  The (stationary) Schr\"{o}dinger equation for atomistic systems is solved
using the adiabatic potential energy curves (PECs) and the associated adiabatic
approximation. Despite being very simplistic, this approach is very powerful
and used in nearly all practical applications. In cases when interactions
between electronic states become important, the associated non-adiabatic
effects are taken into account via the derivative couplings (DDRs), also known
as non-adiabatic 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 non-diagonal
diabatic couplings (DCs) ensue. The two representations are fully equivalent
and so should be the rovibronic energies and wavefunctions which result from
the solution of the corresponding Schr\"{o}dinger 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 wavefunctions are computed
using a new diabatic module implemented in variational rovibronic code DUO. We
show that it is important to include both the Diagonal Born-Oppenheimer
Correction (DBOC) and non-diagonal DDRs. We also show that 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.
