33.. ' . 2.1. a: . .. filrnnn: \al. .. may... t he. .31. , 5.5:. .5 bl. Ix? ! 3v ‘3 . .v)‘. 0'. 3%.. $3 gun».- ‘ 4%? t. . 5d,. wom- N9. Lrih ‘ E a 3 «m; «a.» . t 33.) i. . 151, t. h .ixiuabh .. a: 3!“. . r. :3, . 35“.? . 11$ a: funk. 31.:1Liov 3 p L “:3 2 3;}: , A. 53033;}: ‘ unhdmu i.) . . v\ ‘57; $2? {HESG ll!llllllllllllll)Ill(lllllllllllllllllll 301389 3627 This is to certify that the thesis entitled The Study Of Lone Pair Electrons Using Electon Density And Molecular Electrostatic Potential. presented by LaVetta Applebv has been accepted towards fulfillment of the requirements for ’ MI S . degree in fihemistrL / .. Major professor VJ (__(,,f' 0-7 639 MS U is an Affirmative Action/Equal Opportunity Institution LIBRARY Michigan State University PLACE IN RETURN BOX to romavothlo checkout from your record. TO AVOID FINES romm on or More data duo. DATE DUE DATE DUE DATE DUE MSU Is An Atfimotivo Action/Equal Opportunity Instituion gamma THE STUDY OF LONE PAIR ELECTRONS USING ELECTRON DENSITY AND MOLECULAR ELECTROSTATIC POTENTIAL BY LaVetta Appleby A THESIS Submitted to Michigan State University in partial fiJlfillment of the requirements for the degree of MASTERS OF SCIENCE Department of Chemistry 1 996 ABSTRACT THE STUDY OF LONE PAIR ELECTRONS USING ELECTRON DENSITY AND MOLECULAR ELECTROSTATIC POTENTIAL. By LaVetta Appleby There is little doubt that lone pair electrons play a crucial role in chemistry and an understanding of their nature would provide valuable insights into this role. While classical theories such as the Lewis electron dot structures and Valence Shell Electron Pair Repulsion Theory (VSEPR) are insightful they do not characterize precisely the nature of a lone pair. In our effort to understand lone pairs, we have examined the electron density and the associated molecular electrostatic potential (MEP) for various molecules using ab initio wavefimctions. The molecules studied include ammonia, phosphine, water, hydrogen sulfide, formaldehyde, carbon monoxide, hydrogen fluoride and hydrogen chloride. From these studies we conclude that while the electron density is not a sensitive indicator for the presence of lone pairs, the MEP exhibits minima in regions of space where one would expect to find lone pair electrons. In memory of my mother, Cora Appleby, who gives me the inpiration. My siblings: Pamela, Ben, Patrick, Yolanda, Perry, Steven and Charles. Special Friends: Theresa, Andrea and Tracee. iii First, I would like thank my Higher Power who has given me the wisdom and the stamina that has made all of this possible. I would like to thank Dr. James F. Harrison for all of his help and guidance. Thanks also to the faculty and staff of the Department of Chemistry at Michigan State University for their help, guidance and support. Sincere thanks to the Harrison Research Group and friends for their patience and encouragement. Finally, I would like to most graciously thank my family and special friends for their support and encouragement, you guys were truly send from Heaven. iv TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES CHAPTER I INTRODUCTION BIBLIOGRAPHY CHAPTER II ELECTRON DENSITY INTRODUCTION METHODS RESULTS A. NH3 AND PH3 B. H20 AND SH2 C. CHZO D. CO E. HF AND HCl CONCLUSIONS BIBLIOGRAPHY CHAPTER III MOLECULAR ELECTROSTATIC POTENTIAL INTRODUCTION METHODS RESULTS A. NH3 AND PH3 B. H20 AND 8H2 C. CHZO D. CO . E. HF AND HCi CONCLUSIONS FUTURE WORK BIBLIOGRAPHY Page vii 00k) 10 10 12 13 18 18 77 22 26 27 29 3O 3] 34 4] 48 52 56 65 67 68 LIST OF TABLES CHAPTER II Table 1. Optimized and experimental geometries. CHAPTER 111 Table 1. Molecular Electrostatic Potential. Page 11 33 LIST OF FIGURES CHAPTER I Figure 1 2 3 . Lewis electron dot formulae for ammonia and water. . VSEPR for ammonia and water. . Molecules of discussion. CHAPTER 11 Figure 1 2. 3. . Isosurface of electron density for the NH3 molecule. Isosurface electron density for the PH3 molecule. . Various electron density contours for the PH3 molecule. . Isosurface of electron density for the H20 molecule. . Isosurface of electron density for the SH2 molecule. . Isosurface of electron density for the CHZO molecule. . Isosurface of electron density for the CO molecule. . Isosurface of electron density for the HF molecule. 10. Isosurface of electron density for the HCl molecule. vii Various electron density contours for the NH3 molecule. Page 14 15 17 19 21 23 24 CHAPTER 111 Figure 9. 10 11 12. 13. 14. 15. 16. 17. 