Search

A far-wing line shape theory that satisfies the detailed balance principle is applied to the H[sub 2]O–H[sub 2]O system. Within this formalism, two line shapes are introduced, corresponding to band averages over the positive and negative resonance lines, respectively. Using the coordinate representation, the two line shapes can be obtained by evaluating 11-dimensional integrations whose integrands are a product of two factors. One depends on the interaction between the two molecules and is easy to evaluate. The other contains the density matrix of the system and is expressed as a product of two three-dimensional distributions associated with the density matrices of the absorber and the perturber molecule, respectively. If most of the populated states are included in the averaging process, to obtain these distributions requires extensive computer CPU time, but only have to be computed once for a given temperature. The 11-dimensional integrations are evaluated using the Monte Carlo method, and in order to reduce the variance, the integration variables are chosen such that the sensitivity of the integrands on them is clearly distinguished. Numerical tests show that by taking into account about 10[sup 7] random selections, one is able to obtained converged results. We find that it is necessary to consider frequency detuning, because this makes significant and opposite contributions in the two band-averaging processes and causes the lines to be asymmetric. Otherwise, the two line shapes become symmetric, are the same, and equal to the mean of the two shapes obtained including the frequency detuning effects. For the pure rotational band, we find that the magnitude of the line shape obtained from the positive line average is larger than that obtained from the negative line average for ω>0 and vice versa for ω<0, and their relative gap increases as the frequency displacement from the line center increases. By adopting a realistic potential model a... [ABSTRACT FROM AUTHOR]

A new representation is introduced in which the rapidly varying time-dependent part of the time displacement operator can be factored out and the remaining part, which varies with time more slowly, can be expanded in the usual perturbational fashion. The lowest order approximation leads to the far-wing quasistatic line shape theory developed previously, whereas the next order approximation, related to the noncommutation of the Liouville operators describing the unperturbed absorber and bath molecules and the interaction between them, leads to a near-wing correction. Explicit expressions are derived for both the corrections to the spectral density and the statistical band-average line shape function assuming an anisotropic dipole–dipole interaction. Detailed computations for the case of self-broadened H2O are carried out for the line-shapes and the corresponding absorption coefficients for several temperatures and for frequencies to 10 000 cm-1. From these results, we conclude that the near-wing corrections generally increase the line shape function between 10 and 200 cm-1, and that this increase is more important for lower temperatures than for higher ones. This in turn leads to increased absorption nearer the band centers, especially for lower temperatures, and thus to improved agreement between theory and experiment. [ABSTRACT FROM AUTHOR]

The far wing line shape theory developed previously and applied to the calculation of the continuum absorption of pure water vapor is extended to foreign-broadened continua. Explicit results are given for H2O–N2 and H2O–CO2 in the frequency range from 0 to 10 000 cm-1. The theory is based on the quasistatic and binary collision approximations and assumes for the interaction potential an isotropic Lennard-Jones part and the leading anisotropic multipolar (dipole–quadrupole) term. For H2O–N2, the positive and negative resonant frequency average line shape functions and absorption coefficients are calculated for a number of temperatures between 296 and 430 K for comparison with existing laboratory data. In general, the agreement is very good, especially at the higher temperatures for which the experimental absorption is larger and the corresponding error limits are smaller. For H2O–CO2 for which no experimental data exists, the calculations are made only at 296 K. Because of the significantly different line shapes for self vs foreign broadening, the ratio of the corresponding continuum absorption coefficients varies widely as a function of the frequency. The implications of this for absorption in the Earth’s atmosphere are discussed briefly. [ABSTRACT FROM AUTHOR]

