NAC-TDDFT: Time-dependent density functional theory for nonadiabatic couplings

TL;DR

This paper critically analyzes various NAC-TDDFT methods for calculating nonadiabatic couplings, concluding that the equation of motion-based variant is the most appropriate, and discusses future improvements.

Contribution

It provides a clear analysis of NAC-TDDFT variants, identifying the equation of motion-based approach as the most suitable for nonadiabatic coupling calculations.

Findings

Equation of motion-based NAC-TDDFT is the preferred method.

Critical comparison of NAC-TDDFT variants.

Guidelines for implementation and future development.

Abstract

First-order nonadiabatic coupling matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice. However, the lack of wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. The present account aims to analyze the available variants of NAC-TDDFT in a critical but concise manner and meanwhile point out the proper ways for implementation. It can be concluded, from both theoretical and numerical points of view, that the equation of motion-based variant of NAC-TDDFT is the right choice. Possible future developments of this variant are also highlighted.