Abstract
Diabatization of the molecular Hamiltonian is a standard approach to remove 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.
Highlights
The celebrated Born–Oppenheimer approximation,1 which treats the electronic and nuclear motions in molecules separately, is no longer valid for describing processes involving two or more strongly vibronically coupled electronic states
We have shown that the common practice of neglecting the residual nonadiabatic couplings between quasidiabatic states can substantially lower the accuracy of nonadiabatic simulations and that the decrease in accuracy depends on the system, initial state, and employed quasidiabatization scheme
Because it is potentially dangerous to employ an approximation without evaluating its impact, we have proposed a method to rigorously quantify the errors caused by ignoring the residual couplings
Summary
The celebrated Born–Oppenheimer approximation, which treats the electronic and nuclear motions in molecules separately, is no longer valid for describing processes involving two or more strongly vibronically coupled electronic states. We propose a general method that quantifies the importance of the residual couplings by comparing nonadiabatic simulations performed either with the exact quasidiabatic Hamiltonian—. For a valid comparison, one needs a time propagation scheme that can treat even the nonseparable exact quasidiabatic Hamiltonian and that ensures that the numerical errors are negligible to the errors due to neglecting the residual couplings. To find out how the errors due to ignoring the residual couplings depend on the sophistication of the quasidiabatization and on the initial state, in Sec. III C, we compare the first- and second-order regularized diabatization schemes on the model of a displaced excitation of NO3
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