  Diabatization of the molecular Hamiltonian is a standard approach to removing
the singularities of nonadiabatic couplings at conical intersections of
adiabatic potential energy surfaces. In general, it is impossible to eliminate
the nonadiabatic couplings entirely -- the resulting "quasidiabatic" states are
still coupled by smaller but nonvanishing residual nonadiabatic couplings,
which are typically neglected. Here, we propose a general method for assessing
the validity of this potentially drastic approximation by comparing quantum
dynamics simulated either with or without the residual couplings. To make the
numerical errors negligible to the errors due to neglecting the residual
couplings, we use the highly accurate and general eighth-order composition of
the implicit midpoint method. The usefulness of the proposed method is
demonstrated on nonadiabatic simulations in the cubic Jahn--Teller model of
nitrogen trioxide and in the induced Renner--Teller model of hydrogen cyanide.
We find that, depending on the system, initial state, and employed
quasidiabatization scheme, neglecting the residual couplings can result in
wrong dynamics. In contrast, simulations with the exact quasidiabatic
Hamiltonian, which contains the residual couplings, always yield accurate
results.
