Born-Oppenheimer expansion at constant energy

Area of Science:

• Quantum Chemistry
• Molecular Physics
• Computational Chemistry

Background:

• The Born-Oppenheimer approximation is a cornerstone of molecular physics, simplifying calculations by separating nuclear and electronic motion.
• Standard approximations assume constant quantum numbers, leading to corrections proportional to M(-3/4) for nuclear mass M.
• Conical intersections present challenges due to singular coupling terms, limiting the accuracy of standard methods.

Purpose of the Study:

• To investigate corrections to the Born-Oppenheimer approximation under different conditions.
• To analyze the impact of holding energy constant instead of quantum numbers.
• To develop a more accurate theoretical framework for molecular systems with conical intersections.

Main Methods:

• Expansion of molecular properties in inverse powers of nuclear mass (M).
• Application of a quasidiabatic transformation to remove singular coupling terms near conical intersections.
• Analysis of the lowest-order correction to the molecular wave function under the modified conditions.

Main Results:

• The standard Born-Oppenheimer expansion yields corrections proportional to M(-3/4).
• By holding energy constant and removing singular coupling terms, the lowest-order correction is reduced to M(-1/2).
• This indicates a significant improvement in the convergence of the expansion.

Conclusions:

• The quasidiabatic transformation effectively mitigates singularities at conical intersections.
• Holding energy constant provides a more favorable expansion parameter for molecular wave functions.
• The findings offer a pathway to more accurate and efficient quantum chemical calculations, particularly for systems exhibiting non-adiabatic effects.