A Density Functional Valence Bond Study on the Excited States

The accurate description of excited states is crucial for the development of electronic structure theory. In addition to determining excitation energies, strong state interactions arise when electronic states with the same symmetry are degenerate or nearly degenerate, often requiring a multi-state treatment. These strong correlation effects and state interactions can be effectively handled by the Hamiltonian matrix correction-based density functional valence bond (hc-DFVB) method, a multi-reference density functional theory capable of accurately describing electronic state interactions. In this paper, we explore the low-lying excited states of four isoelectronic systems (C2H, CN, CO+, BO) using valence bond methods, including the valence bond self-consistent field (VBSCF) and hc-DFVB methods. Our results show that the hc-DFVB method provides significantly better excitation energies compared to VBSCF. Furthermore, hc-DFVB can reliably predict the correct ordering of excited states, whereas VBSCF shows some ordering inconsistencies. By categorizing the VB structures into groups based on point group symmetry, we can extract the key structural contributions and bonding pictures of each state from the weight distribution of these groups. Additionally, we study the potential energy curves for lithium fluoride (LiF) and a mixed-valence spiro cation, demonstrating the superior performance of hc-DFVB when applied to the study of near-degenerate excited states in the avoided crossing region.