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In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and electrons in a molecule can be treated separately, based on the fact that the nuclei are much heavier than the electrons.
Path integral molecular dynamics (PIMD) is a method of incorporating quantum mechanics into molecular dynamics simulations using Feynman path integrals.In PIMD, one uses the Born–Oppenheimer approximation to separate the wavefunction into a nuclear part and an electronic part.
The Renner-Teller effect is a phenomenon in molecular spectroscopy where a pair of electronic states that become degenerate at linearity are coupled by rovibrational motion. [ 1 ] The Renner-Teller effect is observed in the spectra of molecules that have electronic states that allow vibration through a linear configuration.
The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to ...
In the vicinity of conical intersections, the Born–Oppenheimer approximation breaks down and the coupling between electronic and nuclear motion becomes important, allowing non-adiabatic processes to take place. The location and characterization of conical intersections are therefore essential to the understanding of a wide range of important ...
For these systems, it is necessary to go beyond the Born–Oppenheimer approximation. This is often the terminology used to refer to the study of nonadiabatic systems . A well-known approach involves recasting the molecular Schrödinger equation into a set of coupled eigenvalue equations.
The Eckart conditions, named after Carl Eckart, [1] simplify the nuclear motion (rovibrational) Hamiltonian that arises in the second step of the Born–Oppenheimer approximation. They make it possible to approximately separate rotation from vibration.
The inclusion of all n levels of excitation for the n-electron system gives the exact solution of the Schrödinger equation within the given basis set, within the Born–Oppenheimer approximation (although schemes have also been drawn up to work without the BO approximation [13] [14]).