On quantifying the vibronic interaction between electronic states

An accurate estimation of the interstate vibronic coupling strength is of particular relevance for the treatment of nonadiabatic dynamics. This is not a trivial task because direct interactions between electronic states have to be separated from intrinsic frequency shifts. Surprisingly, this issue has not been discussed in detail in the literature so far. An analysis of the error dependence is given for two formulas derived from linear vibronic coupling theory. The difficulty in estimating the interstate coupling parameters is shown to originate from the initially unknown contribution of the diagonal quadratic coupling coefficients to the total vibronic coupling. An interpretation of the error analysis including a numerical case study is followed by a more general discussion of the different mechanisms that can shape adiabatic electronic potential energy functions. Qualitative criteria are formulated for the differentiation between interstate and intrastate vibronic coupling effects based on electronic structure information. These ideas are then applied to investigate vibronic coupling problems in pyrazine as well as trans- and cis-hexatriene.