Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the low rank perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation. A pair of two n-atom isotopic molecules ii and B which are identical except for isot opic substitutions at rho atomic sites is considered. Relations which expre ss vibrational frequencies omega (k) and normal modes Psi (k) of the pertur bed isotopic molecule B in terms of the vibrational frequencies v(i) and no rmal modes Phi (i) of the unperturbed molecule A are derived. In these rela tions complete specification of the unperturbed normal modes Phi (i) is not required. Only amplitudes (tau\Phi (i)) of normal modes Phi (i) at sites t au affected by the isotopic substitution an needed.