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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.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

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