Nuclear motions in molecules and related properties

Abstract

In the framework of the Born-Oppenheimer separation (§7.1), once that the electronic state has been described and the eigenvalue E _e (R) and wavefunction φ _e (r,R) have been found, then the motions of the nuclei are described by a function φ ^(g) _ν (R), where g represents the quantum label for the electrons and ν are the quantum numbers (to be found) for the nuclei. This wavefunction is solution of the Equation

$$ \{ - \sum\limits_\alpha {\frac{{\hbar ^2 }} {{2M_\alpha }}\nabla _\alpha ^2 + E_e (R)} \} \phi _\nu ^{(g)} (R) = E_{g,\nu } \phi _\nu ^{(g)} (R) $$

(10.1)

(note that V _nn in Eq. 7.3 and 7.5 has been included in E _e (R), see for example Eq. 8.1).