18. . Schematic of energy Vs. distance. . Isosurface of MEP for the NH3 molecule. . Various isosurfaces of MEP for the NH3 molecule. . Contour plot of MEP for the NH3 molecule. . Isosurface of MEP for the PH3 molecule. . Various isosurfaces of MEP for the PH3 molecule. . Contour plot of MEP for the PH3 molecule. . Isosurface of MEP for the H20 molecule. Various isosurfaces of MEP for the H20 molecule. . Contour plot of MEP for the H20 molecule. . Isosurface of MEP for the SH2 molecule. Various isosurfaces of MEP for the SH2 molecule. Contour plot of MEP for the SH2 molecule. Isosurface of MEP for the CHZO molecule. Contour plot of MEP for the CHZO molecule. Isosurface of MEP for the CO molecule. Various isosurfaces of MEP for the CO molecule. viii Various isosurfaces of MEP for the CH20 molecule. 36 37 38 39 4O 43 44 45 46 47 ‘49 50 51 53 54 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Contour plot of MEP for the CO molecule. Isosurface of MEP for the HF molecule. Various isosurfaces of MEP for the HF molecule. Various isosurfaces of MEP for the HF molecule side view. Contour plot of MEP for the HF molecule. Isosurface of MEP for the HCl molecule. Various isosurfaces of MEP for the HCl molecule. Various isosurfaces of MEP for the HCl molecule side view. Contour plot of MEP for the HCl molecule. Trends of MEP and rn_m. ix 55 57 58 59 6O 61 62 63 64 66 CHAPTER I INIRQDUCIIQN It is well known that lone pair electrons play a crucial role in chemistry. This can be seen in may aspects of chemistry such as 'acid/base reactions, hydrogen bonding and Van der Waals interactions. However, the precise nature of lone pair electrons is still not completely understood. In 1916, ON. Lewis developed the electron-dot formulael that bears his name. These formulae show the arrangement of valence electrons in a molecule and suggest schemes in which atoms can bond. He described lone pair electrons as a pair of nonbonding electrons that were localized on the central atom of the molecule and represented them as dots as seen in figure (1). The solid lines represents bonding electrons. The Lewis electron-dot formulas are helpfirl in identifying the number of lone pair electrons and the Valence Shell Electron Pair Repulsion Principle (VSEPR) gives insightinto how the shape of a molecule is affected by the locations and number of lone pair electrons. Through the use of VSEPR the geometry of a molecule can be suggested by postulating the relative energy of repulsion between lone pairs, lone pairs and bonds, and between bondsz. Consider H20, for f! c . a H ammonia molecule /0\ water molecule H H Figure 1. The Lewis electron dot structures for the water and the ammonia molecules. which the electron-dot fonnula is shown in figure (1). The four pairs of valence electrons around the central oxygen atom can be considered to reside in four localized MOS, two of which are lone pairs and two of which are bonding. Because of the electrostatic interaction, there is a repulsive interaction between the electron pair of one localized MO and the pairs in the other localized M05. The energetically most favorable geometry will have the four localized MOS separated spatially as much as possible to minimize the coulombic repulsion. The most separated configuration for four localized MOS around a central atom occurs when the MOS point to the four comers of a tetrahedron. In this model it is therefore expected that the four valence electron pairs around oxygen will be approximately tetrahedrally disposed. Since the tetrahedral bond angle is 109.50, it is expected that H20 is bent, with a 109.50 bond angle. This prediction can be refined a bit by realizing that the lone pair localized MOS in H20 are not exactly equivalent to the bonding localized M05. The electrons in each bonding MO are strongly attracted to two nuclei (the O and one H), whereas the electrons in a lone pair MO are localized only on one nucleus (the 0). All things being equal, the lone pair MOS will be more diffuse then the bonding M05 and they will exert greater repulsion's than the pairs in the bonding M05. The more diffuse lone pair MOS will therefore push the bonding MOS together slightly, thereby reducing the bond angle somewhat below 109.50. For the ammonia molecule, there are again four valence electron pairs around the central atom but there is only one lone pair to push the ammonia molecule water molecule Figure 2. VSEPR representations for the ammonia and the water molecules. bonding MOS together (figure 2). Hence, it is predicted that the bond angle between the nitrogen atom and the hydrogen atoms will be closer to 109.50 as observed. While these theories, Lewis Electron -Dot Formulas and VSEPR, are insightful, they do not address the nature of a lone