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 and nuclei, knowledge ofnnot only the first-order but also the second-order nonadiabatic couplings (NACs) is required. Here,nwe propose a method to efficiently calculate the second-order NAC from time-dependent densitynfunctional theory (TDDFT), on the basis of the Casida ansatz adapted for the computation of first-norder NAC, which has been justified in our previous work and can be shown to be valid for calcu-nlating second-order NAC between ground state and singly excited states within the Tamm-Dancoffnapproximation. Test calculations of the second-order NAC in the immediate vicinity of Jahn-Tellernand Renner-Teller intersections show that calculation results from TDDFT, combined with modifiednlinear response theory, agree well with the prediction from the Jahn-Teller/Renner-Teller models.nContrary to the diverging behavior of the first-order NAC near all types of intersection points, thenCartesian components of the second-order NAC are shown to be negligibly small near Renner-Tellernglancing intersections, while they are significantly large near the Jahn-Teller conical intersections.nNevertheless, the components of the second-order NAC can cancel each other to a large extent innJahn-Teller systems, indicating the background of neglecting the second-order NAC in practical dy-nnamics simulations. On the other hand, it is shown that such a cancellation becomes less effectivenin an elliptic Jahn-Teller system and thus the role of second-order NAC needs to be evaluated in thenrigorous framework. Our study shows that TDDFT is promising to provide accurate data of NACnfor full quantum mechanical simulation of nonadiabatic processes. © 2011 American Institute of