Calculations are carried out of the rotational–vibrational energy levels of H2O and D2O for J≤10 by a variational method. The full Watson Hamiltonian is employed, with the potential function in valence displacement coordinates and with the integrations over normal coordinates carried out by Gauss–Hermite quadrature. The basis set consists of products of vibrational functions and symmetric top functions; the vibrational functions diagonalize the Hamiltonian for J=0. Comparison is made with experiment, and also results obtained with different force fields are compared. The mixing of different vibrational functions into a wave function for a given rotational–vibrational state is studied; mixing is found to be quite prevalent.
A new variational calculation of the inversion spectrum of ammonia is reported in which all six vibrational degrees of ammonia are employed. By fitting spectroscopic data, an inversion barrier of 1810 cm"1 is obtained.
The energies of lower lying vibrational states (J=0) of formaldehyde in its ground electronic state are calculated variationally for H2CO and D2CO. The functions of the basis set correspond to products of harmonic oscillator functions. The full Watson Hamiltonian is used and integrals are evaluated by Gauss–Hermite numerical quadrature. Two different potential functions in internal displacement coordinates, which have been given in the literature, are employed in the calculations. Calculations are carried out for A1, B2, and B1 symmetries with 196, 165, and 108 basis functions, respectively. The forms of some of the eigenvectors are reported.
The present study presents a numerical test on the equivalence of potential expansions in normal and valence displacement coordinate space by calculating the lower vibrational states in a variational procedure. The calculations are performed for HjO and they indicate that a fourth-order Taylor series expansion in valence coordinates is not well represented by an expansion in normal codrdinates which is truncated at fourth order.
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