The State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China.
J Chem Phys. 2013 Apr 28;138(16):164120. doi: 10.1063/1.4801632.
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.
本文应用了本系列第一篇论文中提出的非正交轨道的约化密度矩阵（RDM）方法，提出了 VB 结构与价键自洽场（VBSCF）方法中能量梯度之间矩阵元的有效算法。这两种算法的积分变换仅为 nm(4)，VB 矩阵元的计算和 3-RDM 评估为 d(2)n(β)(2)，而其他步骤的计算成本可以忽略不计，其中 n、m、d 和 n(β)分别是变分占据活性轨道、基函数、行列式和活性β电子的数量。利用本系列第一篇论文中提出的关于轨道系数的能量梯度张量性质，引入了部分正交辅助轨道集，以降低 VBSCF 计算中灵活定义轨道的计算成本。对丁二烯和乙烯的 Diels-Alder 反应的测试计算表明，该新算法对于 VBSCF 计算非常有效。
