Vibronic coupling calculations made quantitative

John F. Stanton,1 Takatoshi Ichino1

1Institute of Theoretical Chemistry, University of Texas at Austin, Austin, TX 78712

The vibronic coupling model introduced by Köppel, Domcke and Cederbaum (KDC) in the seventies has been extremely successful in the identification and analysis of non-adiabatic effects in spectroscopy and chemical dynamics. In its most frequent mode of application, known as the “linear vibronic coupling” (LVC) model, an electronically quasidiabatic basis is used. The nuclear kinetic energy operator is then assumed to be diagonal, and the potential matrix is based on the assumption that the diabatic states behave as harmonic oscillators with a coupling that is linear in the coordinates. Such a model captures the essential qualitative physics for the majority of vibronic coupling problems and has been used by our group to treat NO3, for example.

If one attempts to achieve quantitative accuracy, the LVC model is not sufficient. While including quadratic coupling terms in the so-called QVC model has been done long ago, calculations with this approach are rather more scarce than with the LVC approximation. In addition, the parametrization of such a model from ab initio calculations is less straightforward than it is for the LVC approach. In recent work, we have done three things to improve the quantitative accuracy of the KDC treatment:

  1. We have introduced the so-called “adiabatic parametrization” in which the adiabatic potential energy surfaces obtained via diagonalization of the model Hamiltonian coincide (to some order) with the ab initio surfaces at the position of the final state minima. This is slightly different from the usual practice where the region of coincidence is chosen to be that of the vertical geometry.
  2. An ansatz for quasidiabatic states has been made within the framework of equation-of-motion coupled cluster theory (EOM-CC). This allows the precise analytical calculation of the vibronic coupling constants, a vast improvement over fitting procedures based on two-state models. It also allows the coordinate dependence of the coupling constants to be determined in a straightforward way.
  3. The totally symmetric diabatic potentials, which (due to the ansatz above) are coincident with the adiabatic surfaces, are treated by a quartic Taylor series expansion.

Application of this more sophisticated model to the very simple BNB system is presented; eigenvalues of the vibronic Hamiltonian are generally within 10-20 cm-1 of experimental level positions. Agreement for HCO2 and its deuterated isotopologue is even better, and has allowed the complicated SEVI spectrum of Neumark and co-workers to be unambiguously assigned. Finally, the question “if I did a full CI calculation in an infinite basis set and calculated the vibrational levels with an exact variational treatment of the potential surface from the perfect ab initio calculations, how accurate would it be?” is discussed in the context of strongly coupled molecular systems.