Effects on Calculated Half-Widths and Shifts from the Line Coupling for Asymmetric-Top Molecules

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%

Magnetic and electrical properties of dhcp NpPd3 and U(1-x)Np(x)Pd3

We have made an extensive study of the magnetic and electrical properties of double-hexagonal closepacked NpPd3 and a range of U(1-x)Np(x)Pd3 compounds with x=0.01, 0.02, 0.05, and 0.50 using magnetization, magnetic susceptibility, electrical resistivity, and heat capacity measurements on polycrystalline samples, performed in the temperature range 2-300 K and in magnetic fields up to 9 T. Two transitions are observed in NpPd3 at T=10 and 30 K. Dilute Np samples (x<0.05) exhibit quadrupolar transitions, with the transition temperatures reduced from those of pure UPd3.Comment: 10 pages, 18 figure

Two dimensional symmetric correlation functions of the Ŝ operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

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 Ŝ 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

Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Coupling and Line Mixing Effects on NH3 Lines in the nu4 Band

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular nu4 band. As in the pure rotational and the parallel nu1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the nu1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 = K2 = 0, whose matrix elements require the selection rule ∆k = 0, the formalism is applicable for the nu4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS (Energy-Corrected Sudden) and IOS (Infinite-Order Sudden) models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model

Landform evolution in the headwaters area of Araguaia river (Mato Grosso and Goiás states, Brazil).

Editors: Francisco Gutiérrez, Mateo Gutiérrez, Gloria Desir, Jesús Guerrero, Pedro Lucha, Cinta Marín, José María García-Ruiz

Genesis and evolution of voçorocas on Botucatu formation rocks (Uper Araguaia river, Goiás and Mato Grosso states, Brazil).

Editors: Francisco Gutiérrez, Mateo Gutiérrez, Gloria Desir, Jesús Guerrero, Pedro Lucha, Cinta Marín, José María García-Ruiz

A far-wing line shape theory which satisfies the detailed balance principle

A far-wing theory in which the validity of the detailed balance principle is maintained in each step of the derivation is presented. The role of the total density matrix including the initial correlations is analyzed rigorously. By factoring out the rapidly varying terms in the complex-time development operator in the interaction representation, better approximate expressions can be obtained. As a result, the spectral density can be expressed in terms of the line-coupling functions in which two coupled lines are arranged symmetrically and whose frequency detunings are omega - 1/2(omega(sub ji) + omega (sub j'i'). Using the approximate values omega - omega(sub ji) results in expressions that do not satisfy the detailed balance principle. However, this principle remains satisfied for the symmetrized spectral density in which not only the coupled lines are arranged symmetrically, but also the initial and final states belonging to the same lines are arranged symmetrically as well