The time-dependent Born-Oppenheimer approximation
Gianluca Panati, Herbert Spohn, Stefan Teufel
TL;DR
This paper reviews and refines the mathematical foundation of the time-dependent Born-Oppenheimer approximation, introducing higher order corrections and new derivations, with applications to molecular dynamics near conical intersections.
Contribution
It provides a systematic scheme for higher order corrections and a new elementary derivation of the second-order approximation, enhancing understanding of molecular quantum dynamics.
Findings
Clarified the incomplete nature of the conventional derivation.
Presented a new elementary derivation of the second-order approximation.
Discussed applications to conical intersections and reactive scattering.
Abstract
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.
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