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...

The basis-set convergence of singlet and triplet pair energies of coupled-cluster theory including single and double excitations is accelerated by means of extrapolations based on the distinct convergence behaviors of these pairs. The new extrapolation procedure predicts a nonrelativistic Born–Oppenheimer inversion barrier of 1767 ± 12 cm−1 for NH3. An effective one-dimensional, vibrationally a...

We show how linear vibronic spectra in molecular systems can be simulated efficiently using first-principles approaches without relying on the explicit use of multiple Born–Oppenheimer potential energy surfaces. demonstrate and analyze performance mean-field beyond-mean-field dynamics techniques for H2 molecule one dimension, later case capturing structure quite accurately, including quantum Fr...

Abstract The first part of this article attempts to highlight in chronological order some prominent papers that have direct connexion with the Born‐Oppenheimer approximation. This timeline successively points role level crossing, notions gauge field and geometrical or Berry phase, early experiments were accounted for concept, its major understanding anomalous transport solids. second analyzes t...

The Born-Oppenheimer approximation [1] can be used whenever the hamilto..ian of a fast system depends on the coordinates of a slow system . In some textbooks, the problem is solved by freezing the coordinates of the slow system and solving the hamiltonian of the fast system; then the energy of the fast system enters the effective hamiltonian for the slow system as a potential energy term. This ...

The dust ball collapse is studied in the context of "rainbow metric" approach (where matter content supplemented with a scalar field perturbation) to Oppenheimer-Snyder scenario within framework loop quantum cosmology. global spacetime structure determined for this and subsequently used evaluate entanglement entropy via slight adaptation existing formulas. resulting model shown qualitatively re...