ADT: A Generalized Algorithm and Program for Beyond Born-Oppenheimer Equations of "N" Dimensional Sub-Hilbert Space.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Beyond Born-Oppenheimer (BBO) treatments are computationally intensive due to complex adiabatic to diabatic transformation (ADT) equations.
• Nonadiabatic coupling terms (NACTs) can present singularities in the nuclear configuration space, complicating calculations.

Purpose of the Study:

• To develop a generalized algorithm, "ADT," for symbolic manipulation and numerical computation of nonadiabatic equations.
• To construct accurate diabatic potential energy surfaces (PESs) for molecular processes involving excited electronic states.
• To overcome the computational bottlenecks associated with higher-dimensional sub-Hilbert spaces in BBO treatments.

Main Methods:

• The "ADT" algorithm formulates analytic functional forms for ADT angles and diabatic potential energy matrices.
• It numerically solves coupled differential equations to evaluate ADT angles, residues, ADT matrices, and diabatic PESs.
• The software accepts ab initio data (adiabatic PESs and NACTs) or generates them via MOLPRO interfacing.

Main Results:

• The "ADT" package successfully computed diabatic PESs for six realistic molecular systems with significant nonadiabatic interactions.
• These systems include NO2 radical, H3+, F + H2, NO3 radical, C6H6+ radical cation, and 1,3,5-C6H3F3+ radical cation.
• The algorithm efficiently handles singularities in NACTs through unitary transformations.

Conclusions:

• The developed "ADT" algorithm provides an efficient and accurate method for generating diabatic surfaces in BBO calculations.
• This tool simplifies the treatment of nonadiabatic dynamics, particularly for systems with multiple interacting electronic states.
• The "ADT" package is publicly available, facilitating further research in computational quantum chemistry.