Water vapor millimeter wave foreign continuum: A Lanczos calculation in the coordinate representation

The water vapor foreign-continuum absorption has been calculated theoretically from first principles for the millimeter wave spectral region as a function of frequency f and temperature T. The calculations are made using the Lanczos algorithm by writing the resolvent operator (omega-L)(-1) as continued fractions. In order to guarantee the quick convergence of the continued fractions, the line space of H2O is divided into two subspaces: one consists of the positive resonance lines and the other the negative ones. By ignoring the coupling between them, (omega-L)(-1) is expressed as a sum of two continued fractions. The parameters appearing in each of the fractions are functions of the matrix elements of powers of the Liouville operator L between the starting vectors spanning the corresponding subspaces. In the present work, we have taken into account all powers of L up to 5. With the coordinate representation in which the orientations of the H2O-N-2 collision pair are chosen as the basis functions in Hilbert space, the anisotropic interaction potential is diagonal, and calculations of the matrix elements are transformed to multidimensional integrations. The latter are evaluated with the Monte Carlo method. In order to reduce the lengthy calculations, we assume that the anisotropic potential has rotational symmetry about the Z axis of H2O, and consists of the long-range dipole-quadrupole part and a short-range repulsive site-site model. Once the parameters of the continued fractions are known, one can calculate the poles and residues and then carry out the ensemble average over the translational motion. Within the quasistatic approximation, one can treat the latter classically and obtain contributions to the absorption coefficient at the poles. Finally, the absorption coefficient at frequency f can be derived by an interpolation method. The results are fitted to a simple function of f and T, and are compared with experimental data and with two different versions of Liebe's empirical model. In general, the theoretical results are in good agreement with the experiment. Meanwhile, the magnitudes of the theoretical absorption are between those of the 1989 and 1993 versions, but the temperature dependence is closer to the latter one. (C) 2002 American Institute of Physics.