The molecular hamiltonian

A complete hamiltonian for a translating, rotating, vibrating molecule in the presence of a constant external electromagnetic field is derived starting with the Breit equation reduced to a non-relativistic form, correct to order c -2. A number of new terms appear, which have not been obtained in less precise derivations. These include mass polarization corrections to the orbital Zeeman, spin-orbit and orbit-orbit interactions together with spin-vibration, orbit-vibration and orbit-rotation interactions. In addition there is a vibrational Zeeman interaction which in certain circumstances may be of the same order of magnitude as rotational Zeeman terms. The final hamiltonian provides a starting point for future investigations of the possible effects of these new interactions on the microwave and radiofrequency spectra of both open and closed-shell molecules.