Approximate constant of motion for molecular ions in a magnetic field

For neutral molecules in a homogeneous magnetic field there exists a constant of motion, the pseudomomentum, which allows a complete pseudoseparation of the center-of-mass motion. For molecular ions a complete set of constants of motion is not known, neither exactly nor approximately. In this paper we investigate the structure an approximate constant of motion for a molecular ion can have in general and arrive at an interesting formula. An explicit approximate constant of motion that obeys this structure formula is derived from a physically intuitive picture that says that an approximately conserved quantity can be obtained as the pseudomomentum relative to the instantaneously fixed-nuclei center of charge of the system. Some special examples are discussed in detail.