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INFORMATION to USERS This Manuscript Has INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in ^ew riter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI University Microfilms International A Bell & Howell Information Company 300 Nortfi Zeeb Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9505236 The graphical unitary group approach to configuration interaction calculations: An application to the dipole moment and potential energy surface of the water molecule Kedziora, Gary Steven, Jr., Ph.D. The Ohio State University, 1994 UMI 300 N. Zeeb RA Ann Aibor, MI 48106 The Graphical Unitary Group Approach to Configuration Interaction Calculations: an Application to the Dipole Moment and Potential Energy Surface of the Water Molecule. Dissertation Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University By Gary S. Kedziora Jr. The Ohio State University 1994 Dissertation Committee: Approved by Professor Isaiah Shavitt Professor Russell M. Pitzer Professor Sherwin Singer Advisor Department of Chemistry DEDICATION To my dear Barbara ACKNOWLEDGMENTS I would like to thank Professor Isaiah Shavitt for teaching me much of what went into this dissertation and pushing me to think carefully and clearly. He has been a superb example of a scientist and will continue to inspire my career. Steven Parker provided frequent and gracious help in preparing this document. I would also like to thank Lars Ojamae and Jean Blaudeau for interesting and fruitful scientific discussions, and my fellow Shavitt group members, Eric Stahlberg, Robert Zellmer, and Galen Gawboy for their help with the COLUMBUS codes. Ill VITA September 22, 1965 ................................................................Bom - Oscoda, Michigan 1987 B. S., - University of Minnesota 1987-1994 .......................................... Teaching Associate - The Ohio State University Publications P.S. Portoghese, G.S. Kedziora, D.L. Larson, B.K. Bernard, and R.L. Hall, “Reactivity of Glutothione with a,/?-Unsaturated Keytone Flavoring Substances,” Food and Chemical Toxicology, 27, 773 (1989). FIELDS OF STUDY MAJOR FELD: Chemistry Theoretical Chemistry, Professor Isaiah Shavitt IV TABLE OF CONTENTS DEDICATION.................................................................................................................... ii ACKNOWLEDGMENTS........................................................................................... iii VITA ..................................................................................................................................iv LIST OF TABLES.......................................................................................................... vi LIST OF FIGURES .................................................................................................... ix CHAPTER PAGE I. Introduction and T heory .......................................................................................1 A. Introduction .....................................................................................................1 B. Electronic Structure M ethods ....................................................................3 C. Spin Symmetry of Many-Eiectron Wave Functions ............................14 D. GUGA..............................................................................................................20 E. The COLUMBUS Programs: A GUGA Implementation ...................28 F. S um m ary ........................................................................................................32 G. Tables and Figures ......................................................................................33 II. Triple- and Quadruple-Excitation Correlation Corrections ..........................42 A. Corrections and complexity .................................................................... 42 B. Triple- and Quadruple-Excitation Loop Extensions ........................... 47 0 . S um m ary ....................................................................................................... 53 D. Tables and Figures ......................................................................................54 III. Ground-State Potential Energy and Dipole Moment Surface of the Water Molecule ...................................................................................................... 61 A. Introduction ..................................................................................................61 B. M e th o d s ....................................................................................................... 65 1. Basis S e t s ............................................................................................. 65 2. Reference Space ................................................................................. 70 0. Results and Discussion ............................................................................. 72 E. Sum m ary : ....................................................................................... 81 F. Tables and Figures ......................................................................................82 APPENDIX .....................................................................................................................99 BIBLIOGRAPHY..........................................................................................................134 LIST OF TABLES TABLES p a g e Table I Partitions of the integer 5 and classes of Sjsj ............................... 33 Table 2 Step numbers defined in terms of changes in the Paldus a, b, and c values, intermediate occupation and spin ........................ 36 Table 3 The distinct row table (DRT) for the basis in Figure 3. See text for definitions ...........................................................................37 Table 4 The output generated by the depth-first tree-search program, corresponding to the depth-first tree given in Figure 9. See the caption of Figure 9 for an explanation of some of the data. Wo and Wj are the segment values corresponding to Equation (42) of Chapter I. In the cases where the segment value lies between the Wq and W; columns, it is a contribution from a one-body segment value, W. Aq and A] are the internal contributions to the two terms (x = 0 , 1) of the coupling coefficient. In this table the total contributions are Ai n Wa; (H Wo = 0 in these cases). Each p or q level index may be selected from a range of valid level indices defining a single loop extension (see text for examples).. 56 Table 5 For each loop type and number of external indices, the number of loop extensions starting at each set of boundary vertices is shown next to the boundary vertex pairs. If there is no valid loop extension of a given type for a pair of boundary vertices, they are left out of the table ....................... 57 Table 6 The primitives and contractions of the aug-cc-pVQZ-d(f,g) basis set. See text for the origin of the basis set ......................82 Table 7 The primitives and contractions of the ave-ANO+(dg,spf) basis. See text for the origin of the basis set ............................ 84 vi Table 8 Comparison of the two final basis set choices for the surface. The definition of each is given in the text. All calculations were done at the equilibrium geometiy R = 1.811 3o and 6 = 104.48°, with the 6 CAS reference space. 8 6 Table 9 Comparison of the choices for the reference space at various levels of correlation using the aug-cc-pVQZ-d(g,f) basis set. The final four Cl entries for each reference space include the quadruples corrections defined in Chapter 1 ..............................87 Table 10 The dimension of the MR-SDCI spaces for the cases considered in Table 9 in Cs symmetry. See text for a full definition of the spaces ..................................................................8 8 Table 11 Comparison of anharmonic frequencies from ab initio surfaces with experiment. The first two columns are from this work .......................................................................................... 89 Table 12 Comparison with experiment of the anharmonic frequencies calculated in this work with the various energy surfaces using different correlation methods .............................................90
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