Molecular integrals evaluated over contracted Gaussian functions by using auxiliary contracted hyperGaussian functions
Abstract
General recurrence formulas for evaluating molecular integrals over contracted Cartesian Gaussian functions are derived by introducing auxiliary contracted hyperGaussian (ACH) functions. By using a contracted Gaussian function, this ACH represents an extension of the Gaussian function named derivative of Fourierkernel multiplied Gaussian [J. Chem. Phys. 94, 3790 (1991)]. The ACH is reducible to contracted Cartesian Gaussian functions, contracted modified Hermite Gaussian functions, and to contracted Gaussian functions multiplied by phase factors, or the socalled GIAO, and is also reducible to various spatial operators necessary for ab initio molecular orbital calculations. In our formulation, all molecular integrals are expressed in terms of ACH. Therefore, the formulations have wide applicability for calculating various kinds of molecular integrals in ab initio calculations. Recursive calculations based on our formulation do not depend on the number of contraction terms, because the contraction step is completed at the evaluation of the initial integrals. Therefore, we expect that more efficient recursive calculations will be accomplished by using our formulas for evaluating molecular integrals over contracted Gaussian functions.
 Publication:

Journal of Chemical Physics
 Pub Date:
 July 2002
 DOI:
 10.1063/1.1485958
 Bibcode:
 2002JChPh.117.1457H
 Keywords:

 integration;
 orbital calculations;
 ab initio calculations;
 Cartesian Coordinates;
 Orbit Calculation;
 31.15.p;
 Atomic and Molecular Physics;
 Calculations and mathematical techniques in atomic and molecular physics