to be measured. Briefly, an ENDOR experiment is done at a fixed magnetic field strength, and therefore, a fixed effective g-value, geff. This geff is given by 1 B 2 2 2 2 2 2 2 2 g   ( g sin  cos   g sin  sin   g cos  )2 eff xx yy zz h where gxx, gyy, and gzz are the principal values of the g tensor and ,describe the orientation of the magnetic field, B, with respect to the g tensor axes. Thus, at a fixed field, only ,combinations that satisfy the above equation contribute to the data. The effect of this “orientation selection” on 1H-ENDOR spectra was illustrated by Hurst[57], et al. The black traces of figures 4.16 and 4.18 show W-band 1H ENDOR spectra collected for BNN radical #1 near the gx (figure 4.18a), gy (figure 4.16a), and gz (figure 4.18b) orientations of the g tensor at 3342.3, 3351.3, and 3358.2 mT, respectively. These data were collected with identical ENDOR pulse sequences and show pronounced lineshape difference arising from 63 orientation selection. The spectra are centered at the proton Larmor frequency of 1H, which varies from 142.3 MHz at 3342.3 mT to 143.0 MHz at 3358.2 mT. To gain an understanding of these spectra in terms of hyperfine couplings and their relationship to molecular structure, we turned to DFT calculations. Figure 4.17 (top) provides a numbering scheme for the protons of BNN radical #1. Table 4.6 shows the results of DFT calculations with respect to these nuclei. The table is presented as above, with the columns providing coupling constants and Euler angles obtained for four different values of the phenyl group dihedral angle, 0o, 43o, 47o, and 90o. These results show that the 1H hyperfine couplings most sensitive to the orientations of the phenyl group are those from H-16 and H-18. These couplings are influenced by a strong dipole-dipole interaction with the unpaired spin density concentrated on the NO group. This dipolar field shows T = 3.45 MHz at 0o dihedral angle and only 0.75 MHz at 90o because of the change in distances and electronic structure that occur as the molecule goes from its planar to perpendicular orientations. For the 0o, 43o and 47o angles, the strongest hyperfine coupling due to H16 and H18 would be resolved along gy, at 3351.3 mT. The simulations in figure 4.16 (red traces) show this feature as a pair of peaks that are separated by nearly 11 MHz at 0o dihedral angle (figure 4.16a) and drop to just over 3 MHz 64 at 90o (figure 4.16d). The data at 43o and 47o show the extremes of this coupling at 140.0 and 145.5 MHz, matching the experimental data. The traces shown in red in figure 4.16 are simulations for all of the proton couplings listed in table 4.6. It is clear that an intermediate dihedral angle of 45o best accounts for these data. A composite drawing showing how all of the proton hyperfine couplings combine to yield the simulation shown in figure 4.16c (red trace) is provided in figure 4.17 (bottom). Using the calculation results for the 47o phenyl group orientation from table 4.7, we also ran simulations of the ENDOR spectra obtained at 3342.3 mT (gx) and 3358.2 mT (gz), and these results are shown plotted with experimental data in figure 4.18a and 4.18b, respectively. 65 (a) Exp@3351.3mT A00D Normalized 1 0 140 MHz 145 150 (b) Exp@3351.3mT A43D Normalized 1 0 140 MHz 145 150 Figure 4.16 (a-d): Easyspin simulation by PBE0/N07D/PCM parameters and BNN radical #1 ENDOR spectrum at magnetic field = 3351.3 mT 66 continued figure (c) Exp@3351.3mT A47D Normalized 1 0 140 MHz 145 150 Figure 4.16 (a-d): Easyspin simulation by PBE0/N07D/PCM parameters and BNN radical #1 ENDOR spectrum at magnetic field = 3351.3 mT 67 figure continued (d) Exp@3351.3mT A90D Normalized 1 0 140 MHz 145 150 Figure 4.16 (a-d): Easyspin simulation by PBE0/N07D/PCM parameters and BNN radical #1 ENDOR spectrum at magnetic field = 3351.3 mT Figure 