Calculating excited states properties and transition energies can be a tough task with MO-CI methods, even for small molecules. The difficulties that are encountered are of two kinds: (i) if the ground and excited states are of different symmetries, state-specific calculations can be performed, but it is essential that the correlation energies be calculated in a balanced way for both states. This can be difficult when the two states have very different demands of dynamic electron correlation, e.g., with ionic excited states displaying a lot of dynamic charge fluctuation. (ii) If the two states are of like symmetry, a state-averaged treatment is required, but the accuracy is penalized by the necessity for both states to share the same orbital set, which is a compromise that cannot be optimal for either of the two states.
These two difficulties are resolved by the breathing-orbital valence bond method (BOVB), which exerts a direct approach to both static and dynamic electron correlations, made possible by the freedom to deal with non-orthogonal orbitals. The dynamic correlation is fully included right at the orbital optimization step, by allowing each VB structure to have its specific set of orbitals.
For the excited states having the same symmetry as the ground state, the state-averaged BOVB method has the unique advantage to be free from the constraint for the different states to share the same unique set of orbitals.
The ability of the BOVB method to describe excited states and to compute accurate transition energies from the ground state is tested on the challenging 1¹B_1u ionic state of ethylene, and to the five lowest-lying singlet states of ozone and sulfur dioxide, among which the challenging 1¹B₂ and 2¹A₁states. 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 orbital framework, despite the extreme compactness of the BOVB wave functions, made of no more than 4-9 valence bond structures in all cases, vs. up to 350 million configurations in valence-CASSCF-MRCISD calculations for ozone and sulfur dioxide. Finally, the description of the excited states is insightful and displays some important, albeit unexpected, Lewis structures.

Wei Wu

Appearances