This Perspective presents a survey of several issues in ab initio valence bond (VB) theory with a primary focus on recent advances made by the Xiamen VB group, including a brief review of the earlier history of the ab initio VB methods, in-depth discussion of algorithms for nonorthogonal orbital optimization in the VB self-consistent field method and VB methods incorporating dynamic electron correlation, along with a concise overview of VB methods for complex systems and VB models for chemical bonding and reactivity, and an outlook of opportunities and challenges for the near future of the VB theory.

A valence bond (VB) block-diagonalization approach, named VBBDA, is proposed to construct the charge-localized diabatic state explicitly within the framework of ab initio VB theory. Since the VB structure built upon the localized orbitals represents the charge localized character of the diabatic state faithfully, we are able to obtain accurate electronic coupling between diabatic states by using a very compact VB wave function. Moreover, the potential energy curves of the diabatic states and hence the crossing points of them can be accurately evaluated. The pilot applications showed that the electronic couplings computed by the VB method are consistent with the complete active space self-consistent field method and may even be close to the results of other high-level ab initio methods such as full configuration interaction and multireference configuration interaction. In addition, the computed electronic couplings show the expected exponential attenuation for the donor-acceptor systems as the distance increases. Moreover, VBBDA has the capability for handling complicated systems based on either two-state or multi-state treatment. Finally, because of the outstanding performance of the Xiamen Valence Bond software package, which is an ab initio VB program, VBBDA is capable for systems consisting more than 1000 basis functions.

We present a full analysis of the magnitude and orientation of the diabatic transition matrix element of a general vectorial physical observable during the adiabatic-to-diabatic transformation. The diabatic transition is a function of the adiabatic-to-diabatic transformation angle and the two basic vectors of the adiabatic states, which are the off-diagonal matrix element and the difference between the two diagonal matrix elements. To the best of our knowledge, this is the first time that the transformation has been accomplished in a more general two-dimensional scale for a vectorial physical observable. All possible extreme values of a diabatic transition are deduced for systems with different features. By using an approximate diabatic transition dipole, the pilot implementation of the analysis produces an electronic coupling curve nearly identical to that obtained by the generalized Mulliken–Hush method for the testing molecule. Evidently, this complete analysis of a diabatic transition will be very useful in determining the adiabatic-to-diabatic transformation angle by using a physical observable and can also be used to evaluate the quality of various approximations for constructing the diabatic states.

In this paper, we develop a general but very simple mathematical foundation for the predefined coefficient graphical method of Hückel molecular orbital theory (HMO). We first present the general solution for the recurrence relation of the coefficients of Hückel molecular orbitals (MOs). Subsequently, for all the three unbranched hydrocarbons, i.e., open-chain, cyclic Hückel and Möbius polyenes, different boundary conditions are explored for obtaining the MOs and their energy levels. The analytic continuation of the recurrence relation, in which one extends the domain from integral to real, allows us to analyze the symmetric properties of Hückel MOs in an elegant fashion without even knowing the actual expressions. In fact, we can use the symmetric properties to derive the Hückel MOs of the unbranched hydrocarbons and some branched hydrocarbons such as naphthalene. Consequently, this work also provides a pedagogical alternative to present the HMO model for students in an advanced physical chemistry course. Finally, the graphical approach could be a good mnemonic device for students’ comprehension of the HMO theory.

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathingorbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1 1 B 2 and 2 1 A 1 are the challenging ones. As the 1 1 A 2 , 1 1 B 1 , and 1 1 B 2 states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2 1 A 1 states and the 1 1 A 1 ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5−9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1 1 B 2 states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2 1 A 1 ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2 1 A 1 state of ozone and predicting some diradical character in the socalled "ionic" 1 1 B 2 states.