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Quantum Mechanical Calculations Of: I Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1968 Quantum Mechanical Calculations Of: I. Azabenzenes, II. Ethylene; IIi. Hydrogen-Disulfide. Brent J. Bertus Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Bertus, Brent J., "Quantum Mechanical Calculations Of: I. Azabenzenes, II. Ethylene; IIi. Hydrogen-Disulfide." (1968). LSU Historical Dissertations and Theses. 1378. https://digitalcommons.lsu.edu/gradschool_disstheses/1378 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. This dissertation has been microfilmed exactly as received 68-10, 720 BERTUS, Brent J ., 1939- QUANTUM MECHANICAL CALCULATIONS OF: L AZABENZENES; IL ETHYLENE; m. HYDROGEN DISULFIDE. Louisiana State University and Agricultural and Mechanical College, Ph. D., 1968 Chemistry, physical University Microfilms, Inc., Ann Arbor, Michigan QUANTUM MECHANICAL CALCULATIONS OF I. AZABENZENES II. ETHYLENE III. HYDROGEN DISULFIDE A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Chemistry by Brent J. Bertus B.S., Louisiana State University in New Orleans, 1963 January, 1968 ACKNOWLEDGMENT The author wishes to acknowledge the inspiration of Dr. S.P. McGlynn, for it was through Dr. McGlynn that the direction and environment necessary for this work was achieved. A debt of gratitude must be expressed to Dr. A.T. Armstrong, Dr. J.V. Russell and Dr. L.C. Vanquickenborne. At this time, I would also like to thank Mrs. Anne Wahlborg for proofreading this manuscript. Financial support is gratefully acknowledged from the United State Army, the United States Atomic Energy Commission-Biology Branch, and the Dr. Charles E. Coates Memorial Fund of the Louisiana State University Foundation donated by George H. Coates. To My Family An iota of the recognition due for their contribution to my education TABLE OF CONTENTS PAGE ACKNOWLEDGMENT .................................................... ii LIST OF T A BLES................................................‘. iv LIST OF FIGURES...................................................... vi ABSTRACT............................................................vii THEORY A. Mulliken-Wolfsberg-Helmholtz Method (M-H-W). 2 B. Transition Probability ............................ 4 C. Spin Orbit Coupling (S.O.C.) .......... 5 D. Variable Electronegativity Self-Consistent Field (V.E.S.C.F.) ................................. 7 CHAPTER I. PYRIDINE A. Introduction ................... 12 B. Computation........................................... 14 C. Results and Discussion.............................. 17 1. M-W-H Treatment.................................17 2. V.E.S.C.F. Treatment............................ 25 3. S.O.C. Treatment. .......... 28 4. Theory. ............. 30 D. Conclusions. ........... ........... .. 32 CHAPTER II. ETHYLENE A. Introduction......................................... 35 B. Computations ...... ........... ....... 35 C. Results and Discussion ........ ......... 36 D. Conclusions. ................... 57 CHAPTER III. HYDROGEN DISULFIDE A. Introduction .... ......... .......... 60 B. Computations ....... ....... 62 C. Results and Discussion . ............ ..... 62 D. Conclusions............. 73 APPENDIX I ...........................................................77 APPENDIX II...........................................................85 VITA ................................................................. 87 LIST OF TABLES TABLE PAGE Chapter I I. Coulomb Integrals. 15 II. Orbital Energies Associated With the Ground Configuration of Pyridine. ............. ......... ..... 18 III. The Eigenvectors and Values Associated with the Filled Shell Configuration of Pyridine. ........... 20 IV. Population of Pyridine for Closed and Open Shell Configurations ..... ........... ........... 26 Chapter II I. Eigenvectors and Eigenvalues of Ethylene Ground State MO's Set 1, rr(0.8) a(l.l)....................................... 38 II. Eigenvectors and Eigenvalues of Ethylene Ground State MO's Set 2, tt(0. 8) a ( 1 . 0 ) ....................................... 41 III. Eigenvectors and Eigenvalues of Ethylene Ground State M O ’s Set 3, tKI.O) a(1.0)....................................... 44 IV. Ionization Potentials of Ethylene. ............ 47 V. Total Energy of Ethylene Ground State and Excited States Sets 1, 2, and 3 . ...................... 52 VI. Unfilled MO's in Ethylene....................................... 54 VII. Population of Ethylene Ground State and Excited States . 55 Chapter III I. Coulomb Integrals. .................... 