Nonadiabatic couplings from time-dependent density functional theory. II. Successes and challenges of the pseudopotential approximation

Abstract

We present extensive calculations of nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, using time-dependent density functional theory (TDDFT) within (modified) linear response [C. Hu et al. J. Chem. Phys. 127, 064103 (2007)]. Our approach is implemented in the pseudopotential framework, with the consideration of nonlinear core corrections. The features of either the ordinary Jahn-Teller conical intersections in X(3) (X=Li, Na, K, Cu, Ag, Au) trimers, or the elliptic Jahn-Teller conical intersections in NaH(2), have been well reproduced. In particular, anticipated results for the H-H(2) collision near the avoided crossing are obtained, showing appealing improvement over the first, real-time, TDDFT calculation. The other important type of intersections, Renner-Teller glancing intersection, has also been studied for several typical molecular systems (BH(2), AlH(2), CH(2)(+), SiH(2)(+)), giving results in reasonable agreement with the theoretical model. Despite these successes, it is found that for some systems, including both Jahn-Teller and Renner-Teller systems, the pseudopotential scheme might give inaccurate results for some NAC components on nonhydrogen atoms. By trying different construction schemes of pseudopotentials, e.g., using local pseudopotentials, the results of NACs are found scheme-dependent and show improvement for some cases. Since there is much freedom in constructing ab initio nonlocal pseudopotentials, our findings on TDDFT calculation of NACs in the pseudopotential scheme might be helpful to give clues for constructing more "realistic" pseudopotentials.

Excited-state nuclear forces on adiabatic potential-energy surfaces by time-dependent density-functional theory

“…The Casida-ansatz forces are also different from the ND values, and the differences become smaller when approaching the zero point, which is the same for all cases. In an analogous way, the accuracy problem for the first-order NAC is also reported by Hu et al [37]. They found that the sum rule for NAC vectors [42] from the h-matrix formulations is not satisfied when nonhydrogen atoms are involved.…”

“…Extrapolation of the APES indicates that the Renner-Teller glancing intersection point is located at the linear geometry [corresponding to y = 0 in Fig. 3(a)], as shown in a previous study [37]. Figure 3(c) represents the calculated y-direction forces on the Si atom.…”

Trajectory‐Based Nonadiabatic Dynamics with Time‐Dependent Density Functional Theory

“…This equation was derived by Casida [54] and then applied by Tavernelli et al [14,156,157] and Hu et al [214,215] for the calculation of the NAC vectors between the ground state and an excited state. A similar equation was also given in ref.…”

Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance

“…30 Since the publication of Ref. 28, several competing methods have been developed along similar lines, [31][32][33][34][35][36][37][38][39][40] only some of which have employed an atom-centered basis. The Gaussian-basis implementation of the method of Hu et al includes Pulay terms associated with the one-electron integrals.…”