Both the efficiency and capability of the seniority number truncated valence bond (VB) methods are highly improved by using our recently proposed extension of Malmqvist’s algorithm for the reciprocal transformation of many-electron bases constructed by nonorthogonal orbitals [Zhou, Chen, and Wu, J. Chem. Phys. 149(4), 044111 (2018)] and by the adoption of the direct technique in solving the generalized eigenvalue problem. Due to the compactness of the wave function that benefited from seniority number restriction, the memory need and computational cost for energy evaluation and orbital optimization in valence bond self-consistent field calculation are largely reduced. The last obstacle in nonorthogonal orbital based ab initio VB calculation is thus removed. Consequently, we can accomplish seniority number truncated VB calculation at the same computational scaling as that of the most general configuration selected multiconfigurational self-consistent field with a memory cost much less than the corresponding complete active space self-consistent field (CASSCF). Test on Hn string molecules shows that the seniority number truncated VB calculation maintains the majority of static correlation by using a more compact wave function than CASSCF.

No abstract

No abstract

No abstract

Implementing deep neural networks for learning the solution maps of parametric partial differential equations (PDEs) turns out to be more efficient than using many conventional numerical methods. However, limited theoretical analyses have been conducted on this approach. In this study, we investigate the expressive power of deep rectified quadratic unit (ReQU) neural networks for approximating the solution maps of parametric PDEs. The proposed approach is motivated by the recent important work of G.