The averaged density matrix in the coordinate representation: Application to the calculation of the far-wing line shapes for H2O

Abstract

The far-wing line shape theory within the binary collision and quasistatic framework developed previously for linear molecules using the coordinate representation has been generalized to symmetric- and asymmetric-top molecular systems. However, due to more variables needed to specify the orientation of these complicated molecules, one has to evaluate multidimensional integrals with higher dimensionality and this would be intractable for practical calculations. In cases where the anisotropic interaction contains cyclic coordinates, one can carry out the integration of the density matrix over these coordinates analytically and obtain the “averaged” density matrix. This reduces the dimensionality of the multidimensional integrals and thus dramatically reduces the computational time necessary to obtain converged results. In addition, a new interpolation method that enables one to treat more realistic potential models has been formulated. Using these results, calculations for the band-average far-wing line shapes and corresponding absorption coefficients in the spectral range 300–1100 cm−1 have been carried out for H2O–H2O and H2O–N2 pairs for a few temperatures. These results improve the agreement with experimental data over previous calculations that were limited in the number of states that could be included and in the sophistication of the anisotropic interaction potential model that was used.