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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.
This is justified by the large disparity between the mass of an electron, and the typical mass of a nucleus and leads to the Born–Oppenheimer approximation and the idea that the structure and dynamics of a chemical species are largely determined by nuclear motion on potential energy surfaces.
BeH has only 5 electrons and is the simplest open shell neutral molecule, and is therefore extremely important for the benchmarking of ab initio methods. With such a light mass, it is also an important benchmark system for studying the breakdown of the Born–Oppenheimer approximation.
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 ...
The reduction from a fully quantum description to a classical potential entails two main approximations. The first one is the Born–Oppenheimer approximation, which states that the dynamics of electrons are so fast that they can be considered to react instantaneously to the motion of their nuclei. As a consequence, they may be treated separately.
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 ...
This is to be contrasted with the Jahn–Teller effect which occurs for polyatomic molecules in electronic states that allow vibration through a symmetric nonlinear configuration, where the electronic state is degenerate, and which further involves a breakdown of the Born-Oppenheimer approximation but here caused by the vibrational kinetic ...
It is only when both limits are attained that the exact solution, up to the Born–Oppenheimer approximation, is obtained.) The Hartree–Fock energy is the minimal energy for a single Slater determinant. The starting point for the Hartree–Fock method is a set of approximate one-electron wave functions known as spin-orbitals.