First-order nonadiabatic couplings in extended systems by time-dependent density functional theory

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Nonadiabatic couplings (NAC) are crucial for understanding molecular dynamics and chemical reactions.
• Accurate calculation of NAC is computationally demanding, especially for extended systems.
• Existing methods often rely on approximations or are limited in scope.

Purpose of the Study:

• To develop a rigorous ab initio formulation for calculating first-order nonadiabatic couplings (NAC).
• To enable accurate nonadiabatic molecular dynamics in extended systems.
• To overcome limitations of previous formulations, particularly concerning Kohn-Sham virtual orbitals and derivative calculations.

Main Methods:

• Utilizing time-dependent density functional theory (TD-DFT) with planewave bases and projector augmented-wave pseudopotentials.
• Employing hybrid exchange-correlation functionals for enhanced accuracy.
• Deriving analytic expressions for NAC matrix elements using linear and quadratic time-dependent response theory.
• Introducing Lagrangian functionals to circumvent expensive derivative calculations of Kohn-Sham orbitals.

Main Results:

• A novel formulation for rigorous calculation of first-order NAC is presented.
• Explicit references to Kohn-Sham virtual orbitals are eliminated.
• The method circumvents computationally expensive derivative calculations.
• Validation through accurate calculation of NAC matrix elements for LiH and HeH+ molecules, showing good agreement with previous results.

Conclusions:

• The developed formulation provides a computationally efficient and accurate method for calculating NAC.
• This advancement facilitates accurate ab initio nonadiabatic molecular dynamics in extended systems.
• The method has broad implications for studying complex chemical processes and materials.