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INFORMATION to USERS the Quality of This Reproduction Is INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly fium the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter free, ixdiile others may be from any type o f 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 afreet 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. 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UMI A Bell & HoweU Infoimation Conqmy 300 North Zed) Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 CONFIGURATION INTERACTION WITH NON-ORTHOGONAL SLATER DETERMINANTS APPLIED TO THE HUBBARD MODEL, ATOMS, AND SMALL MOLECULES DISSERTATION Presented in Partied Fulfillment of the Requirement for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University by SVEN PETER RUDIN, DIPL. EL. INC. ETH The Ohio State University 1997 Dissertation Committee: John VV. Wilkins Approved by Charles A. Ebner Arthur J. Epstein I/O. UD Advisor Department of Physics UMI Number: 9721160 UMI Microform 9721160 Copyright 1997, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 © Sven Peter Rudîn 1997 ALL RIGHTS RESERVED ABSTRACT The energy of a truncated configuration interaction (Cl) electronic wave func­ tion depends on the quality of the underlying basis set and the form of the expan­ sion, i.e., which determinants are included. Given an expansion with fixed basis set and form, a unitary transformation of the basis functions can significantly alter the result by changing the form of the orbitals. Two examples are given for the advantage of one particular unitary transfor­ mation, natural orbitals, over the self-consistent-field orbitals: (i) For the nitrogen dimer the use of natural orbitals improves the energy of a 01 wave function by 1.3 millihartree over a benchmark study, in which the dissociation energy was un­ derestimated by approximately the same amount, (ii) A well-defined, orbital-based truncation of the Cl wave function in natural orbitals for first-row supermolecules (dimers with large nuclear separation) accurately reproduces the energy of the two atoms treated independently. The determinants in Cl expansions are traditionally required to be mutually orthogonal. This forces the entire expansion to be done with the same unitary transformation of the basis set. Without the restriction of orthogonality between determinants each determinant can have a different unitary transformation of the basis set. A computer code to calculate expansions in non-orthogonal determinants was implemented and applied to the Hubbaxd model, atoms and molecules. The ii resulting wave functions have a lower energy than a wave function of equal length expanded in orthogonal determinants. Starting from a reference determinant with localized orbitals is found to further improve the energy. Application to the Hub­ bard model in one and two dimensions leads to a systematic expansion which dis­ plays a pronounced hierarchy observable only with non-orthogonal determinants. For singlet states of atoms (Be, Ne) and small molecules (H 2, HeH"^, HgO, N2, C2, C2H2, C2H4, C2H6) a few dozen non-orthogonal determinants account for roughly 90% of the correlation energy in the basis sets used. The definition of a degree of excitation for non-orthogonal determinants is used to illustrate the significant differences between expansions with orthogonal and non-orthogonal determinants. Ill Dedicated to the memory of David Lera (1968 — 1993) IV ACKNOWLEDGMENTS It is amazing what you can accomplish if you do not care who gets the credit. - Harry S. Truman John Wilkins and Matthew Steiner deserve a lot of credit for what this document represents: My understanding. So, John and Matthew: Thank you. My thanks also goes to many other people, who contributed each in their own way: Marijan Adam, Edward Adelson, Mebarek Alouani, Todd Anderson, Wilfried Aulbur, Janna Auvinen, Sapna Batish, Mary Heather Bents, Ravi Bhagavatula, Sue Blaker, Jim Blatchford, Thomas Blcizek, Thomas Boltshauser, Verena Bolt- shauser, Richard Bomfreund, Richard Boyd, Judith Braendle, William Brinker- hoff, Jill Brotman, Francesca Brotman-Orner, Shoshana Brotman-Omer, Pamela Brown, Joe Broz, Joy Bums, Mary-Lou Capozzi, Dave Casdorf, Emily Cassani, Joe