pair. Our present investigation examines the electron density and the associated molecular electrostatic potential for various molecules using ab initio calculations in order to gain greater insight into the nature of the lone pair electrons. The molecules studied include ammonia, phosphine, water, hydrogen sulfide, formaldehyde, carbon monoxide, hydrogen fluoride and hydrogen chloride , shown in figure (3). This series of molecules studies one, two and three lone pair systems, and will also examine the effect of atomic size on the lone pair electrons. Figure 3. Molecules of discussion. BIBLIOGRAPHY (1) Bader, R.F.W., Atoms In Molecules, Oxford, 1994. (2) Atkins, P.W., Beran, J. A, General Chemistry, Scientific American Books, 1992. CHAPTER II WW With the quantitative formulation of Molecular Orbital Theory by Roothann et al the ability to calculate the electron density on small systems was made possible. In this theory the total electron density is written as a summation of the electron densities of the individual electrons which in turns is given by the square of the molecular orbital hosting the electrons. Accordingly, the total electron density is represented by the following equation: pi?) = zzlri‘r')!‘ where p(;) is the electron density and ‘I’,(;) is the spatial part of the molecular orbital hosting electron i. We assume all orbitals are doubly occupied and thus the factor of 2. The purpose of this chapter is to examine the electron density to gain insight into the nature of lone pair electrons. MEIHQDS Ab initio calculations were performed by Gaussian 92/DF T (Gaussian, lnc.)l. The electron densities were calculated using a 10 11 Table 1. Optimized and expermental geometries. molecule r“l (A) 4“, (degrees) rap (A) Aupmegrees) NH3 1.001 107.37 1.012 106.70 PH3 1.408 95.70 1.420 93.35 H20 0.941 105.47 0.957 104.50 8H2 1.331 94.20 1.336 92.12 CHZO 0C 1.178 122.09 0C 1.208 116.5 HC 1.095 HC 1.116 CC 1.105 -------- 1.128 ........ HF 0.892 -------- 0.917 -------- HCI 1.269 -------- 1.275 -------- rm, calculated bondlength 4“. calculated bond angle rm, experimental boncllength‘4 Lew experimental bond angle4 12 restricted Hartree F ock (RI-IF) wavefunction. The basis sets employed for C, O, S, N, P, Cl, and F were the 6-311G**. While the hydrogen atom was described by 53 primitives contracted to 35 with a single p function with an exponent of 0.75. The geometries of the molecules discussed have been determined by minimizing the energy at the RHF level. (See table 1) The electron densities were generated using Gaussian 92 and visualized using the Science Animation Program (SciAn)2 . RESULTS Ab initio calculations of the electron density of ammonia, phosphine, water, hydrogen sulfide, formaldehyde, carbon monoxide, hydrogen chloride and hydrogen fluoride are summarized in figures (1-8). These are three dimensional isosurfaces on which the electron density has the value 0.022 eA‘3. Recent work done by D. Young and J .F. Hanison3 examined the electron density for the water molecule. A sequence of three dimensional isosurfaces were pictured as the electron density was decreased from 0.148 eA'3 to 0.00148 eA'3. It was shown that even at low isosurface values, that the electron density was rather featureless, especially in the lone pair region. 13 NH3 and PH3 : Figures (1) and (2) are the three dimensional isosurfaces of the NH3 and PH3 molecules. In figure (1), the isosurface of NH3, the dark blue sphere represents the nitrogen atom and the red spheres represents the hydrogen atoms. Based on the Lewis electron dot formulas, NH3 and PH3 each should have one lone pair of electrons, localized on the nitrogen atom in NH3 and on the phosphorous atom in PH3. The isosurface of the ammonia molecule shown in figure (1) displays no evidence of lone pair electrons. Figure (2) shows the isosurface of PH3, where the blue sphere represents the phosphorous atom and the red spheres represent the hydrogen atoms. The shape of the isosurface is similar to that of NH3 molecule. In similar fashion to the NH3 molecule, the region around the phosphorus atom is featureless with no visual evidence that lone pair electrons are present. In figure (3)N1-13 shows a sequence of three dimensional isosurfaces of the electron density beginning at 0.0074] eA'3 and increasing to 0.0741 eA'3 and figure (4) shows a similar sequence for the P113 molecule beginning at 0.00741 eA'3 increasing to 0.148 eA'R. MLWMWMfmflnmm szmaammmmmmm 16 0.00741 0.00148 0.0296 - 0.0445 0.0593 0.0741 Figure 3. The electron density for the ammonia molecul Values from 0. 