N-Body Reduced Density Matrix-Based Valence Bond Theory and Its Applications in Diabatic Electronic-Structure Computations

Abstract

Valence bond (VB) theory, as a helpful complement to the more popular molecular orbital theory, is a fundamental electronic-structure theory that aims at interpreting molecular structure and chemical reactions in a lucid way. Both theoretical and experimental chemists have shown great interest in VB theory because of its capability of providing intuitive insight into the nature of chemical bonding and the mechanism of chemical reaction in a clear and comprehensible language rooted in Lewis structure. Therefore, there is a great call for the renaissance of VB theory. Nevertheless, this is possible only after a series of methods and algorithms were developed and efficiently implemented in user-friendly programs so as to serve computational chemists for general applications. In the past three decades, we have devoted a great amount of scientific enthusiasm toward this goal. In this Account, we will concisely summarize and briefly but insightfully discuss recent developments in ab initio VB theory, especially the N-body reduced density matrices (RDM)-based approach and its applications in diabatic electronic-structure computations, which is very useful for the vivid interpretation of many fundamental chemical processes such as electron and energy transfers. Furthermore, because of the fundamentally important role that the diabatic state plays in electron and energy transfers, which are two frontier research topics in both molecular and biochemical sciences, there are a broad range of applications that VB theory can handle.We start by briefly reviewing the general feature of ab initio VB wave functions. In particular, we focus on the multistructural ab initio VB theory that uses strictly localized orbitals, including the fundamental VB self-consistent field (VBSCF) and two post-SCF methods, VBCI and VBPT2, that use the VBSCF wave function as reference. We then allot a section to describing the recent developments of the RDM-based VB approach in the second quantization language. In this section, the enhanced Wick theorem is first outlined, followed by a brief discussion of its applications in evaluating VBSCF energy gradients and a Hessian with respect to the orbital expansion coefficients, together with a short review of the implementation of an automatic formula and code generator (AFCG) designed for many-body methods with nonorthogonal orbitals. Then, we introduce the application of the RDM-based approach in implementing the post-SCF method that addresses dynamic electronic correlation via perturbation theory, viz., the icVBPT2 method that adopts an internal contraction technique naturally. We finish this section by incorporating VB theory with the concept of seniority number, in which the tensor analysis technique is carefully exploited with the RDM-based approach, resulting in significant improvements in both the number of the active electrons/orbitals and in the speedup of the computational efficiency, thus pushing VB theory to its new limit. With these achievements available, we present the applications of VB theory in diabatic electronic-structure computations by using the intuitive insight rendered by VB theory. Therefore, we believe that there is a bright future in VB theory with true opportunities and new challenges coexisting both for theoretical developments and computational applications.