SGA derivation of matrix elements between spin-adapted perturbative wave functions

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The symmetric group approach (SGA) is used to derive formulas for the Hamiltonian matrix elements between perturbatively generated, highly contracted configuration state functions (CSF). The first-order Moller–Plesset, Epstein–Nesbet, and Krylov corrections are examples of such CSFs. They have been recently employed within the superdirect configuration interaction (Sup-CI) method, which combines the efficiency and simplicity of the many-body perturbation theory (MBPT) with the robustness of variational methods. The linear Sup-CI expansion in terms of such perturbative correction functions leads to a problem of efficient evaluation of matrix elements of the third power of the Hamiltonian in the usual CSFs. Using SGA and previously developed algebra of unitary group generators and circular operators one may express such matrix elements, similarly to MBPT, in terms of sums of product of two-electron integrals. Maple code enhancing greatly the algebraic manipulations has been developed and is available upon request. All the main steps in the derivation are discussed and the formulas are given in a compact form. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 123–133, 1999

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