Mass scaling in molecular systems

Abstract

The scaling of the electron and nuclear masses in molecular systems for which both the electronic and the nuclear motions are quantum mechanically described is examined. Exact closed expressions for both the total contribution to the energy coming from the nuclear motion and for the total energy of any given state of a molecular system are obtained in terms of the nuclear kinetic energy density and the total kinetic energy density functions, respectively. It is shown that the problem of determining the energy levels of a system with n electrons and N nuclei can be reduced to one of determining effective kinetic energy density functions, one for each state of the system, which depend only on three variables. An expression is given for the isotopic effect on the energy of any given state in terms of the exact kinetic energy contribution of the isotopically substituted nucleus. On the other hand, the energy of each state of every system lying on a certain kind of trajectory in a molecular parameter space (to be defined in Sec. I) is given in terms of the energy levels of only one system lying on the same trajectory. Some exact relations between electronic and mesic systems are obtained.