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INFORMATION TO USERS The most advanced technology has been used to photograph and reproduce this manuscript from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter 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 corner 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. University Microfilms International A Bell & Howell Information C om pany 3 0 0 North Z eeb Road, Ann Arbor. Ml 48106-1346 USA 313.761-4700 800'521-0600 Order Number 9111690 Large-scale ab initio molecular electronic structure calculations Comeau, Donald Clifford, Ph.D. The Ohio State University, 1990 UMI 300 N. ZeebRd. Ann Arbor, MI 48106 L a r g e -S c a l e Ab Initio M o l e c u l a r E l e c t r o n ic S t r u c t u r e C alculations dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Donald Clifford Comeau, B.S. The Ohio State University 1990 Dissertation Committee: Approved by Charles F. Bender C. Weldon Mathews j <^> ^^jjj Russell M. Pitzer Adviser isaiant • u Diiavitbci 'u Department of Chemistry To Kathy and Kim ii A cknowledgements I would like to thank my advisor, Professor Isaiah Shavitt, for his guidance, instruction, suggestions, and support. While the friendship and support of all my fellow graduate students and post-docs is acknowledged, special assistance to this project was provided by Randy Diffenderfer, Kyungsun Kim, Melanie Pepper, Eric Stahlberg, and Bob Zellmer. Professor Russell M. Pitzer also provided help at several points. Portions of this work were supported by a Graduate School Fellowship and a Presidential Fellowship, both from The Ohio State University. Computer time was provided by the Instruction and Research Computer Center of The Ohio State University, the NASA-Lewis Research Center, Boeing Computing Services, the Pittsburgh Supercomputing Center, and the Ohio Supercomputer Center. Special thanks go to Kathy for her patience and encouragement, to Kim for her squeals of delight, and to my parents for instilling my thirst for knowledge and for guiding my early steps on the road of learning. V i t a April 26, 1961 ................................................. Born—Anchorage, Alaska 1982 .................................................................. B. S., summa cum laude, Columbia Union College, Takoma Park, Maryland 1983-198 4 .......................................................... Graduate Teaching Associate Department of Chemistry The Ohio State University Columbus, Ohio 1984-198 6 ...........................................................Graduate Research Associate Department of Chemistry The Ohio State University Columbus, Ohio 1987-1988 .......................................................... Graduate Research Associate Department of Chemistry The Ohio State University Columbus, Ohio 1989-1990 Graduate Research Associate Ohio Supercomputer Center Columbus, Ohio IV P ublications “An Ab Initio Determination of the Potential-Energy Surfaces and Rotation-Vibra- tion Energy Levels of Methylene in the Lowest Triplet and Singlet States and the Singlet-Triplet Splitting,” D. C. Comeau, I. Shavitt, P. Jensen, and P. R. Bunker, J. Chem. Phys., 90, (1989), 6491-6500. “A Progress Report on the Status of the COLUMBUS MRCI Program Sys tem,” R. Shepard, I. Shavitt, R. M. Pitzer, D. C. Comeau, M. Pepper, H. Lischka, P. G. Szalay, R. Ahlrichs, F. B. Brown, and J.-G. Zhao, Int. J. Quant. Chem. Symposium, 2 2 , (1988), 149-165. “The Location and Characterization of Stationary Points on Molecular Poten tial Energy Surfaces,” D. C. Comeau, R. J. Zellmer, and I. Shavitt, in: Geometrical Derivatives of Energy Surfaces and Molecular Properties, (P. J 0 rgenson and J. Si mons, eds.), D. Reidel Publishing, (1986), 243-251. F i e l d s o f S t u d y Major Field: Chemistry Theoretical Chemistry. Professor Isaiah Shavitt. v T a b l e o f C o n t e n t s DEDICATION ........................................................................................................ ii ACKNOWLEDGEMENTS ............................................................................. iii VITA ............................................................................................................................ iv LIST OF FIGURES .............................................................................................. ix LIST OF TABLES ................................................................................................. xi CHAPTER PAGE I Introduction .................................................................................................. 1 II Electronic Structure M ethods ............................................................. 4 III Potential Energy Surface Stationary Points ................................... 1 1 3.1 Potential Energy Surfaces ........................................................ 11 3.2 Gradients .......................................................................................... 12 3.3 Internal Coordinates \ . 13 3.3.1 Traditional Internal Coordinates ........................... 14 3.3.2 Nonredundant Subset of Cartesian Coordinates 16 3.4 Analytic Polynomial Potential Surfaces .......................... 19 3.5 Geometry Optimization ............................................................ 20 3.5.1 Newton-Raphson ............................................................ 20 3.5.2 Hessian U pdate ................................................................ 2 1 3.5.3 Our Method for Finding Stationary Points . .. 22 3.6 MINPT Program ............................................................................... 25 3.7 Least Squares Equations ............................................................ 26 3.8 Frequencies ...................................................................................... 33 3.9 Test Case ......................................................................................... 41 3.10 Calculations on CHs"............................................................... 41 3.11 Further W ork............................................................................... 46 IV Computer Programming .................................................................. 48 4.1 Optimization............................................................................... 50 4.1.1 Algorithm...................................................................... 50 4.1.2 Clean Code ................................................................... 52 4.1.3 Clean Inner Loops....................................................... 54 4.1.4 Computational Kernels............................................. 55 4.1.5 Unrolling Loops............................................................. 57 4.2 Portability..................................................................................... 58 4.2.1 I O ...................................................................................... 59 4.2.2 Clean Code .................................................................... 60 4.2.3 Isolate Dependencies ................................................. 61 4.2.4 Original Methods.......................................................... 62 4.2.5 MDC...................................................................................... 64 4.2.6 Logical Expressions in MDC....................................... 68 4.2.7 Com putational K e r n e ls .............................................. 69 4.3 Cray Matrix Operations......................................................... 72 4.3.1 Ordinary Matrix Multiplication.............................. 73 4.3.2 Symmetric Matrix Operations................................. 76 4.4 Formula Tape Loops ............................................................... 79 4.4.1 Distinct Row Table .................................................... 81 4.4.2 External Space Treatment....................................... 85 4.4.3 Symmetry ....................................................................... 87 4.4.4 Numbering the Configurations.............................. 88 4.4.5 Matrix Element Evaluation.................................... 93 4.4.6 Matrix Element Contributions from Integrals with External Indices ............................................... 97 4.5 Results ............................................................................................ 102 4.6 Further Work..............................................................................