R. B. Wattson

Direct numerical diagonalization : wave of the future

Abstract The direct numerical diagonalization (DND) technique has been developed for use in calculations of atmospheric opacity due to molecular absorption under conditions which cannot be duplicated in an Earth-based laboratory. DND is an adaptation of the well-known variational method for solving the quantum mechanical equations of the rovibrational molecular Hamiltonian. The method has made possible the analysis and assignment of CO 2 lines for bands that have not been observed before due to the density of the neighboring spectra. Comparison of DND predicted line intensities for the 10 μm laser bands with recent measurements, obtained from two separate laboratories, indicate that the predicted line intensities are basically as good as the best measurements available today. Venus atmosphere simulations, using the most recent DND results, show excellent agreement with new Venus spectra in the 1 μm region, although no Earth-based laboratory is probably capable of measuring the line parameters used in the simulation. Recently, the rectilinear (normal) coordinate formulation of the method used for the CO 2 calculations has been extended to curvilinear (valence) coordinates, and the method was then applied to the calculation of the opacity of H 2 O. We plan to solve the rovibrational problem for N 2 O, SO 2 , O 3 and NO 2 , as well as to extend the technique to small molecules having more than three atoms, such as NH 3 and CH 4 .

Determination of vibrational energy levels and parallel band intensities of 12C16O2 by Direct Numerical Diagonalization

Abstract The Direct Numerical Diagonalization (DND) technique has been applied to the principal symmetric species of carbon dioxide. A three-dimensional formulation of the DND method has been implemented as a first step in using the method to calculate properties of simple polyatomic molecules. Recent high-resolution observations of both line positions and intensities have been incorporated into the method to yield new values for the potential function and the dipolar coefficients. The results are compared with the potential functions calculated by earlier DND efforts as well as the contact transformation approach. The results are also discussed in terms of the effects of truncation errors caused by the use of finite matrices to represent the Hamiltonian operator. The resulting eigenvectors have been used to determine a dipole moment function from 21 observed band intensity values. This dipole moment function in turn has generated a large list of band intensity estimates for 12 C 16 O 2 parallel bands which are being used to update the AFGL line parameter compilation. This list represents the first published set of band intensity values derived from a consistent quantum mechanical model for a linear polyatomic molecule.

Intensities and self-broadening coefficients of 13C16O2 lines in the laser band region

Abstract The intensities of 13 C 16 O 2 lines have been measured in the three bands centered at 883.145, 913.425, and 1017.659 cm − , using Fourier transform spectra. The square of the transition dipole moment and the Herman-Wallis coefficients have been determined; the band intensities deduced from these results are in good agreement with the ones obtained by calculations employing the Direct Numerical Diagonalization method. In addition, the self-broadening coefficients of 75 lines have been measured in the two strongest bands.

12C16O2 line intensities in the 4.8 μm spectral region

Abstract In the 4.8 μm spectral region, intensities of lines belonging to the 3 following perpendicular bands of 12 C 16 O 2 have been measured: the ∏←∑ cold band 11101-00001 centered at 2076.856 cm -1 , the Δ←∏ hot band 12201-01101 centered at 2093.345 cm -1 , and the ∑←∏ hot band 20001-01101 centered at 2129.756 cm -1 . Fourier transform spectra, under a resolution limit of about 0.0023 cm -1 , have been used. For each band, the square of the vibrational dipole-moment matrix element and the Herman-Wallis coefficients have been determined. These results are compared with the previous experimental results included in the last edition of the HITRAN molecular database, as well as with new results obtained by the Direct Numerical Diagonalization method.

High temperature absorption measurements and modeling of CO2 for the 12 micron window region

Abstract High temperature absorption measurements were made for CO2 gas in Local Thermodynamic Equilibrium (LTE) with a hot cell and high resolution interferometer. The experimental data were compared to band-model and line-by-line model transmittance calculations using line parameters from the HITRAN and HITEMP data bases. The line-by-line calculations using HITEMP were in excellent agreement with experimental measurements, while the model calculations using the HITRAN data underpredicted the absorption by approx. 10%.