Use of Euler series to fit spectra with application to water

Power series expansions of water eigenstate energies in J and K converge poorly and show alternating signs of the coefficients of the power series. Euler series can be used effectively to change an alternating series into one where all the coefficients have the same sign and where the radius of convergence is increased. This paper extends the Euler series to a two-dimensional series in K2 and [J (J + 1) − K2]. Application of this Euler series to the rotational energies of the ground state and the first 4 excited vibrational states of water allows a fit to experimental accuracy to J = 22 and K = 22. This fit has good convergence and also has predictive capability. It is much easier to fit the perturbed states because the Euler series allows the zero-order energy the perturbed states to be predicted with more confidence.