First-order derivative couplings between excited states from adiabatic TDDFT response theory

Abstract

We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation

“…Simulations including several excited states and all nonadiabatic couplings between them have been reported, but rely on approximations with questionable validity such as the neglect of orbital relaxation 17,19,[28][29][30][31][32] or single Slater determinant models for the excited state. A rigorous theoretical approach to general couplings between excited states in the TDDFT framework has only recently been devised, [33][34][35] but little is known about its performance in photochemical applications.…”

Charge transfer in time-dependent density functional theory

“…Non-adiabatic couplings between the ground and excited states can be extracted from linear response theory, but those between excited states cannot be. They are available from quadratic response theory but recently it was shown that the adiabatic approximation yields unphysical divergences when the difference between the energies of the two excited states equals a ground-to-excited excitation energy [113][114][115][116][117].…”

Excited-state dynamics of molecules with classically driven trajectories and Gaussians

“…LR-TDDFT, within the adiabatic approximation for the exchange-correlation kernel [61], can fail to describe electronic states with a charge-transfer character [80][81][82][83][84][85][86], conical intersections between the ground and first excited state [87], electronic states with double-excitation character [87][88][89][90][91], and can formally only be used to describe ground-to-excited-state quantities like nonadiabatic coupling vectors [92][93][94][95][96][97][98][99] (or spin-orbit coupling matrix elements [100]), even if linear-response theory already offers a good approximation [101] (quadratic response theory can be used but unstable within the adiabatic approximation [99,102,103]). Different benchmarks of LR-TDDFT and exchange/correlation functionals for the description of electronic energies have been proposed in the literature (see , e.g.…”