OPCORR: AN APPROACH TO HYBRID

           AB INITIO / SEMI-EMPIRICAL

                    CALCULATIONS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                        APPROVED:

 

                                  Supervisor:  ___________________________________

                                                       Michael J. S. Dewar

 

                                                       ___________________________________

                                                       Marye Anne Fox

 

                                                       ___________________________________

                                                       Nathan L. Bauld

 

 

 

                          Dedicated to the spirit of pragmatism

OPCORR: AN APPROACH TO HYBRID

AB INITIO / SEMI-EMPIRICAL

CALCULATIONS

 

 

by

 

 

James White Boughton,  B.S.

 

 

 

THESIS

 

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

MASTER OF ARTS

 

 

 

THE UNIVERSITY OF TEXAS AT AUSTIN

August   1990

 

ABSTRACT

 

OPCORR: AN APPROACH TO HYBRID

AB INITIO / SEMI-EMPIRICAL

CALCULATIONS

 

by

 

James White Boughton,  B.S.

 

Supervising Professor:   Michael J. S. Dewar

 

 

 

Various models for electron correlation are explored and parametrized.  These models are incorporated into a conventional ab initio treatment, giving a hybrid ab initio / semi-empirical method.  The final presented version of this approach is named OPCORR (Overlapping Probability CORRelation CORRection) and has 5 parameters.

The average magnitude of the error in the molecular zero-point electronic energies, at the 6-31G* level, has been reduced to about 0.0504 hartrees with a standard deviation of 0.0339.  The dipole moment errors are comparable to those of conventional ab initio.

 

                             Table of Contents

 

Introduction................................................................. 1

Chapter 1  -  Model Rationale...................................... 2

Requirements................................................... 2

The OPCORR Correlation Model..................... 4

Problems and Remarks..................................... 7

Chapter 2  -  OPCORR Program Particulars................ 12

Chapter 3  -  Experimental Data.................................. 16

Chapter 4  -  Parametrization....................................... 26

Linear vs. Nonlinear Problems........................ 26

Approaches to Nonlinear Optimization........... 28

Derivatives...................................................... 32

Constrained Optimization............................... 38

Other Parametrization Surfaces....................... 40

Chapter 5  -  Initial Results.......................................... 42

Superoverlap based models............................ 42

Overlap based models.................................... 50

Scaled Repulsion Integral model.................... 52

Summary of Initial Results.............................. 55

Remarks and Miscelaneous Results................ 57

Chapter 6  -  Final Results........................................... 58

Chapter 7  -  Conclusion............................................. 66

Concerning future work.................................. 66

Appendix 1  -  The Superoverlap Integral................... 69

Bibliography.............................................................. 74

 

                           List of Tables

 

 

TABLE 3.1 - Experimental and Relativistic Atomic Energies.. 17

TABLE 3.2 - 298˚ K energies.................................................. 19

TABLE 3.3 - Data for Parametrization and Test sets................ 22

TABLE 5.1 - Intra-SCF Superoverlap-Based Models............... 46

TABLE 5.2 - Intra-SCF Superoverlap-Based Models............... 47

TABLE 5.3 - Post-SCF Superoverlap-Based Models............... 48

TABLE 5.4 - Post-SCF Superoverlap-Based Models............... 49

TABLE 5.5 - Post-SCF Overlap-Based Models....................... 53

TABLE 5.6 - Post-SCF Overlap-Based Models....................... 54

TABLE 5.7  -  Comparison of Model Optimizations............... 55

TABLE 5.8  -  Comparison of Model Tests............................. 56

TABLE 6.1 - Model Optimization Record.............................. 58

TABLE 6.2 - Final Parameters................................................ 59

TABLE 6.3 -  Eexptl - Ecalc................................................... 65

TABLE 6.4 -  Dipole Moments............................................... 65

 

                       List of Figures

 

 

Figure 1.1 - Deficiencies of simple LCAO methods.................. 2

Figure 1.2 - Atomic Relativistic and Correlation Energies......... 3

Figure 1.3 - Proper intra-MO and inter-MO model effects......... 9

Figure 1.4 - Model effects with J and K corrected, OPCORR.... 9

Figure 1.5 - Model effects with only J corrected....................... 9

Figure 3.1 - Energy Accounting.............................................. 16

Figure 4.1 - Linear Least-Squares Representation.................... 27

Figure 4.2 - Representation of Nonlinear Residuals................. 27

Figure 4.3 - Nonlinear Least-Squares Representation.............. 27

Figure 6.1 - Zero-Point Energy errors  (3-21G)....................... 60

Figure 6.2 - Zero-Point Energy Errors   (6-31G)...................... 61

Figure 6.3 - Zero-Point Energy Errors   (6-31G*).................... 62

Figure 6.4 - Dipole Moments  (3-21G).................................... 63

Figure 6.5 - Dipole Moments   (6-31G)................................... 64