Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. II. An efficient algorithm for matrix elements and analytical energy gradients in VBSCF method

In this paper, by applying the reduced density matrix (RDM) approach for nonorthogonal orbitals developed in the first paper of this series, efficient algorithms for matrix elements between VB structures and energy gradients in valence bond self-consistent field (VBSCF) method were presented. Both a...

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Vydáno v:The Journal of chemical physics Ročník 138; číslo 16; s. 164120
Hlavní autoři: Chen, Zhenhua, Chen, Xun, Wu, Wei
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States 28.04.2013
Témata:
Algorithms
Butadienes - chemistry
Ethylenes - chemistry
Quantum Theory
ISSN:1089-7690, 1089-7690
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Shrnutí:In this paper, by applying the reduced density matrix (RDM) approach for nonorthogonal orbitals developed in the first paper of this series, efficient algorithms for matrix elements between VB structures and energy gradients in valence bond self-consistent field (VBSCF) method were presented. Both algorithms scale only as nm(4) for integral transformation and d(2)n(β)(2) for VB matrix elements and 3-RDM evaluation, while the computational costs of other procedures are negligible, where n, m, d, and n(β )are the numbers of variable occupied active orbitals, basis functions, determinants, and active β electrons, respectively. Using tensor properties of the energy gradients with respect to the orbital coefficients presented in the first paper of this series, a partial orthogonal auxiliary orbital set was introduced to reduce the computational cost of VBSCF calculation in which orbitals are flexibly defined. Test calculations on the Diels-Alder reaction of butadiene and ethylene have shown that the novel algorithm is very efficient for VBSCF calculations.
Bibliografie:ObjectType-Article-1
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ISSN:1089-7690
1089-7690
DOI:10.1063/1.4801632