(132) |

The potential energy for a system of charged particles is

(133) |

For a molecule, it is reasonable to split the kinetic energy into two summations--one over electrons, and one over nuclei. Similarly, we can split the potential energy into terms representing interactions between nuclei, between electrons, or between electrons and nuclei. Using

where , , and . This is known as the ``exact'' nonrelativistic Hamiltonian in field-free space. However, it is important to remember that this Hamiltonian neglects at least two effects. Firstly, although the speed of an electron in a hydrogen atom is less than 1% of the speed of light, relativistic mass corrections can become appreciable for the inner electrons of heavier atoms. Secondly, we have neglected the spin-orbit effects. From the point of view of an electron, it is being orbited by a nucleus which produces a magnetic field (proportional to L); this field interacts with the electron's magnetic moment (proportional to S), giving rise to a spin-orbit interaction (proportional to for a diatomic.) Although spin-orbit effects can be important, they are generally neglected in quantum chemical calculations.