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An application of perturbation theory ideas in configuration interaction calculations
Author(s) -
Gershgorn Z.,
Shavitt I.
Publication year - 1968
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.560020603
Subject(s) - wave function , excitation , diagonal , exponential function , configuration interaction , excited state , perturbation theory (quantum mechanics) , basis function , basis (linear algebra) , full configuration interaction , perturbation (astronomy) , physics , function (biology) , quantum mechanics , statistical physics , mathematical analysis , mathematics , geometry , evolutionary biology , biology
Configuration interaction calculations of electronic wave functions for atoms and molecules have generally been limited to relatively small basis sets because of the exponential increase in the number of configurations as basis functions are added. While higher than quadruply excited configurations are of negligible importance in CI wave functions, it is shown that the effect of triple and quadruple excitation configurations can be substantially included even when the matrix elements between such configurations are neglected, leaving only their diagonal elements and the elements connecting them with the single and double excitations. This approximation is seen to be formally practically equivalent to a first‐order perturbation expression for the wave function (second‐order for the energy) based on an optimum linear combination of the zero, single, and double excitation configurations as the zero‐order function. If suitable procedures are used, the amount of computational effort involved in such a calculation is roughly proportional to the fourth power of the number of basis functions employed, thus preventing the CI stage of the calculation from increasing in magnitude much faster than the stages involving the calculation and manipulation of the elementary integrals.