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Direct quantum chemical integral evaluation
Author(s) -
Dunlap Brett I.
Publication year - 2001
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/1097-461x(2001)81:6<373::aid-qua1007>3.0.co;2-3
Subject(s) - gaussian , exponential type , exponential function , mathematics , invariant (physics) , exponent , quantum , product (mathematics) , multiple integral , physics , mathematical analysis , quantum mechanics , pure mathematics , geometry , linguistics , philosophy
Performing quantum chemical integral evaluation directly, without recursion and without direct coupling of angular momenta according to the rotation group is analyzed. The rotation group limits the structure of these closed‐form expressions. The result of all cross differentiation is a rotational invariant. Closed‐form expressions are obtained for the general three‐ and four‐center Gaussian integral. The solid harmonic addition formula can be used to express these integrals as sums of products of an exponent‐independent (angular) factor and a molecular‐orientation‐independent (exponential) factor in a variety of ways. The results are products of two such factors summed over the set of distinct, relevant polynomials of the exponents. The coefficients of these polynomials, angular factors, are complicated but common to all n ‐center matrix elements and independent of any type of contraction. Derivatives must be obtained using the product rule. An implementation in the Solid Spherical Harmonic Gaussian (SSHG) computer code is outlined and preliminary comparison is made. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 373–383, 2001