0074] to 0.0741 electrons lAngstrom‘B. 0.0148 0.0296 0.0445 0.0593 0.148 Figure 4. The electron density for the hlne molecule. Values from 0.00741 to 0.1 electmm/Angstrom"3. 18 H20 and 8H2: Figures (5) and (6) are the three dimensional isosurfaces of H20 molecule and the SH2 molecule. Figure (5), the isosurface of H20, the yellow sphere represents the oxygen atOm and the red spheres represents the hydrogen atoms. Based on the Lewis Electron Dot formulas, H20 and SH2 have two lone pairs of electrons. The lone pairs are said to be localized on the oxygen atom in H20 and localized on the sulfur atom in SHZ. Figure (5), the isosurface for the water molecule, shows that the density around the oxygen atom is featureless and provides no indication of the presence of the two sets of lone pair electrons. Figure (6), the isosurface of SHZ, the magenta sphere, represents the sulfur atom and the red spheres represents the hydrogen atoms. The shape of the isosurface is similar to that of H20 molecule and, as in the H20 molecule, the region around the sulfur atom is featureless and it is not evident that the two lone pair electrons are present. CH20 : Figure (7) shows the three dimensional isosurface for the CHZO molecule . The yellow sphere represents the oxygen atom, the green l9 MEdeecuundeultyforfllemtu-M 20 Figure almrfaceofdemndelfltyforthehydrogumlfidemolemle. 21 Figun1.lsoalrfeeeoldedlondelfltyforthefonmldehydenrleule sphere represents the carbon atom and the red spheres represents the hydrogen atoms. Based on the Lewis electron dot formulas, CHZO should have two lone pairs of electrons localized on the oxygen atom in CHZO. However, as in H20, the region around the oxygen atom in CHZO is featureless, and does not suggest the presence of the lone pair electrons. CO : Figure (8) shows the three dimensional isosurface for the CO molecule, the yellow sphere representing the oxygen atom and the green sphere the carbon atom. Based on the Lewis model , CO should have two lone pairs . One localized on the carbon atom and the other localized on the oxygen atom in CO. There is no evidence of the presence of the two pairs of lone pair electrons. HF and BC]: Figures (9) and (10) are the three dimensional isosurfaces of the HF and the HCl molecules. In figure (9), the isosurface of HF, the magenta sphere represents the fluorine atom and the red sphere represents the hydrogen atom. Based on the Lewis formulas, HF and HCl each should have three lone pairs of electrons, localized on the 23 Flgm$lmrfaceofdeehondalltylortheurbonmomxidenolecule 24 m9Jso-Iflnoeofdecu'ondeldtyforfllehydrogenfluorflemnlecule. 25 Figunlfilmflnceofdecflondafltyforflnehydmgendflofldemoleeule 26 fluorine and chlorine respecting. In figure (9), the isosurface for the hydrogen fluoride molecule, shows that the region around the fluorine atom is featureless. In figure (10), the isosurface of HCl, the purple sphere represents the chlorine atom and the red sphere represents the hydrogen atom. The shape of the isosurface is similar to that of HF molecule and like that of the HF molecule, the region around the chlorine atom is featureless and it is not evident that the three lone pair electrons are present. CONCLUSIONS Although the electron density has been instrumental in understanding electronic structure of molecules, it does not reveal a great deal of information about the nature of lone pair electrons. In figures 1-8, isosurfaces of electron densities, there was no evidence that lone pair electrons were present. Apparently we must look elsewhere for evidence of the existence of lone pair electrons. 27 BIBLIOGRAEHX (1) Gaussian 92/DFT, Revision F.3, Frisch, M., Trucks, G., Schlege, H., Gill, P., Johnson, 8., Wong, M., Foresman, J ., Robb, M., Head-Gordon, M., Replogle, E., Gomperts, R., Andres, J., Raghavachari, K., Binkley, J ., Gonzalez, C., Martin, R., 'Fox, D., Defiees, D., Baker, J., Stewart, J ., and Pople, J ., Gaussian, lnc., Pittsburgh, PA, 1993. (2) Pepke, E., Murray, J ., Lyons, J ., and ku, T-Y., Supercomputer Computation Research Institute of Florida State University. (3) Young, D., Harrison, J .F ., Electronic Chemistry Conference. (4) CRC Handbook Chemistry and Physics 75 Edition, CRC Press, 1994-1995. CHAPTER III INTRODUCTION MOLECULAR ELECTROSTATIC POTENTIAL The Molecular Electrostatic Potential (MEP) can be obtained from electron density by the following equation: nuclear — pm "W Z. (DR =- —_—dV+ -—:—— ( ) IIR—rl .2. IR-m (1.) this equation (DJ?) is the molecular electrostatic potential at the point R, Zk is the charge on nucleus K, located at rk and pG) is the electron density. In recent work the MEP has been