4.17: This is an Easyspin ENDOR simulation of the 47 degree phenyl dihedral angle of BNN radical #1 with PBE0/N07D/PCM parameters. We can proof that two small shoulders at 140.0 MHz and 145.5 MHz only contribute from H18 and H16 and 68 they are dependent of phenyl dihedral angles. ENDOR simulation is a frequency histogram so peak intensity doesn’t matter. figure continued H22 H21 H20 H18 H16 H11 H10 H09 H08 Sum a. u. 0.0015 0.0000 140 MHz 145 150 Figure 4.17: This is an Easyspin ENDOR simulation of the 47 degree phenyl dihedral angle of BNN radical #1 with PBE0/N07D/PCM parameters. We can proof that two small shoulders at 140.0 MHz and 145.5 MHz only contribute from H18 and H16 and they are dependent of phenyl dihedral angles. ENDOR simulation is a frequency histogram so peak intensity doesn’t matter. 69 PBE0_N07D_PCM 00D 43D 47D 90D aH8(MHz) -3.19 -3.05 -3.04 -2.97 aH9 -2.33 -2.29 -2.29 -2.27 aH10 -2.33 -2.29 -2.29 -2.27 aH11 -3.19 -3.05 -3.04 -2.97 aH16 4.00 2.32 2.11 0.65 aH18 4.00 2.32 2.11 0.65 aH20 -1.84 -1.40 -1.32 -0.71 aH21 -1.84 -1.40 -1.32 -0.71 aH22 3.69 2.20 1.94 0.17 Txx8(MHz) -1.92 -1.90 -1.90 -1.88 Tyy8 0.17 0.14 0.14 0.13 Tzz8 1.75 1.76 1.76 1.75 Txx9 -1.39 -1.37 -1.36 -1.35 Tyy9 -0.79 -0.77 -0.77 -0.76 Tzz9 2.17 2.13 2.13 2.11 Table 4.8: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D) 70 continued table Txx21 -0.71 -0.61 -0.59 -0.38 Tyy21 -0.14 -0.09 -0.09 -0.10 Tzz21 0.85 0.70 0.68 0.48 Txx22 -1.21 -0.55 -0.44 -0.18 Tyy22 -0.37 -0.27 -0.25 -0.14 Tzz22 1.58 0.82 0.69 0.32 A.paα8(rad) 0.00 0.00 0.00 0.00 A.paβ8 1.57 -1.57 -1.57 1.57 A.paγ8 1.01 1.05 1.05 1.01 A.paα9 1.57 1.57 1.57 1.57 A.paβ9 1.57 1.57 1.57 1.57 A.paγ9 1.27 1.27 1.27 1.27 A.paα10 1.57 1.57 1.57 1.57 A.paβ10 1.57 -1.57 -1.57 1.57 A.paγ10 -1.27 -1.27 -1.27 -1.27 Table 4.8: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D) 71 continued table A.paα11 0.00 0.00 0.00 0.00 A.paβ11 1.57 1.57 1.57 1.57 A.paγ11 -1.01 -1.05 -1.05 -1.01 Table 4.8: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D) 72 continued table A.paα16 1.57 0.55 0.51 1.57 A.paβ16 1.57 -1.03 -1.01 1.57 A.paγ16 -1.43 1.44 1.39 -1.43 A.paα18 1.57 0.55 0.51 1.57 A.paβ18 1.57 1.03 1.01 1.57 A.paγ18 1.43 -1.44 -1.39 1.43 A.paα20 1.57 0.58 0.49 1.57 A.paβ20 1.57 -1.07 -1.06 1.57 A.paγ20 -0.94 -1.27 -1.33 -0.94 A.paα21 1.57 0.58 0.49 1.57 A.paβ21 1.57 1.07 1.06 1.57 A.paγ21 0.94 1.27 1.33 0.94 A.paα22 1.57 1.57 1.57 1.57 A.paβ22 1.57 0.00 0.00 1.57 A.paγ22 0.00 0.00 0.00 0.94 Table 4.8: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different phenyl ring dihedral angles (degree, D) 73 (a) Exp@3342.3mT A47D Normalized 1 0 140 MHz 145 150 (b) Exp@3358.2mT A47D Normalized 1 0 140 MHz 145 150 Figure 4.18 (a-b): BNN radical #1 ENDOR spectrum at magnetic fields 3342.3 mT and 3358.2 mT 74 The black traces in figure 4.19 and 4.21 show the 1H ENDOR spectra obtained for BNN radical #2 at magnetic field position near the principal values of the radical's g-tensor. An analogs procedure identical to that used for BNN radical #1 was done and numerical results are provided in table 4.8. The best simulation as judged by the predicted frequencies, were found for a pyridyl dihedral angle at 40o and shown in figure 4.19b (gy component), 21a (gz component) and 21b (gx component). (a) 3352.9mT A00D Normalized 1 0 140 MHz 145 150 Figure 4.19 (a-c): Easyspin simulation with PBE0/N07D/PCM parameters and BNN #2 ENDOR spectra at magnetic field = 3352.9 mT 75 figure continued (b) 3352.9mT A40 Normalized 1 0 140 MHz 145 150 (c) 3352.9mT A90D Normalized 1 0 140 MHz 145 150 Figure 4.19 (a-c): Easyspin simulation with PBE0/N07D/PCM parameters and BNN #2 ENDOR spectra at magnetic field = 3352.9 mT 76 H20 H19 H18 H16 H11 H10 H9 H8 Sum a. u. 0.0015 0.0000 140 MHz 145 150 Figure 4.20: This is an Easyspin ENDOR simulation of the 47 degree pyridyl dihedral angle of BNN radical #2 with PBE0/N07D/PCM parameters. ENDOR simulation is a frequency histogram so peak intensity doesn’t matter. 