Ab initio Valence Bond Theory with Density Functional

The accurate description of strongly correlated systems, also known as multireference systems, requires a balanced treatment of static and dynamic correlations and is an important target for developing quantum chemical methods. An appealing treatment to economically describe strongly correlated systems is the multireference density function theory (MRDFT) approach, in which the static correlation is included in the multiconfigurational wave function, while the density function includes the dynamic correlation. This mini-review focuses on the recent progress and applications of the density functional methods based on valence bond theory. A series of density functional valence bond (DFVB) methods are surveyed, including the dynamic correlation correction-based and Hamiltonian matrix correction-based DFVB methods, the hybrid one-parameter DFVB methods, the block-localized density functional theory and the multistate density functional theory. These methods have been applied to various chemical and physical property calculations of strongly correlated systems, including resonance energies, potential energy curves, spectroscopic constants, atomization energies, spin state energy gaps, excitation energies, and reaction barriers. Most of the test results show that the density functional methods based on VB theory give comparable accuracy but require lower computational cost than high-level quantum computational methods and thus provide a promising strategy for studying strongly correlated systems.