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Four‐center Slater‐type orbital molecular integrals without orbital translations
Author(s) -
Hoggan Philip E.
Publication year - 2010
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/qua.22213
Subject(s) - slater type orbital , atomic orbital , slater integrals , orbital overlap , sto ng basis sets , exponential type , molecular orbital , physics , quantum mechanics , molecular orbital theory , linear combination of atomic orbitals , type (biology) , cubic harmonic , coulomb , basis set , electron , mathematics , mathematical analysis , molecule , ecology , biology
Abstract This article advocates the use of atomic orbitals which have direct physical interpretation, i.e., hydrogen‐like orbitals. They are exponential‐type orbitals (ETOs). Convenient nodeless linear combinations are used, namely Slater‐type orbitals (STOs), with a product of a single power of r and an exponential as radial factor. Until 2008, such orbital products on different atoms were difficult to manipulate for the evaluation of two‐electron integrals. The difficulty was mostly due to cumbersome orbital translations involving slowly convergent infinite sums. These are completely eliminated using Coulomb resolutions. They provide an excellent approximation that reduces these integrals to a sum of one‐electron overlap‐like integral products that each involve orbitals on at most two centers. Such two‐center integrals are separable in prolate spheroidal coordinates. They are thus readily evaluated. Only these integrals need to be re‐evaluated to change basis functions. The above is still valid or three‐center integrals. In four‐center integrals, the resolutions require translating one potential term per product. This is outlined here and detailed elsewhere. Numerical results are reported for the H 2 dimer. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010