Nonempirical Effective Operators of the Dipole Moment of Vibrational-Rotational Bands of Polyatomic Molecules

The energy level systems of vibrational-rotational absorption bands of polyatomic semirigid molecules are routinely described using reduced effective Hamiltonians in Watson form. An equally important problem is the selection of a convenient form of the effective molecular dipole moment operator. This is necessary for the most accurate approximation of line intensities of experimental spectra and the solution of the corresponding inverse spectroscopic problem. It is shown that a direct calculation of the effective dipole moment operator, taking into account rotational reduction transformations, can be performed based on contact transformations of operator perturbation theory using the technique of normal ordering of vibrational $$({{a}^{\dag }},a)$$ and rotational $$({{J}_{z}},{{J}_{ \pm }})$$ ladder operators, as well as Wigner functions $$(D_{{0,\varepsilon }}^{1})$$ for the dipole moment. For asymmetric top molecules, a new convenient universal form of the effective dipole moment operator with a Hermitian rotational dependence is proposed. The effectiveness of the proposed method is illustrated using the example of the vibrational-rotational $${{\nu }_{2}}$$ absorption band of SO2 and D2O molecules.