The multifacet graphically contracted function method. I. Formulation and implementation

Journal Article · Thu Aug 14 04:00:00 EDT 2014 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4890734· OSTI ID:22420011

Shepard, Ron; Brozell, Scott R. ^[1]; Gidofalvi, Gergely ^[2]

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1. Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
2. Department of Chemistry and Biochemistry, Gonzaga University, 502 E. Boone Ave., Spokane, Washington 99258-0102 (United States)

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N{sup 2}n{sup 4}) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N{sub 2} dissociation, cubic H{sub 8} dissociation, the symmetric dissociation of H{sub 2}O, and the insertion of Be into H{sub 2}. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.

• OSTI ID: 22420011
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 6 Vol. 141; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
DENSITY MATRIX
DISSOCIATION
ELECTRONIC STRUCTURE
ELECTRONS
HAMILTONIANS
KERNELS
SLATER METHOD
SPIN