Vibronic Coupling - Difficulties and Alternatives

Difficulties and Alternatives

Although crucial to the understanding of nonadiabatic processes, direct evaluation of vibronic couplings has been very limited.

Evaluation of vibronic couplings is often associated with severe difficulties in mathematical formulation and program implementations. As a result, the algorithms to evaluate vibronic couplings are not yet implemented in many quantum chemistry program suits.

The evaluation of vibronic couplings also requires correct description of at least two electronic states in regions where they are strongly coupled. This requires the use of multi-reference methods such as MCSCF and MRCI, which are very expensive and delicate methods. This is further complicated by the fact that definition of vibronic couplings requires electronic wavefunctions. Unfortunately, wavefunction based methods are usually too expensive for larger systems and popular methods for larger systems such as density functional theory and molecular mechanics cannot generate wave function information. As a result, direct evaluation of vibronic couplings are mostly limited to very small molecules. The magnitude of vibronic coupling is often introduced as an empirical parameter determined by reproducing experimental data.

Alternatively, one can avoid explicit use of derivative couplings by switch from the adiabatic to the diabatic representation of the potential energy surfaces. Although rigorous validation of a diabatic representation requires knowledge of vibronic coupling, it is often possible to construct such diabatic representations by referencing the continuity of physical quantities such as dipole moment, charge distribution or orbital occupations. However, such construction requires detailed knowledge of a molecular system and introduces significant arbitrariness. Diabatic representations constructed with different method can yield different results and the reliability of the result relies on the discretion of the researcher.