Detailed description The BO approximation recognizes the large difference between the electron mass and the masses of atomic nuclei, and correspondingly the time scales of their motion. Given the same amount of momentum, the nuclei move much more slowly than the electrons. In mathematical terms, the BO approximation consists of expressing the wavefunction () of a molecule as the product of an electronic wavefunction and a nuclear (vibrational, rotational) wavefunction. . This enables a separation of the Hamiltonian operator into electronic and nuclear terms, where cross-terms between electrons and nuclei are neglected, so that the two smaller and decoupled systems can be solved more efficiently.
detailed description the bo approximation recognizes the large difference between the electron mass and the masses of atomic nuclei and correspondingly the time scales of their motion given the same amount of momentum the nuclei move much more slowly than the electrons in mathematical terms the bo approximation consists of expressing the wavefunction () of a molecule as the product of an electronic wavefunction and a nuclear (vibrational rotational) wavefunction  this enables a separation of the hamiltonian operator into electronic and nuclear terms where cross-terms between electrons and nuclei are neglected so that the two smaller and decoupled systems can be solved more efficiently