THE GENERATING FUNCTION-APPROACH TO THE FORMULATION OF THE EFFECTIVE ROTATIONAL HAMILTONIAN - A SIMPLE CLOSED FORM MODEL DESCRIBING STRONG CENTRIFUGAL-DISTORTION IN WATER-TYPE NONRIGID MOLECULES

We deal with the problem of the divergence of the standard power series expansion of the effective rotational Hamiltonian for high rotational levels. The paper describes a very simple model (G-operator) which takes into account the dominant part of the anomalous centrifugal distortion in H2O-type nonrigid quasilinear molecules in a closed form. This model is derived by taking account of the most important part of the bending-rotational interaction in the zero-order approximation. The main features of the model discussed above are the following. The high-order coefficients of the Taylor series expansion of the model are in accordance with experimental centrifugal distortion parameters for H2O. To a realistic approximation, the new model may be considered as a generating function for Watson's expansion of the rotational Hamiltonian. The "asymptotic behavior" of the calculated energies as Ka → J is in qualitative agreement with available experimental data up to Ka ≤ 20, contrary to the traditional approach. Direct calculations using the G-operator give much more satisfactory EJKcalc than those with a truncated standard power series expansion of Hrot. For the H2O ground state in the interval of quantum numbers J < 20 and 0 < Ka < ( 3 4)J we have typical discrepancies ΔE = |Eobs - Ecal| ≤ 0.5 cm-1 and relative errors ( ΔE E) ≤ 0.00008 (without fitting). The analytical formulas for convergence radii of the standard rotational Hamiltonian derived with the use of the G-operator are in accordance with numerical tests and with previous "empirical" estimates. The conclusion is made that the generating function approach is applicable for quantum number values which are above the convergence radius of the standard expansion. © 1992.