ALBERT

Description: Two basic rules (i.e. the pair identity and the smooth variation) applicable for H2O transitions involving high-J states have been discovered. The origins of these rules are the properties of the energy levels and wavefunctions of H2O states with the quantum number J above certain boundaries. As a result, for lines involving high-J states in individually defined groups, all their spectroscopic parameters (i.e. the transition wavenumber, intensity, pressure-broadened half-width, pressure-induced shift, and temperature exponent) must follow these rules. One can use these rules to screen spectroscopic data provided by databases and to identify possible errors. In addition, by using extrapolation methods within the individual groups, one is able to predict the spectroscopic parameters for lines in this group involving very high-J states. The latter are required in developing high-temperature molecular spectroscopic databases such as HITEMP.

Description: Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used in calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this formalism contains several approximations whose applicability has not been thoroughly justified. One of them is that lines of interest are well isolated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from the line mixing are ignored. Second, when they applied the linked cluster theorem to remove the cutoff, they have assumed the matrix elements of the operator exp(-iS(sub 1) - S(sub 2)) can be replaced by the exponential of the matrix elements of -iS(sub 1) - S(sub 2). With this replacement, effects from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. In the present study, we have developed a new method to evaluate the matrix elements of exp(-iS(sub 1) - S(sub 2)) and have refined the RB formalism such that line coupling can be taken into account. Our numerical calculations of the half-widths for Raman Q lines of the N(sub 2)-N(sub 2) pair have demonstrated that effects from the line coupling are important. In comparison with values derived from the RB formalism, new calculated values for these lines are significantly reduced. A recent study has shown that in comparison with the measurements and the most accurate close coupling calculations, the RB formalism overestimates the half-widths by a large amount. As a result, the refinement of the RB formalism goes in the right direction and these new calculated half-widths become closer to the "true" values.

Description: The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Description: The refinement of the Robert-Bonamy formalism by considering the line coupling for linear molecules developed in our previous studies [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013); 140, 104304 (2014)] have been extended to asymmetric-top molecules. For H2O immersed in N2 bath, the line coupling selection rules applicable for the pure rotational band to determine whether two specified lines are coupled or not are established. Meanwhile, because the coupling strengths are determined by relative importance of off-diagonal matrix elements versus diagonal elements of the operator -iS1 -S2, quantitative tools are developed with which one is able to remove weakly coupled lines from consideration. By applying these tools, we have found that within reasonable tolerances, most of the H2O lines in the pure rotational band are not coupled. This reflects the fact that differences of energy levels of the H2O states are pretty large. But, there are several dozen strongly coupled lines and they can be categorized into different groups such that the line couplings occur only within the same groups. In practice, to identify those strongly coupled lines and to confine them into sub-linespaces are crucial steps in considering the line coupling. We have calculated half-widths and shifts for some groups, including the line coupling. Based on these calculations, one can conclude that for most of the H2O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and reductions of calculated half-widths due to including the line coupling could reach to 5%. Meanwhile, effects on the calculated shifts are very significant and variations of calculated shifts could be as large as 25%.

Description: By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Description: In this work, Complex Robert-Bonamy calculations of half-widths and line shifts were done for N2-broadening of water for 1639 transitions in the rotational band using two models for the trajectories. The first is a model correct to second order in time, the Robert-Bonamy parabolic approximation. The second is the solution of Hamilton's equations. Both models use the isotropic part of the atom-atom potential to determine the trajectories. The present calculations used an intermolecular potential expanded to 20th order to assure the convergence of the half-widths and line shifts. The aim of the study is to assess if the difference in the half-widths and line shifts determined from the two trajectory models is greater than the accuracy requirements of the spectroscopic and remote sensing communities. The results of the calculations are compared with measurements of the half-widths and line shifts. It is shown that the effects of the trajectory model greatly exceed the needs of current remote sensing measurements and that line shape parameters calculated using trajectories determined by solving Hamilton's equations agree better with measurement.