First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• First-order nonadiabatic coupling matrix elements (NACMEs) are crucial for understanding molecular phenomena like nonradiative transitions and excited-state decay.
• Accurate first-principles calculations of NACMEs have been computationally challenging for large molecular systems.
• Existing methods often struggle with consistency and practicality for molecules exceeding a few heavy atoms.

Purpose of the Study:

• To develop and implement a practical, first-principles theory for calculating first-order NACMEs.
• To enable accurate theoretical treatment of nonadiabatic processes in large molecular systems.
• To facilitate nonadiabatic molecular dynamics simulations for systems up to 100 atoms.

Main Methods:

• Developed a time-dependent response approach within time-dependent hybrid density functional theory (TDDFT) to compute NACMEs.
• Implemented the theory using Gaussian basis sets, yielding exact analytical derivative couplings between time-dependent Kohn-Sham determinants.
• Incorporated Pulay-type terms to improve basis-set convergence and utilized the resolution-of-the-identity approximation (RI-J) for computational efficiency.

Main Results:

• The new method provides exact analytical derivative couplings, independent of nuclear degrees of freedom, improving upon the Chernyak-Mukamel formula in finite basis sets.
• Computational cost increases by only ~10% on average for systems up to 147 atoms, with RI-J reducing costs significantly for nonhybrid functionals.
• Benchmarks against full configuration interaction (FCI) for diatomic molecules show excellent agreement for stable ground-state references and well-captured excitations.

Conclusions:

• The developed TDDFT formalism offers a consistent and practical approach for calculating first-order NACMEs in large molecules.
• This methodology significantly enhances the feasibility of performing accurate nonadiabatic molecular dynamics simulations for industrially relevant systems.
• The approach bridges the gap between theoretical accuracy and computational tractability for complex molecular systems.