used to examine the reactivity of various systems. J. Kempfl used the MEP to determine which oxygen atom on the surface of [V10028l6' would be basic enough to serve as a bonding site for small cations. The MEP was calculated using a SCF wavefunction. Kempf found that the oxygen atom with the deepest minimum was more acceptable bonding site to small cations. It was also found that these results agreed with the interpretation of ONMR spectrum proposed by W.G. Klemperer and W. Shumz. Other work that was done by J. Murray3 found direct correlation between experimentally base indices of reactivitiies and MEP. Some of the reactive indices examined included hydrogen bonding and pKa values. 29 30 Murray showed that as the MEP increased, the hydrogen bonding and pKa values increased. These studies done on molecular reactivity has direct relations to lone pair electrons. However, there has been little done to relate the MEP to the location and nature of lone pair electrons. S.R. Gadre4 did a topological study of MEP on various molecules containing lone pair electrons. He found that the topology of MEP does, show enhanced features as compared to that of the elecron density, particularly in the minima due to lone pair electrons. Other work done by D. Young and J .F . Harrison5 used ab initio calculations of MEP to examine the lone pair electrons for the water molecule. They also found that lone pair electrons correspond to regions of minimum electrostatic potential rather then regions of enhanced electron density. The purpose of this chapter is to use the molecular electrostatic potential to gain insight into the nature of lone pair electrons. As we will see the MEP can be used to define the location of lone pair electrons for the molecules under study. MEIHODS Ab initio calculations were performed by Gaussian 92/DF T (Gaussian, Inc)6. The basis set employed for the oxygen atom was 6-311G** augmented with three uncontracted d primitives with exponents of 2.25, 0.75 and 0.25. The basis sets employed for S,N, P,Cl, C and F were the 6-3116“ along with uncontracted d primitives 31 with exponents scaled from those of the oxygen atom exponents. The exponents are as follows: 4.47, 1.49 and 0.497 for S; 1.59, 0.529 and 0.176 for N; 0.958, 0.319 and 0.106 for P; 0.109, 0.382 and 1.24 for CI; 0.218, 0.725 and 2.19 for C; and 0.482, 1.75 and 5.58 for F. The hydrogen atom was described by 53 primitives contracted to 3 with a single p function with an exponent of 0.7 5. The geometry of all molecules were optimized using the standard convergence criteria. The Molecular Electrostatic Potentials were generated by Gaussian 92 and stored in cube files. Visualization of the Molecular Electrostatic Potentials was accomplished by the Science Animation Program (SciAn)7 in order to create isosurfaces and contour plots. The lone pair angles were measured from the contour diagrams. RESULTS A point particle with an infinitesimally small charge q will have an interaction energy given by the product of q and the electrostatic potential at the point of interest. We show schematically in figure 1 the energy of an infinitesimally small point charge q+ as it approach the ammonia molecule. Ideally the energy increases due to the repulsion of the hydrogen atoms and as the point charge nears the nitrogen atom the energy goes to infinity due to the repulsion from the nitrogen nucleus. As the point charge recedes from the nitrogen atom and nears the lone pair region, the energy decreases due to attractive interaction. 32 “‘5 (‘4’ l ROT ' T:— '76 011 Rot-l) ‘ q+ Ill-ti .. “:3qume Figure thorofd‘nunanmniammhunu apple-cindbynpmmnm 33 Table 1. 6-3116" w/ added d-functions molecule r(A ) 4“, (degrees) I' (A) 41...... (degrees) MEP(eV) lI-In N113 1.002 106.68 1.295 ........ -3.548 P113 1.405 95.57 1.871 ........ -1.167 1120 0.942 105.43 1.194 90 -2.385 SH2 1.328 94.66 1.840 145 -1.050 C1120 0c 1.176 121.98 1.233 100 2052 11c 1.093 CO 1.103 ------- 10,“, 1.475 -----... 