Department of Chemistry, University of Minnesota

Introduction to Gaussian functions and integral evaluation

Timothy J. Giese

Abstract:

This talk extends the previous discussions on numerical integral evaluation to analytic approaches: specifically, integrals over Gaussian-type functions. The introduction covers the following topics:
  1. Real spherical harmonics
  2. Cartesian vs. solid harmonic Gaussian functions
  3. L0-, L1-, and L2-normalization conventions
  4. Cartesian-to-solid harmonic transformation
  5. The types of integrals supported by HSERILib
  6. Introduction to DENGLib, the DENsity Gaussian Library
The recurrence relations and derivation are not covered in this introduction. For these details, consult the references below.

Reference Links:

"HSERILib (version 12/22/2006)", Timothy J. Giese, Unpublished , (2006). (See Secs. II and V and Appendices A, B, C, D, E, and F)
"Efficient recursive computation of molecular integrals over Cartesian Gaussian functions", S. Obara and A. Saika, J. Chem. Phys., 84(7), 3963-3974, (1986). [DOI]
"A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations", Martin Head-Gordon and John A. Pople, J. Chem. Phys., 89(9), 5777-5786, (1988). [DOI]
"New variations in two-electron integral evaluation in the context of direct SCF procedures", Tracy P. Hamilton and Henry F. Schaefer III, Chem. Phys., 150(2), 163-171, (1991). [DOI]