Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1989 Overestimation of Basis Set Superposition Error in Molecular Dimer Correlation Potential Energy Calculations. Jia-an Yang Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Yang, Jia-an, "Overestimation of Basis Set Superposition Error in Molecular Dimer Correlation Potential Energy Calculations." (1989). LSU Historical Dissertations and Theses. 4755. https://digitalcommons.lsu.edu/gradschool_disstheses/4755 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]. 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University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9002183 Overestimation of basis set superposition error in molecular dimer correlation potential energy calculations Yang, Jia-an, Ph.D. The Louisiana State University and Agricultural and Mechanical Col., 1989 UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 OVERESTIMATION OF BASIS SET SUPERPOSITION ERROR IN MOLECULAR DIMER CORRELATION POTENTIAL ENERGY CALCULATIONS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agriculture and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Chemistry by Jia-an Yang M.S. Theoretical Chemistry Institute Jilin University, Changchun, Jilin, China, 1981 May 1989 Acknowledgement The author wishes to express thanks to his advisor, Professor Neil R. Kestner. This work would not have been possible without his support, guidance, encouragement and confidence to the author. The author gives special thanks to the Research Programmer, Robert R. Zinn for valuable help with debugging numerous programs. Heartfelt Thanks to Louisiana State University and Department of Energy supporting me as a research assistant during 1983-1986. The author wishes to acknowledge the financial assistance. ii To my parents, who gave me life and my growth; Yang, Zhikui, and Gu, Baochang. To my teachers, who taught me what I know; All my teachers in China and USA. To my wife, who shares weal and woe with me; Dixin. To my brothers and sisters, who spurred me on; Xuemei, Xuelin, Jiashun, Xuefen, Jiadao and Jiade. To my children, who give me hope; Yanwei and Jack. iii "The underlying physical lavs necessary for the mathematical theory of a large part of physics and the vhole of chemistry are thus completely Known, and the difficulty is only that the exact application of these lavs leads to equations much too complicated to be soluble. " P.A.Dirac, Proc. Roy. Soc. (London), 1929, 123, 714. Table of Contents Acknowledgements ................................... ii List of Abbreviations ............................. ix List of Tables .................................... x List of Figures ................................... xxii Abstract ........................................... xxx 1 Introduction ........................... 1 1.1 General Preliminary ............................ 4 1.1.1 Two Categories of Intermolecular Potential Energy Calculations ...................... 4 1.1.2 Energy Calculations Using Basis Functions ................................ 6 1.1.3 Basis Sets ............................... 11 1.1.3.1 Two Types of Basis Sets ........... 11 1.1.3.2 Contractions of Gaussian Basis Functions ........................ 12 1.2 Basis Set Superposition Error (BSSE) ........... 16 1.2.1 Definition of Basis Set Superposition Error .................................... 16 1.2.2 General Characteristics of Basis Set Superposition Error ...................... 19 1.2.2.1 Basis Set Superposition Error and Potential Energy.................. 19 1.2.2.2 Basis Set Superposition Error and Geometry Configuration ........... 21 1.2.2.3 Basis Set Superposition Error and Basis Sets ....................... 21 1.2.2.4 Basis Set Superposition Error at SCF and Post-SCF Levels ........... 23 1.2.2.5 Two Effects of Truncated Basis Sets ....................... 24 v 1.2.2.6 Examples of Basis Set Superposition Error ............................ 25 1.3 Counterpoise Correction (CP) Procedure ......... 27 1.3.1 Definition of the Counterpoise Method .... 27 1.3.2 Observation of Overestimation of Basis Set Superposition Error using Counterpoise Method ............... 29 1.3.3 Argument about Overestimation of Basis Set Superposition Error using Counterpoise Method ................................... 3 0 1.3.4 Pauli Principle and Overestimation of Basis set Superposition Error ............ 32 1.3.5 Current Schemes for Avoiding Overestimation of Basis Set Superposition Error ......... 33 1.3.6 A New Scheme to Eliminate Overestimation of Basis Superposition Error ............. 38 2 Theoretical Approach ............................. 40 2.1 Localized Orbital Pair Correlation Approach .... 41 2.1.1 Choice of Localized Orbitals ............ 41 2.1.2 Localized Orbital Transformation ........ 43 2.1.3 Hartree-Fock Energy ..................... 4 6 2.1.4 Second Order Pair Correlation Energy .... 49 2.1.5 Localized Orbital Pair Correlation ...... 52 2.2 Intermolecular Potential Energy Calculation .... 56 2.2.1 Energy Decomposition .................... 57 2.2.2 Intermolecular Potential Energy Calculations with Non-Counterpoise, Full-Counterpoise and Improved Counterpoise Correction ......... 64 vi 3 Computational Program ............................ 68 3.1 Computational Program Change .................... 69 3.2 Program Structure ............................. 70 4 Computational Results ............................ 73 4.1 He-He ........... 75 4.1.1 Geometry and Basis Sets ................. 75 4.1.2 Results for Hartree-Fock Calculations ... 75 4.1.3 Results for Correlation Calculations .... 76 4.1.4 Energy Component Analysis ............... 79 4.1.5 Accurate Intermolecular Energy .......... 83 4.2 H -H ......................................... 101 2 2 4.2.1 Geometry and Basis Sets ................. 101 4.2.2 Results and Discussion .................. 101 4.3 He-H ......................................... Ill 2 4.3.1 Geometry and Basis Sets ................. Ill 4.3.2 Collinear Geometry ....................... 115 4.3.3 Perpendicular Geometry .................. 120 4.3.4 Discussion .............................. 125 4.4 HLi-HLi ...... ................................. 130 4.4.1 Geometry and Basis Sets ................. 130 4.4.2 Results and Discussion .................. 131 4.5 HF-Li+, H 0-Li+, NH -Li+ and HO-He ........... 13 6 '23 2 4.5.1 Geometry and Basis Sets ................. 13 6 4.5.2 Results and Discussion about HF-Li+, H 0-Li+ and NH -Li+ ...................... 141 2 3 4.5.3 Results and Discussion about H20-He ...... 159 4.6 HF-HF and HO-HO ............................. 166 2 2 4.6.1 Geometry and Basis Sets ................. 166 4.6.2 Results and Discussion .................. 169 vii 5 Conclusion and Discussion ........................ 182 5.1 Concluding Remarks ............................. 183 5.2 Discussion of Future Wo r k ....................... 185 References .......................................... 187 Appendix ............................................ 196 Vita ................................................ 24 0 viii List of Abbreviations SCF Self-consistent field procedure for solving the Hartree-Fock equation. E Electron second order correlation energy at 2 post Hartree-Fock level calculation. MP2 Hartree-Fock calculation followed by a second order Moller-Plesset correlation energy correction. BSSE Basis set superposition error. CP Counterpoise method. FCP Full counterpoise correction method ( i.e. CP ). NCP Non counterpoise correction.