Determination of parameters of the dipole moment of the CO2 molecule

Analytic expressions are obtained for vibrational transition moments of the first, second, and third orders using the eigenfunctions in the second-order perturbation theory. These expressions can be used to solve the inverse electrooptical problem for the ¹²C¹⁶O₂ molecule. The resonance interactions were taken into account by solving secular equations. The mixing coefficients for the eigenfunctions were calculated with an accuracy of 0.1%. The experimental data on purely vibrational transition moments 〈μ〉² used in the solution were obtained by averaging the data available in the literature with the weights that are inversely proportional to the error, resulting in mean-square deviations of (0.1–10)%. Five parameters of the dipole moment of the Σ _u symmetry were calculated using 29 values of the transition moments; five parameters of the π_u symmetry were calculated using 27 values of the transition moments. The accuracy of the solution of the inverse problem is characterized by the quantity Q=Σ(δµ _i ^(theor) /δµ _i ^(exp) )²/(n-m)]^1/2, where δµ _i ^(theor) is the deviation of calculations from the experiment, δμ _(exp) ⁱ is the experimental error, n is the number of the experimental data used, and m is the number of parameters smaller than unity.