The Breathing-Orbital Valence Bond Method: A VB Method That Includes Dynamic Electron Correlation

The article outlines the principles and achievements of the Breathing Orbital Valence Bond method (BOVB), which describes electronic states in terms of Lewis structures, including covalent and ionic structures. BOVB combines good numerical accuracy with a lucid interpretability and compactness of the classical valence bond method. This is achieved by optimizing simultaneously the orbitals and coefficients of the valence bond configurations, while allowing each configuration to have its own specific set of orbitals. As such, the BOVB wave function includes dynamic electron correlation, on top of the static correlation, without increasing the number of configurations. BOVB leads to accurate calculations of bonding energies, weights of Lewis structures, resonance energies, measures of diradical character, etc. New concepts are generated, such as charge-shift bonding, an improved Rundle-Pimentel model for hypervalent molecules, insights into 1,3-dipolar cycloadditions, etc. The article also describes recent developments for excited states, which enable BOVB to produce accurate transition energies in notoriously challenging cases, thus showing that an ab-initio classical valence bond method can be as accurate as standard ab initio molecular orbital based methods like full-valence CASSCF-MRCISD, while being much faster. Future applications will include photochemical reactions.