A theory is presented for the calculation of the continuous absorption due to the far wing contributions of allowed lines. The theory is based on the quasistatic approximation for the far wing limit and the binary collision approximation of one absorber molecule and one bath molecule. In line space, the motion of the dipole moment of the absorber molecule, determined by the time displacement Liouville operator related to the total Hamiltonian of the absorber molecule and the bath molecule, is approximately expressed as the ordered product of two time displacement Liouville operators, one related to the intermolecular potential and the other to the unperturbed Hamiltonian. Using a Laplace transformation, the spectral density is expressed in terms of a Cauchy integral whose integrand is a product of two resolvent operators corresponding to the interaction and to the unperturbed Hamiltonian, respectively. After isolating the effects of the bath variables, the spectral density and subsequently the absorption coefficient are expressed in terms of the individual line coupling functions, or the individual line shape functions. By using two average line shape functions instead of the individual ones, the expression of the absorption coefficient closely matches empirical models. The validity of the present theory is discussed, and some numerical results of the water continuum absorption in the infrared region are presented for comparison with experimental data. A good agreement in both the magnitude and the temperature dependence of the absorption coefficients is obtained. Some further extensions and applications of the present theory are also discussed briefly. [ABSTRACT FROM AUTHOR]

The statistical theory proposed by Rosenkranz to calculate the continuous absorption by water molecules in the high-frequency (infrared) wing of the pure rotational band is reviewed and extended. In the review there is a discussion, in particular, of the approximations that are made, including those that are necessary and which limit the applicability of the theory to other spectral regions, and those that are made for calculational convenience. Then, several extensions to the theory are discussed, including increasing the number of rotational states used to calculate the band-average relaxation parameter, modifying the definition of this parameter to account for near-wing effects, and eliminating the boxcar approximation. This last modification, effected by using asymmetric-top functions instead of symmetric-top functions to calculate matrix elements of the density operator and to diagonalize the dipole–dipole interaction, results in significant enhancement of the relaxation parameter. This improvement, in turn, allows one to eliminate an inconsistency in the original formulation of Rosenkranz while obtaining substantially the same final results. The implications of the present results for the calculation of the absorption in the high-frequency wing of the ν2 fundamental vibration-rotational band of H2O are discussed briefly. [ABSTRACT FROM AUTHOR]

A theory is presented for the calculation of the continuous absorption of water molecules in the millimeter spectral region. The theory is based on a generalization of Fano’s theory in which the spectral density, the Fourier transform of the dipole-moment correlation function, is calculated for a system consisting of a pair of molecules. The internal states are written in terms of the line space of the system, and the resolvent operator is obtained using the well-known Lanczos algorithm. For the interaction between two water molecules, we include only the leading dipole–dipole term of the long-range anisotropic potential, and model the isotropic interaction, used to calculate the statistical weight within the quasi-static approximation, by a Lennard–Jones potential. Using reasonable values for the two Lennard–Jones potential parameters, and the known rotational constants and permanent dipole moment of a water molecule, we calculate the absorption coefficient for frequencies up to 450 GHz for temperatures between 282 and 315 K. The present results are in good agreement with an empirical model for the water continuum based on combined laboratory and atmospheric measurements. We conclude from our results that, contrary to some previous assertions, the strong negative temperature dependence as well as the magnitude of the continuum absorption, at least for the millimeter spectral region, can be explained in terms of the far-wings of allowed rotational transitions. [ABSTRACT FROM AUTHOR]

The far-wing line shape theory within the binary collision and quasistatic framework has been developed using the coordinate representation. Within this formalism, the main computational task is the evaluation of multidimensional integrals whose variables are the orientational angles needed to specify the initial and final positions of the system during transition processes. Using standard methods, one is able to evaluate the seven-dimensional integrations required for linear molecular systems, or the seven-dimensional integrations for more complicated asymmetric-top (or symmetric-top) molecular systems whose interaction potential contains cyclic coordinates. In order to obviate this latter restriction on the form of the interaction potential, a Monte Carlo method is used to evaluate the nine-dimensional integrations required for systems consisting of one asymmetric-top (or symmetric-top) and one linear molecule, such as H[sub 2]O-N[sub 2]. Combined with techniques developed previously to deal with sophisticated potential models, one is able to implement realistic potentials for these systems and derive accurate, converged results for the far-wing line shapes and the corresponding absorption coefficients. Conversely, comparison of the far-wing absorption with experimental data can serve as a sensitive diagnostic tool in order to obtain detailed information on the short-range anisotropic dependence of interaction potentials. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]