Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules

The (time-independent)
Schrödinger equation for
atomistic
systems is solved by using the adiabatic potential energy curves (PECs)
and the associated adiabatic approximation. In cases where interactions
between electronic states become important, the associated nonadiabatic
effects are taken into account via derivative couplings (DDRs), also
known as nonadiabatic couplings (NACs). For diatomic molecules, the
corresponding PECs in the adiabatic representation are characterized
by avoided crossings. The alternative to the adiabatic approach is
the diabatic representation obtained via a unitary transformation
of the adiabatic states by minimizing the DDRs. For diatomics, the
diabatic representation has zero DDR and nondiagonal diabatic couplings
ensue. The two representations are fully equivalent and so should
be the rovibronic energies and wave functions, which result from the
solution of the corresponding Schrödinger equations. We demonstrate
(for the first time) the numerical equivalence between the adiabatic
and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride
(CH) as examples of two-state systems, where YO is characterized by
a strong NAC, while CH has a strong diabatic coupling. Rovibronic
energies and wave functions are computed using a new diabatic module
implemented in the variational rovibronic code Duo. We show
that it is important to include both the diagonal Born–Oppenheimer
correction and nondiagonal DDRs. We also show that the convergence
of the vibronic energy calculations can strongly depend on the representation
of nuclear motion used and that no one representation is best in all
cases.