Perturbation Theory in Closed Form for Heteronuclear Diatomic Molecules

Within the framework of the Born—Oppenheimer approximation questions are considered involving application of time-dependent perturbation theory to diatomic heteronuclear molecules. A potential-energy model of the form $V_i\mathrm{}\left(r\right)=\frac{A_i}{{(r-r_i)}^2}-\frac{B_i}{(r-r_i)}+Q_i$ is proposed which gives a good representation of the true curves of the ground and excited states of a molecule. The relation ${\omega }_e{x}_e=6\mathrm{}\frac{D^2}{m}=\frac{3{\omega }_e^{\frac{4}{3}}}{2m^{\frac{1}{3}}}$ has been obtained between the dissociation energies into free ions $D$, vibrational frequencies ${\omega }_e$, and vibrational anharmonicity parameters ${\omega }_e{x}_e$ of the ground state of polar molecules. Analytical expressions are derived for vibration-rotation spectra, wave functions, and radial matrix elements considered in the first-order perturbation theory. An explicit expression obtained for the Green's function of the model enables a closed form to be given for matrix elements appearing in the higher-order perturbation theory involved in calculation of multiphoton molecular transitions.