A group theoretical approach to geminal product matrix elements

Journal Article · Thu Jan 01 04:00:00 EST 1976 · J. Chem. Phys., v. 64, no. 1, pp. 6-26

DOI:https://doi.org/10.1063/1.431912· OSTI ID:4083440

Siems, W F; Poshusta, R D

Expressions enabling systematic compilation of Hamiltonian and overlap matrix elements for an antisymmetrized multiterm geminal product trial function are derived by using double coset (DC) decompositions and subgroup-adapted irreducible representations of the symmetric group, S/sub N/. The trial function may describe an even electron, atomic, or molecular system in any total spin eigenstate, and the geminals may be nonorthogonal, have arbitrary permutational symmetry, and be explicit functions of interelectronic distance. A DC decomposition is used to factor out permutations not exchanging particle labels between geminals. This reduces the sum over N-factorial permutations to a sum over DC generators. If the irreducible representation lambda (S) of S/sub N/ is adapted to S/sub n$sub 2$/, each geminal is projected into its singlet or triplet component. The DC generators are chosen such that each has the form QP, where Q permutes odd particle labels only and P is a permutation of geminals (element of the exterior pair group, S/sub n/). With the aid of matrices called DC symbols an algorithm for these generators is derived and used to find explicit sets for N=2, 4, 6, and 8. The N-electron Hamiltonian and overlap integrals arising with a particular DC generator QP are factored into products of smaller integrals, called cluster integrals, according to the cycle structure of Q. The cluster integrals are of only three main types. Matrix element compilation is systematic in that all N-electron integrals are products of a relatively small number of different types of cluster integral, and that N-electron integrals with similar factored forms are collected together in the summation. It is concluded that a geminal product calculation not using orbital expansion is feasible only for systems with eight or less electrons. (AIP)

• Research Organization: Department of Chemistry, Washington State University, Pullman, Washington 99163
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-021236
• OSTI ID: 4083440
• Journal Information: J. Chem. Phys., v. 64, no. 1, pp. 6-26, Journal Name: J. Chem. Phys., v. 64, no. 1, pp. 6-26; ISSN JCPSA
• Country of Publication: United States
• Language: English

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