0 04791 rm 1.529 C -0.7833 HF 0.897 -------- 1.238 113 -1473 BC] 1.267 ------- 1.956 150 -0.5065 MEP molecular electrostatic potential r(A ) calculated bondlength A“, calculated bond angle r11-111 distance from nucleus to the MEP minima Am I“, lone pair angle 34 a. NH3 and PH3 Figure (2) shows an isosurface of the MEP for the ammonia molecule. Unlike the isosurface of the electron density for ammonia, the isosurface of the MEP has two regions; an attractive yellow and repulsive blue. The yellow isosurface shown has a value of -1.355 eV and the blue isosurface has a value of 5.442 eV. The optimized geometry has a bond angle of 106.68 degrees and a bond length of 1.002 A. Experimental values are 106.70 degrees and 1.012 A. In figure (3) the negative or attractive isosurface was decreased from -1.355 to -3.252eV. The contour plot in figure (4) has a minima of -3.548 eV. Subsequent contours increase uniformly by 0.080. The outermost blue contour in figure (4) has a value of 5.442 eV and subsequent contours increase by 2.721. The distance from the nitrogen nucleus to the MEP minimum ( rN_m) is 1.294 A. Figure (5) is a MEP isosurface of phosphine, PH3, and like NH3, it's Molecular Electrostatic Potential has two regions. The value of the yellow region of the isosurface is -0.4082 eV and the value of the blue region of the isosurface is 5.442 eV. The optimized geometry has a bond angle of 95.57 degrees and a bond length of 1.405 A. Experimental values are 93.35 degrees and 1.420 A. Figure (6) shows the yellow (negative) isosurface decreasing from -0.4082 eV to -1.088 eV. The contour plot in figure (7) has minima of -1 .167 eV and subsequent contours increase unifonnly by 0.080. The outermost blue contour in figure (7 ) has a value of 5.442 eV and subsequent contours increase by 2.7 21. The distance fi'om the phosphorus nucleus to the minimum contour (rp_m) is 1.871 A. 35 Figurez. IsosurfsceotMEPfoI-theanmonhmolecule. Yellowhosurfncevalue ir—l.355 eVnnrl thelrluebonrbcevalueIsSA-flev. —l.355 eV —1.897 eV —2.439 eV —3.252 cV Flgure3. Themfortheammoniamolealle. 'l'henegaflveMEP(yellow ovrvrasleonrface) «lea-easedfm m..—l.355tho-3252ev 38 Figures. WofMEPforthephoephlI-emdeulle. Yellowhoeufacevdueb-OMZeVand blue bonrhcevalueBSA-fl eV. 39 -0.4082 eV -0.5442 eV 41.8163 eV -1-088 eV Figure 6. The MEP for the Mac moleurle. The negative (y ow Isosurface) was decreased from -0.4088 eV to 4.188 eV. 41 b. H20 and H28 Figure (8) shows an isosurface of the Molecular Electrostatic Potential of the water molecule. The yellow isosurface has a value of -l .633 eV and the blue isosurface has a value of 5.442 eV. The optimized geometry has a bond angle of 105.46 degrees and a bond length of 0.941A. Experimental values are 104.50 degrees and 0.957 A. The yellow region is perpendicular to the plane formed by the three nuclei. In figure (9) the negative isosurface was decreased from -1 .633 eV to -2.367 eV. At this level it is seen that the negative isosurface splits into two regions. These regions are consistent with VSEPR predictions and qualitative notions of lone pairs. The contour plot in figure (10) has a minimum of -2.385 eV. Subsequent contours increase by 0.0952. The outermost blue contour in figure(10) has a value of 5.442 eV and subsequent contours increase by 2.721. The distance from the oxygen nucleus to the MEP minimum (ro_m) is 1.194 A. Figure (11) shows the MEP of the hydrogen sulfide molecule. The yellow region has a value of -0.2204 eV and the blue region has a value 5.442 eV. The optirrrized geometry has a bond angle of 94.66 degrees and a bond length of 1.328 A. Experimental values are 92.12 degrees and 1.336 A. As in the water molecule, the yellow region is perpendicular to the molecular plane. In figure (12) the negative isosurface was decreased from -0.2177 eV to -0.9524 eV. At this level it is seen that the negative isosurface splits into two regions. These regions are in the positions where VSEPR predicts the location of the two lone pair electrons. In figure (13) a contour plot has be made of the 42 Figures. lYeomrfaceofMEPforthewatu-moleufle. ellmwleonrfaeevaluele-lmeVand hlueleonrfacevalueles..442ev —1.633 eV —l.905 (N I —2.177 eV -2.367 eV Figure 9. The MEP for the water molecule. The negative MEP (yellow isomrface) was decreased from —l.633 eV to —2.367 eV. 44 Flpre 10. Contour plot of MEP for the water molecule. hue-mammalia- —2.385 eV 0.0952andthe outermost contqu- 5.442 eV 2.721. 45 Phase 11. la—rbeeolMEl’forthe Yelowbosaflacevahe hm“. eVaadthe Huh-urbavaluehm 46 —0.2177 eV -0.2449 eV —0.4082 eV —0.9524 eV Figure 12. The MEP for the hydrogen sulfide molealle. The neg-fly eMEP (yellow lee-Irfaeewas decreased lrom -0.2177 eV to -0.9524 eV. 47 Figurel3. ContourplotofMEPforfllleola’drovgeumllndmrl lnnermostgreacontour Vstqrsizeo.0952andthe outermost blue coutour5.442 eV mam. 48 MEP perpendicular to the plane of the molecule bisecting the oxygen atom. The innermost green contour in figure (13) has a value of -1.050 eV and subsequent contours increase by 0.0952. The innermost blue contour in figure (13) has a value of 5.442 and subsequent contours increase by 2.7 21. The distance from the sulfur nucleus to the MEP minimum (rs_m) is 1.840 A. c. CHZO Figure (14) shows