Cassani, Lou Cassani, Mary Ann Cassani, Ruggero Castagnetti, Jim Castiglione, Herve Castella, Leena Chandran, Ted Chase, Lauren Chase, Jian Chen, Joyce Chin, Oliver Chung, Sora Cho, Bunny Clark, Jeffrey Clayhold, Chet Cole, Pete Colo- vas. Bill Conable, Cheryl Conel, Erin Conel, Jim Conel, Dan Cooper, Bob Cope, Daniel Cox, Fleda Crawford, Todd Culman, A. Cristina Cunha, Mark Dauben- meier, Mike Degen, Brad Dielman, Heidi Dugger, Bryan Dunlap, Charles Ebner, Doris Eckstein, Carlos Egues, Keith Emptage, Arthur Epstein, Catrin Ericsson- Novak, Son Evans, Melinda Everman, Armin Ezekielian, Maria Faxias, Dres Fehr, Claudia Filippi, Miodrag Filipovic, Jenny Finnell, Linda Fox, Roger Fox, Karolyn Frasier, Sonia Frick, Richard Furastahl, Jorge Gal an. Pilar Galan, Darren Gebler, Avik Ghosh, Jason Gilmore, John Gratsias, Jeffrey Grossman, Peter Hansch, Ed­ ward Harris, Kathy Hart, HaxaJd Haughlin, Fernand Hayot, Saad Hebboul, Mary Heck, Rolf Held, John Heimaster, Steve Herbert, Ron Hinkle, J. B. Hoy, Hung- Chen Hsieh, Susanne Huber, Per Hyldgaard, Laurens Jansen, Mark Jarrell, Sashi Jasty, Ciriyam Jayaprakash, Scott Jessen, Darrell Jones, Lars Jonsson, Jinsoo Joo, Ben Kaczer, Seth Kantor, Brian Keller, Karen Keppler, Gregory Kilcup, Eimsik Kim, Eunsook Kim, Jeongnim Kim, Kihong Kim, Taesnk Kim, Karen Kitts, George Klinich, Randy Kohlman, Tracy Kotrly, Brian Kuban, Rahul Kulka- mi, Lisa Kurth, Alex Kuznetsov, Sanjay Khare, Lisa Kiner, Barbara King, Brian Kuban, Thomas Lemberger, Beth L’Esperance, Richard FumstaM, Lisa Lantz, Bea Latal, Zachary Levine, Jeff LePage, Washington Lima, Mark Mamrack, John Markus, Victor Majtisovits, Meg McConnell, Sylvia McDorman, Janis McKay, Ross McKenzie, Deanna Mears, Brenda Mellett, Ursina Metzger, Alfred Mieth, Robert Mills, Lubos Mitas, Chad Mitchell, Rene Monnier, Brian Morin, Dave Moser, Hydee Moser, Andreas Miinzner, Bernard Mulligan, Ralf Niehaus, William Novak, Pat O’Bannon, Lee Oesterling, Leigh Oesterling, Ursula Oetiker, Luiz Oliveira, Frederick Omer, Keith Omer, Phyllis Omer, Kathleen Paget, Shelley Palmer, William Palmer, Karen Papritan, Don Parsons, Bruce Patton, Steve Pat­ ton, Jack Pawlicki, Charles Pennington, Uri Perrin, Robert Perry, Derek Peter­ man, Cheri Petersen, Ed Petersen, Mary Lou Petersen, Doug Petkie, Lisa Petkie, Pia, Russell Pitzer, Shawn Prendergast, Geoff Prewett, Zack Protegeros, Punky, William Puttika, Eduardo Raposo, Christian Rappan, Jim Raynolds, Bill Reay, Jen­ nifer Recchia-Cox, Charlie Recchia, Lauren Reed, Mark Reed, Mike Reed, Michael Reyzer, Eric Roddick, Markus Roos, Shirley Royer, Andy Rudin, Ann Rudin, Annika Rudin, Edith Rudin, Erik Rudin, Harry Rudin, Jr., Harry Rudin, Sr., Heather Rudin, Karen Rudin, Katy Rudin, Kirsten Rudin, Linda Rudin, Mark Rudin, Jennifer Rufsvold, Seungoh Ryu, Shelly Sabo, David Sasik, Helena Sasik, Roman Sasik, Doug Scalapino, Beatrice Scheurer, Beat Scheurer, Patricia Scheurer, Rosli Scheurer, Thomas Scheurer, Sabina Schiesser, Avi Schiller, Tanya Schneider, Scooter, Jeff Seiple, Andrew Sergeev, Richard Seyler, Cookie Shand, Ernie Shand, Isaiah Shavitt, Vivek Shenoy, Diane Sherwood, Don Sherwood, Paulo Sigg, Amy Simon, Beth Smith, Jeff Smith, Robert Smith, Jenny Sokolski, R. SooryaJcumar, Melissa Spangler, Renee Speh, Rekha Srinivasan, Urs Staub, Ursula Staub, Philip Steden, Renate Steden, Teri Steiner, Andy Stenger, Deborah Storm, Suresh Subra- manian, Charles Thorne, Brad Trees, Dallas Trinkel, A run Tripathi, Brad Turpin, Cyrus Umrigar, Jon Vandegriff, Alan Van Heuvelen, Peter Vaterlaus-Rack, Kitty Wagner, Lukas Wagner, Betty Wallace, Wei Wang, Irene Warren, Chris Weait, John VI Weax, Christoph Weder-Huber, Sandy Weder-Huber, Dorothea Wehlen, Wolfgang Wenzel, John Whitcomb, Philip Wigen, Ken Wilson, Les Wood, Shiwei Zhang, Paul Ziesche, the Zimering family, and Maja Zweifel. I would like to thank the DOE and the Ohio Supercomputer Center for support. I would also like to thank several institutions and their people: Caffé Fino, the Cajun Kitchen, Barley’s, Bemie’s, Brenen’s and the Yogurt Oasis, Columbus Camera Group, Davis Center, Graeter’s, Basting’s General Store, the Institute for Theoretical Physics, Kinko’s, Long’s, the Ohio State University Libraries, the
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