Calculation of vibrational matrix elements of the CO2 molecule in the formalism of polynomials of the quantum numbers

The vibrational energies and the matrix elements of the electric dipole moment function and the rotation function are calculated for an arbitrary linear polyatomic molecule in the first order of perturbation theory using the formalism of polynomials of quantum numbers. The formulas obtained are tested for the example of the CO₂ molecule. The experimental data available at present are briefly analyzed. It is shown that the calculated matrix elements are in good agreement with the corresponding experimental data even in the first order of the theory.