an isosurface of Molecular Electrostatic Potential of the formaldehyde molecule. The MEP isosurface has two regions. The yellow region shown in figure (14) has a value of -l .355 eV and the blue region has a value of 5.442 eV. The optimized geometry has a bond angle of 122.09 degr’e'es and bond lengths of 1.179 A for the oxygen carbon bond and 1.095 A for the hydrogen carbon bond. The experimental bond angle is 116.5 degrees and the experimental bond lengths are 1.208 A for the oxygen carbon bond and 1.116 A for the hydrogen carbon bond. The yellow region is "in the plane of the molecule" and is primarily localized on the oxygen atom. In figure (15) this region was decreased from -1 .355 eV to -2.033 eV. It is seen that the negative isosurface splits into two regions at -l .897 eV. The angle between these two regions and the oxygen atom is 90 degrees. In figure (16) a contour plot has been made of MEP in the plane of the molecule. The innermost green contour has a value of -2.052 eV and subsequent contours increase unifonnly by 0.0952 eV. The outermost 49 .eluoelomebvdehlmoledt'lol‘lflMloeod'lml .01 ring“ haaVeEBLI—ieulaveoahuaodwolle .VeSMAieuleveofimoaleuldedt 50 2 t -1.355 eV —l.626 eV I ‘. -l.89‘7 eV —2.033 eV Figure15.'l‘heMEP£'orthefornfldehylemolearle. The neg-fly eMEP ellow bonrface)was decreased from —l.355 eV to —2.033 eV. 51 ZeVnepeia; 0.0952andthe 2 ContourplotofMEPforg‘f’grmaldehydeurleule. eVdepelan. l. outermost gamma- 5.4—42 FIgure16. 52 blue contour in figure (16) has a value of 5.442 eV and subsequent contours increase by 2.721. The distance from the oxygen nucleus to the MEP minimum (ram) is 1.233 A. (1. CO Figure (17) shows an isosurface of Molecular Electrostatic Potential of the carbon monoxide molecule. This is the first example of a molecule with lone pairs on two nuclei and the isosurface of the MEP has three regions, two yellow, separated by one blue. The yellow regions have a value of «0272] eV and the blue region has a value of 5.442 eV. The optimized bond length is 1.105 A and the experimental bond length is 1.128 A. The yellow regions are cylindrically symmetric with respect to the internuclear line. In figure (18) the negative isosurface was decreased fiom -0.2712 eV to -0.4750 eV. In this figure it is evident that the yellow isosurface on the oxygen atom decreases at a faster rate then the yellow isosurface on the carbon atom. The innermost green contour on the carbon atom in figure (19) has a value of -0.7 833 eV and the innermost green contour on the oxygen atom is -0.4791 eV. Subsequent contours increase uniformly by 0.0430 eV. The outermost blue contour in figure (19) has a value of 5.442 eV and subsequent contours increase by 5.442. The distances from the oxygen (TOM) and carbon (TOM) nuclei to the minimum are 1.475 A and 1.529 A . 53 figure“. IeonrfeceofMEPforthearboamoaoxidemolecule. Ydlowbonrhuvaheh—QMIeVandthe blueioeurfaeevalueiSAfleV. 54 -0.272l eV —0.4082 eV —0.47 14 eV -0.4750 eV Figure 18. The MEP for the carbon monoxide molecule. The negative MEP (yellow isosurface) was from —0.2721 eV to -0.4750 eV. 55 F13nrel9. ContourplotolMEPforthe carlroamonoxldemolecul The lnnennoetgteencontonronthearlronatommreensphere)h -0.7833eVandthelnner-moetgreen connnrrontheoxygenatom here) h—0.4791eVste 0.0430. Theoutennosflrlue contour 5.V442e 56 e. HF and HCl Figure (20) shows an isosurface of the Molecular Electrostatic Potential of the hydrogen chloride molecule. The optimized bond length of 0.896 t: and the experimental bond length is 0.917 A. The yellow region has a value of-1.084 eV and the blue region has a value of 5.442 eV. The yellow region is a cap localized on the fluorine atom. In figure (21) the negative isosurface was decreased form -1.084 eV to -1.463 eV. At -1.355 eV the yellow cap starts turning into a ring. It is seen in figure (21) that the three lone pairs are localized on the fluorine atom as predicted by Lewis Electron Dot Theory, and they form a delocalized ring. In figure (23), the innermost green contour has a value of -1.473 eV and subsequent contours increase uniformly by 0.0408 eV. The outermost blue contour in figure (23) has a value of 5.442 eV and subsequent contours increase by 2.721. The distance from the fluorine nucleus to the MEP minimum (rm) is 1.238 A. Figure (24) shows an isosurface of the Molecular Electrostatic Potential of the hydrogen chloride molecule. The yellow region has a value of -0.1088 eV and the blue region has a value of 5.442 eV. The optimized bond length of 1.269 A and the experimental bond length is 1.275 A. The yellow region is a cap localized on the chloride atom. In figure (25) the negative isosurface was decrease from -0. 