63 II. Hydrogen Disulfide Ground State (0 = 90°)• Eigenvalues, Population Analysis, and Eigenvectors. 64 III. The Slater Zeds Are Adjusted for Sulfur 4s and 3d Atomic Orbitals ......... .................................. 71 IV. Absorption Spectra of Several Cyclic Disulfides and Hydrogen Disulfide ......... ....................... 74 TABLE PAGE Appendix I I. Ionization Potentials of Saturated Molecules ....... 79 II. Ionization Potentials of Unsaturated Molecules ...... 80 III. Ionization Potentials of Ethylene. ............ 82 v LIST OF FIGURES FIGURE PAGE Chapter I I. Schematic of the Different MO Electronic Configurations for the M-W-H Computations 13 II. Pyridine and Its Coordinate A x e s .........................16 III. MO's of Pyridine in the Closed Configuration and Open Shell Configuration. ...... ......... ........ 23 IV. Absorption Spectrum of Pyridine. ............. 24 V. The V.E.S.C.F. Calculated State Energies ................. 27 VI. The Electronic States of Pyridine. ......................29 Chapter II I. Ethylene Molecule and Symmetry Axes. ........... 37 II. MO's of Ethylene Ground State and Excited States Set 1, tt(0.8) a(l.l)............................................... 49 III. MO's of Ethylene Ground State and Excited States Set 2, tt(0. 8) a(1.0)...............................................50 IV. MO's of Ethylene Ground State and Excited States Set 3, tt(1.0) a(1.0)...............................................51 Chapter III I. Hydrogen Disulfide ..... .............................. 61 II. Total Energy of Hydrogen Disulfide Versus the Change in Dihedral Angle (0). .................. 66 111. The Energy of the rf* arid tt MO's Versus the Dihedral Angle (0)................. ................. 68 IV. The Eigenvalues of the Filled MO's of Hydrogen Disulfide in the Ground State as a Function of Dihedral Angle (0). 69 V. The Calculated Energy Difference of the it* and tt MO's Versus Dihedral Angle (-0-). The Observed Energy Split in U.V. Absorption Band ( - O - ) ........................... 75 ABSTRACT Semi-empirical molecular (Mulliken-Wolfsberg-Helmholtz and V.E.S.C.F.) orbital calculations on pyridine are reported. Open shell computations on configurations resulting from tt — tt* and n -» tt* MO excitations have been performed and it has been shown that significant charge redistribution effects occur in the latter instance. In particular, it has been found that the - configuration is of nTi* lower energy than the j. configuration. rm* The origins of the "mystery band" in ethylene are discussed using (M-W-H) open shell computation methods. The "anti-Berry" state n —* o* is found to be of lower energy than either the tt -* n* or the Berry a -* Tt* transitions. Hydrogen disulfide ground state energy as a function of dihedral angle (0) is reported. The barrier to internal rotation was found to be 2.6Kcal/mole. Origins for the first unfilled MO's in H^S^ were reviewed. THEORY A. MILLIKEN-WOLFSBERG-HEIMHOLTZ METHOD (M-W-H) The Mi 1liken-WoIfsberg-HeImholtz method has been the 1-5 subject of several reviews. The approach utilized the linear variational method: § is a linear combination of some finite set of wave functions ^ M *. = Z c. .<f>. 1 j 1J J The minimization of the energy (E) generates M simultaneous homogeneous linear equations for the M unknown coefficients M E c .(H. - S. ,E) = 0 j J ij iJ The coulomb integral (H^) was approximated as the atomic valence state ionization potential (V.S.I.P.). The coulomb b integrals used were those suggested by Cusachs; these integrals were employed in such a way that they were functions of both the atomic charge and the ith atomic orbital population. The general equation used was H. * Ap + B + Cq ii where A, B, and C are a specific set of constants for each atomic orbital; where p is the population of that orbital and q is the 2 3 particular atomic charge. The resonance integral ) was 1+ approximated by H, . = (2- |S. ])(H. + H. )Sij/2 ij 1 ij 1 li jj The atomic overlap was calculated utilizing Slater orbitals or self-consistent field (S.C.F.) combinations of Slater orbitals. Where feasible, the orbital exponent of the single Slater atomic orbital was constructed so as to mimic the overlap properties of the S.C.F. functions over a range of representative 5 bond distances. The energy of a given molecular state was assumed to be identical to that of the corresponding MO configuration and given by E - E n . e. j-i j J where e. is the MO eigenvalue and n. is the
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