77 PBE0_N07D_PCM 0D 40D 90D aH8(MHz) -3.32 -3.18 -3.10 aH9 -2.33 -2.31 -2.30 aH10 -2.33 -2.31 -2.30 aH11 -3.32 -3.18 -3.10 aH16 3.59 2.18 0.58 aH18 3.59 2.18 0.58 aH19 -1.37 -1.13 -0.65 aH20 -1.37 -1.13 -0.65 Txx8(MHz) -1.86 -1.85 -1.83 Tyy8 0.25 0.23 0.22 Tzz8 1.61 1.62 1.61 Txx9 -1.39 -1.38 -1.37 Table 4.9: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D) 78 continued table Tyy9 -0.78 -0.77 -0.76 Tzz9 2.18 2.15 2.13 Txx10 -1.39 -1.38 -1.37 Tyy10 -0.78 -0.77 -0.76 Tzz10 2.18 2.15 2.13 Txx11 -1.86 -1.85 -1.83 Tyy11 0.25 0.23 0.22 Tzz11 1.61 1.62 1.61 Txx16 -3.94 -2.90 -1.45 Tyy16 -3.05 -1.50 0.56 Tzz16 6.99 4.41 0.89 Txx18 -3.94 -2.90 -1.45 Tyy18 -3.05 -1.50 0.55 Tzz18 6.99 4.41 0.89 Table 4.9: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D) 79 continued table Txx19 -0.60 -0.56 -0.39 Tyy19 -0.17 -0.12 -0.12 Tzz19 0.78 0.69 0.51 Txx20 -0.60 -0.56 -0.39 Tyy20 -0.17 -0.12 -0.12 Tzz20 0.78 0.69 0.51 A.paα8(rad) 0.00 0.00 0.00 A.paβ8 1.57 1.57 1.57 A.paγ8 -0.92 -0.97 -0.99 A.paα9 1.57 1.57 1.57 A.paβ9 1.57 -1.57 1.57 A.paγ9 -1.28 -1.28 -1.28 Table 4.9: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D) 80 continued table A.paα10 1.57 1.57 1.57 A.paβ10 -1.57 1.57 -1.57 A.paγ10 1.28 1.28 1.28 A.paα11 0.00 0.00 0.00 A.paβ11 -1.57 -1.57 -1.57 A.paγ11 0.92 0.97 0.99 A.paα16 1.57 0.53 0.00 A.paβ16 1.57 1.05 1.08 A.paγ16 1.46 -1.46 -1.57 A.paα18 1.57 0.53 -0.14 A.paβ18 1.57 -1.05 -1.08 A.paγ18 -1.46 1.46 1.57 Table 4.9: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D) 81 continued table A.paα19 1.57 0.62 0.00 A.paβ19 1.57 1.11 1.19 A.paγ19 1.01 1.30 -1.57 A.paα20 1.57 0.62 0.00 A.paβ20 1.57 -1.11 -1.19 A.paγ20 -1.01 -1.30 -1.57 Table 4.9: Proton parameter table obtained from Gaussian03 (PBE0/N07D/PCM) with different pyridyl ring dihedral angles (degree, D) 82 (a) 3359.9mT A40D Normalized 1 0 140 MHz 145 150 (b) 3348.4mT A40D Normalized 1 0 140 MHz 145 150 Figure 4.21 (a-b): BNN radical #2 ENDOR spectrum and Easyspin ENDOR simulation at magnetic fields 3359.9 mT (a) and 3348.4 mT (b) 83 Chapter 5 Potential energy surfaces (PES) of BNN radical #1 and #2 The results of our 14N-ESEEM and 1H-ENDOR experiments lead to the conclusion that both BNN radicals studied in this thesis prefer a conformation in frozen toluene when the plane of the phenyl or pyridyl group are at 45o angle with respect to the plane of the BNN group. To suggest these finding further, we undertook calculations of the potential energy surface. We found that UHF-reference QCISD, a quadratic configuration iteration calculation including single and double substitutions, predicted 40o dihedral angle as the minimum energy conformation for both BNN radical #1 and #2 in toluene environments. These results are shown in figure 5.1. 84 (a) BNN radical #1_UHF-QCISD_6-31G*_toluene Total Free Energy in Toluene (Hartree) -758.377 -758.378 0 10 20 30 40 50 60 70 80 90 -758.379 -758.38 -758.381 -758.382 -758.383 -758.384 dihedral angles (b) Total Free Energy in Toluene (Hartree) BNN radical #2_UHF-QCISD_6-31G*_toluene -774.388 0 10 20 30 40 50 60 70 80 90 -774.39 -774.392 -774.394 -774.396 -774.398 -774.4 -774.402 -774.404 dihedral angles Figure 5.1 (a-b): UHF reference QCISD, a quadratic configuration iteration calculation including single and double substitutions by Pople[58] is in fair agreement with our experiment at 10 K in which the minimum energy conformation is in the pyridyl or phenyl ring near 40 degree dihedral angle.[59] 85 Chapter 6 Conclusion The present article reports the results of a systematic computational and experimental study devoted to a better understanding of magneto-structural relationships in BNNs. 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