Nonadiabatic dynamics with intersystem crossings: A time-dependent density functional theory implementation

Abstract

In this work, we derive a method to perform trajectory-based nonadiabatic dynamics that is able to describe both nonadiabatic transitions and intersystem crossing events (transitions between states of different spin-multiplicity) at the same level of theory, namely, time-dependent density functional theory (TDDFT). To this end, we combined our previously developed TDDFT-based trajectory surface hopping scheme with an accurate and efficient algorithm for the calculation of the spin-orbit coupling (SOC) matrix elements. More specifically, we designed two algorithms for the calculation of intersystem crossing transitions, one based on an extended Tully's surface hopping scheme including SOC and the second based on a Landau-Zener approximation applied to the spin sector of the electronic Hilbert space. This development allows for the design of an efficient on-the-fly nonadiabatic approach that can handle, on an equal footing, nonadiabatic and intersystem crossing transitions. The method is applied to the study of the photophysics of sulfur dioxide (SO2) in gas and liquid phases.

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics

“…168 For this reason, in the last few years, the incorporation of SOC into NA-MQC schemes to simulate intersystem crossing (ISC) dynamics has become an active area of research. 129,[169][170][171][172][173][174] In NA-MQC, SOC is usually included by considering the coupling term Granucci and Persico have shown, however, that the spin-diabatic representation poses some severe challenges to control the SOC phases during the dynamics, which usually results in wrong hopping probabilities. 172 In contrast, these problems are not present if dynamics is propagated in a spin-adiabatic (sa) representation ( Fig.…”

“…Several investigations in this field worked the spin-diabatic (sd) representation, where the electronic wavefunctions are spin-eigenstates 115,171,173,[175][176][177]. (This spin-diabatic representation is simply the conventional adiabatic representation commonly used in quantum chemistry; seeFig.…”

Evaluation of Spin-Orbit Couplings with Linear-Response Time-Dependent Density Functional Methods

“…39,40 , while those using approximate CI-like wave functions, either based on Casida's 41 or Sternheimer's 42,43 formalism, are discussed in Refs. [44][45][46] . In the framework of the X2C Hamiltonian, spin-adapted TDDFT has been combined with a perturbational SOC treatment to evaluate the fine-structure splittings of excited states of open-shell systems 47 .…”

Surface hopping dynamics including intersystem crossing using the algebraic diagrammatic construction method

“…Among the single-reference electronic structure methods, so far only time-dependent density functional theory (TDDFT) has been applied for ISC-focused dynamics simulations. 34,51 Although here computational efficiency and dynamical correlation are in principle given, in TDDFT the choice of the appropriate exchange-correlation functional can strongly affect the quality of the results.…”