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 ~(12)C~(16)O_2 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_i~(exp) is the experimental error, i is the number of the experimental data used, and m is the number of parameters smaller than unity.
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