Nuclear motions in molecules and related properties.

In the framework of the Born-Oppenheimer separation (§ 7.1), once that the electronic state has been described and the eigenvalue Ee(R) and wavefunction φe(r,R) have been found, then the motions of the nuclei are described by a function φν(g)(R), where g represents the quantum numbers for the electrons and ν are the quantum numbers (to be found) for the nuclei. This wavefunction is solution of the Equation 10.1$$ \{ - \sum\limits_\alpha {\frac{{\hbar ^2 }} {{2M_\alpha }}\nabla _\alpha ^2 + E_e (R)\} \phi _\nu ^{(g)} } (R) = E_{g,\nu } \phi _\nu ^{(g)} (R) $$ (note that Vnn in Eq. 7.3 and 7.5 has been included in Ee(R), see for example Eq. 8.1). [ABSTRACT FROM AUTHOR]