Second-order nonadiabatic couplings from time-dependent density functional theory: Evaluation in the immediate vicinity of Jahn-Teller/Renner-Teller intersections

摘要

For a rigorous quantum simulation of nonadiabatic dynamics of electrons andnuclei, knowledge of not only first-order but also second-order nonadiabaticcouplings (NAC), is required. Here we propose a method to efficiently calculatesecond-order NAC from time-dependent density functional theory (TDDFT), on thebasis of the Casida ansatz adapted for the computation of first-order NAC,which has been justified in our previous work and can be shown to be valid forcalculating second-order NAC between ground state and singly excited stateswithin the Tamm-Dancoff approximation. Test calculations of second-order NAC inthe immediate vicinity of Jahn-Teller and Renner-Teller intersections show thatcalculation results from TDDFT, combined with modified linear response theory,agree well with the prediction from the Jahn-Teller / Renner-Teller models.Contrary to the diverging behavior of first-order NAC near all types ofintersection points, the Cartesian components of second-order NAC are shown tobe negligibly small near Renner-Teller glancing intersections, while they aresignificantly large near the Jahn-Teller conical intersections. Nevertheless,the components of second-order NAC can cancel each other to a large extent inJahn-Teller systems, indicating the background of neglecting second-order NACin practical dynamics simulations. On the other hand, it is shown that such acancellation becomes less effective in an elliptic Jahn-Teller system and thusthe role of second-order NAC needs to be evaluated in the rigorous framework.Our study shows that TDDFT is promising to provide accurate data of NAC forfull quantum mechanical simulation of nonadiabatic processes.