Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. I. Formalism

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Analytic gradients and derivative coupling terms (DCTs) are crucial for accurate molecular dynamics simulations.
• Existing methods for calculating these terms were limited and not applicable to relativistic State-Averaged MultiReference Configuration Interaction with Singles and Doubles (MRCI-SD) wavefunctions.
• The Born-Oppenheimer approximation, which assumes off-diagonal contributions are zero, limits accuracy in certain systems.

Purpose of the Study:

• To review and extend methods for calculating analytic gradients and DCTs for relativistic MRCI-SD wavefunctions within the COLUMBUS program.
• To present a formalism for calculating transition density matrices and analytic DCTs for systems with spin-orbit coupling.
• To enable more accurate computational modeling of molecular dynamics involving non-adiabatic transitions.

Main Methods:

• Review of existing analytic gradient and DCT calculation methods for MRCI-SD wavefunctions.
• Development and implementation of methods for relativistic MRCI-SD Hamiltonians.
• Formalism for calculating transition density matrices and analytic DCTs.

Main Results:

• Analytic gradients and DCTs are now available for relativistic MRCI-SD wavefunctions.
• The developed methods significantly reduce computational cost compared to finite difference approaches.
• A formalism for transition density matrices and analytic DCTs for spin-orbit split systems is presented.

Conclusions:

• The availability of analytic gradients and DCTs for relativistic MRCI-SD wavefunctions is a significant advancement in computational chemistry.
• These methods are critical for accurately modeling the dynamics of systems with significant spin-orbit coupling, such as in laser applications.
• The presented formalism facilitates more precise simulations of non-adiabatic processes.