1088 eV to -0.4081eV. At 0136] eV the yellow cap starts turning into a ring. Just as in the case of the hydrogen fluoride molecule, the three lone pairs 57 more”. MofMEl’torthehydrogenflnorflemoleule. Yelowhoearlaeevalaeh—l.084eVaadthe hlnehoeuhcevahrehmev. 58 O 0» —l.084 eV -1.355 eV —1.442 eV -l.463 eV Figure 21. The MEP for the hydrogen fluoride molecule. Thenegative MEP (yellow hour-face) was from-1.084tho—1H463ev 59 1- 1- -1.084 eV —1.355 eV —l.442 eV —1.463 eV [figure 22.. The MEP for the hydrogen fluoride molecule. The negative MEP (yellow Isosurface) was decreasedfro m-l .084 eV to -l. 463 eV. 60 Figure 23. Contour plot of MEP for the hyrogen fluoride molecule. Innermost green contour —l.473 eV stepsize 0. outermost blue contour 5.442 eV stepsize 2. 0408andthe 721 61 .It‘ .21 . «\xlvssfi l 1lg‘lwngandIl-elrlue lib-re“ IaoelrrlaceolMEPforthe Yellowho-Irfacevalueh bourrlacevelnehSAfleV. 62 —0.l088 eV —0.1361 eV 0 O -0.l905 eV -0.4081 eV Figure 25. The MEP for the hydrogen chloride. The negative MEP (yellow isosurface) was decreased Iron—0.1088 eV to 4.4081 eV. 63 -0.l088 eV —0.136l eV -0.l905 eV —0.4081 eV Figure 26. The MEP for the hydrogen cfloride. The negative MEP (yellow leonrrface) was from -0.1088 eV to —0.4081 eV. Flgure27. ContourplotofMEPfordrehydrogencHorldemoleulle. Innumostyeencontour-05065eV stepsheo.04flandthe 65 on the hydrogen chloride molecule are localized on the chloride atom as predicted by Lewis Electron Dot Theory . In a contour plot of HCI shown in figure (27), the innermost green contours has a value of -0.5065 eV and subsequent contours increase uniformly by 0.0408 eV. The outermost blue contour in figure (27) has a value of 5.442 eV and subsequent contours increase by 2.721. The distance from the fluoride nucleus to the MEP minimum (rem) is 1.956 A. CONCLUSIONS: 3. Lone pairs The Molecular Electrostatic Potential exhibits minima in regions where one would expect to find lone pair electrons, suggesting that lone pairs correspond to regions of space in which the MEP has a rrrinima, rather than where the electron density is concentrated. b. Trends It is seen in figure (28), that as one goes from ammonia to hydrogen fluoride, across the periodic the table, the Molecular Electrostatic Potential increases and as one go down periodic table the, Molecular Electrostatic Potential increases. Also as one go down period, the distance from the nucleus to the minima increases. 66 MEP increases 1'1"". I \\H H/O.\H ”‘4’ Hi\fi H/"S°'\H ": ' MEP increases r”, 1ncreases F igurc 28. Trends of MEP and rm. 67 w Another method that is being use to explore the nature of lone pair electrons is the Laplacian of the Electron Density function. The Laplacian of the Electron Density function is the second derivative of the electron density function, p(;), in three dimensional space. The model is base on a theorem in calculus that states: if a function, f(x), is greater than its neighboring points then the second derivative of f(x) is greater thftoii zero and thus, f(x) is concentrated. When f(x) is lessn than its neighboring points, the second derivative of f(x) is less the’ zero and thus, f(x) is depleted. Hence, when the Laplacian of the Electron Density function,V7- p(;), is greater their zero, than the electron charge is concentrated and if , V2 p(;), is less 0152210, thin the electron charge is depleted. Recent work] demonstrates that various molecules with lone pair electrons show charge concentrations in positions where VSEPR model predicts lone pair electrons. . Our future work includes generating plots of the Laplacian of the Electron Density function for the ammonia, phosphine, water, hydrogen sulfide, formaldehyde, carbon monoxide, hydrogen fluoride and hydrogen chloride molecules and compare regions of charge concentrations to our MEP minimas generated. 68 BIBLIOGRABHX (1) Kempf, J., 1992,J. AM. Chem, 114, 1136. (2) Klemperer,W.G., Shum, W., 1977, J. AM. Chem. Soc, 99, 3544. (3) Murray, J. S., Brinck, T., 1991, Journal of Molecular Structure, 256, 29. (4) Gadre, SR, 1991, J. Chem. Phys, 96, 5253. (5) Young, D., Harrison, J .F., Electronic Chemistry Conference. (6) Gaussian 92/DFT, Revision F.3, Frisch, M., Trucks, 6., Schlege, H., Gill, P., Johnson, 3., Wong, M., Foresman, J ., Robb, M., Head-Gordon, M., Replogle, E., Gomperts, R., Andres, J ., Raghavachari, K., Binldey, J ., Gonzalez, C., Martin, R., Fox, D., Defiees, D., Baker, J ., Stewart, J ., and Pople, J ., Gaussian, Inc., Pittsburgh, PA, 1993. 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