Approximate inversion method for obtaining polyatomic potential energy surfaces from ro-vibrational spectra

The extension to polyatomic molecules of the RKR procedure for inversion of ro-vibrational spectra to deduce the intramolecular potential surface depends on solving the semiclassical quantization problem for coupled modes. The semiclassical self-consistent field theory (SC-SCF) proposed recently provides an approximate method for solving the coupled mode problem, and thereby provides a means to extend RKR. We derive a closed-form, convenient expression for the inversion transform that constructs directly the potential surface from the spectral data. The inversion should be valid in the region (well below the quasi-continuum) for which SC-SCF holds. We test the method for a model problem of two coupled modes, and find that it works very well. For practical inversions, difficulties in assignment or in obtaining the requisite number of frequencies might occur; nevertheless, the extended RKR is direct, non-iterative, and potentially useful.