Analytic derivative couplings in time-dependent density functional theory: Quadratic response theory versus...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Derivative couplings are crucial for understanding non-adiabatic dynamics in excited states.
• Existing methods for calculating these couplings in time-dependent density functional theory (TDDFT) have limitations.

Purpose of the Study:

• To derive and implement analytic derivative couplings between excited states using quadratic response theory within TDDFT.
• To compare the performance of this new response-theory formulation against previous pseudo-wavefunction and direct differentiation methods.
• To validate the accuracy and computational efficiency of the new approach.

Main Methods:

• Derivation and implementation of analytic derivative couplings using quadratic response theory in TDDFT.
• Numerical comparison with pseudo-wavefunction formalism and direct differentiation of Kohn-Sham determinants.
• Validation against full configuration interaction (FCI) calculations for molecular systems.
• Formal proof for spin-flip TDDFT derivative couplings.

Main Results:

• The response-theory formulation of derivative couplings performs comparably to previous methods for many molecular systems.
• Accurate potential energy surfaces from the underlying DFT method are essential for reliable results.
• Response contributions are significant for high-symmetry systems and add moderate computational cost.
• Formal identity proven between response theory and pseudo-wavefunction methods for spin-flip TDDFT.

Conclusions:

• The quadratic response theory approach provides an accurate and validated method for calculating excited-state derivative couplings in TDDFT.
• This method is particularly useful for systems where symmetry plays a role.
• The findings support the use of pseudo-wavefunction formalisms for spin-flip TDDFT derivative couplings.