Application of Watson's centrifugal distortion theory to water and light asymmetric tops. General methods. Analysis of the ground state and the ν2 state of D 2O 16

Abstract

Watson's reduced Hamiltonian proved adapted for treating the rotation of light molecules which show very large effects of centrifugal distortion. In order to determine which terms are required and which are negligible (choice of an effective model), we have studied the order of magnitude of the terms from a theoretical point of view. This order depends on the coefficient and the operator. It is shown (1) that the order of the coefficients depends not only on the degree of the components of the angular momentum but also on the asymmetry of the molecule and (2) that the factor due to the operator depends on the asymmetry and on the rotational quantum numbers J and K −1. It is established that diagonal and off-diagonal terms are of similar importance for small K −1 while, for large K −1, the diagonal terms are the leading ones. Further, the number of terms of high degree may be reduced by numerically telescoping the series. The terms to be retained are best determined by a statistical analysis. Terms resulting from telescoping completely or partially lose their original meaning. The previous theory has been applied to the ground state and to the ν 2 state of D 2O 16. Thirteen new microwave lines are reported in this paper. In the rotational analysis, microwave and infrared data were used simultaneously: 22 constants could be determined for the groundstate and only nine for the ν 2 state. The constants related to the z-axis are most affected in the latter. The A, B, C constants corresponding to the standard Hamiltonian, i.e., the Kivelson-Wilson Hamiltonian, are, in MHz: A gr=462 291.70, B gr=217 982.29, C gr=145 301.13, A v2=498 746, B v2=219 960, C v2=143 672.