Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density...

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Theoretical Chemistry

Background:

• Analytic derivative couplings are essential for studying non-adiabatic dynamics and conical intersections in molecules.
• Existing methods for calculating these couplings, particularly for variants of configuration interaction singles (CIS), can be computationally intensive.
• Efficient algorithms are needed to accurately model excited-state potential energy surfaces and reaction pathways.

Purpose of the Study:

• To derive and implement analytic derivative couplings for the spin-flip variant of configuration interaction singles (SF-CIS).
• To extend this formalism to time-dependent density functional theory (TD-DFT) using the Tamm-Dancoff approximation (TDA).
• To demonstrate the computational efficiency and accuracy of the new method for locating conical intersections.

Main Methods:

• Derivation of analytic derivative couplings based on the CIS analytic energy gradient algorithm.
• Implementation of the SF-CIS derivative couplings.
• Ad hoc extension to TD-DFT/TDA by incorporating an exchange-correlation term, avoiding quadratic response theory.
• Application to ethylene and H3 systems to locate minimum-energy crossing points and study conical intersections.

Main Results:

• The developed algorithm for analytic derivative couplings is closely related to existing CIS gradient methods and is computationally inexpensive.
• The method successfully located minimum-energy crossing points on conical seams for ethylene at a substantially reduced cost compared to branching-plane algorithms.
• Application to H3 near its D(3h) geometry correctly reproduced the topology near a degenerate conical intersection.

Conclusions:

• The new analytic derivative couplings for SF-CIS and TD-DFT/TDA provide an efficient and accurate approach for studying conical intersections.
• The method offers a significant computational advantage for locating important seam points on excited-state potential energy surfaces.
• This work facilitates the investigation of non-adiabatic processes and molecular dynamics involving conical intersections.