Robert H. Hunt

Resolution Enhancement of Spectra

A numerical method has been developed to correct high-resolution infrared spectra for the distortion introduced by the spectrometer. The method involves, first, an accurate determination of the spectrometer response function and, then, deconvolution by a point-successive over-relaxation procedure. The method is applied to portions of the Q branches N2O and CH4 near 3.3 μ. The spectra are observed at pressures below 1.0 torr with spectrometer response-function half-widths less than 0.02 cm−1. The deconvolved spectra show an improvement of resolution which approaches the limit set by the Doppler widths of the lines. Line separations measured from the deconvolved spectra are within 0.001 cm−1 of the calculated values. The reduction of line overlap in the deconvolved spectra considerably increases the number of lines whose positions may be accurately measured.

Line strengths, line widths, and dipole moment function for HCl

Abstract Previous expressions for the dipole moment matrix elements of the vibration-rotation bands of diatomic molecules, based on a quintic anharmonic oscillator potential, a cubic dipole moment function, and third order perturbation theory, are extended for the 1-0 and 2-0 bands to include second-order contributions. Line intensities in the 1-0 band of HCl are measured with 0.02 cm−1 resolution and analyzed to obtain a band intensity S 0 1 of 135 cm−2 atm−1 at 300°K and the following Herman-Wallis factor: F 0 1 (m) = 1 − 0.0260 m + 4.5 × 10 −4 m 2 . Similar measurements are made in the 2-0 band of HCl with 0.04 cm−1 resolution and yield S 0 2 = 3.73 cm −2 atm −1 and F 0 2 (m) = 1 − 0.0086 m + 4.1 × 10 −4 m 2 . These results and the previous 3-0 band intensity data are incorporated with the dipole moment matrix elements above to obtain the following dipole moment function for HCl: M(r) = 1.095 + 0.905(r - re) − 0.066(r - re)2 − 0.73(r - re)3, where r - re is in angstroms and M(r) is in Debyes. The half-widths of self-broadened lines of HCl in the 2-0 band are measured directly. The results are somewhat lower than previous measurements for |m|

Line intensities in the 3-0 band of CO and dipole moment matrix elements for the CO molecule☆

Abstract Line intensities in the 3-0 band of CO have been determined by the method of equivalent widths for near Doppler lines. The data were obtained with sample pressures between 4 and 40 Torr and a spectral slit width of 0.04 cm −1 . The values found for the band intensity at 273°K and the linear and quadratic Herman-Wallis coefficients were 0.0135 cm −2 atm −1 , 0.0118 and 1.8 × 10 −4 , respectively. The expressions for the dipole moment matrix elements derived in Part I were then evaluated for the vibrational band intensities used by Young and Eachus in order to test the present theory. Good agreement with the results of Young and Eachus was obtained both for the dipole moment coefficients of CO and for the Herman-Wallis factors for the 2-0 and 3-0 bands. New dipole moment coefficients and Herman-Wallis factors based on revised 1-0, 2-0, and 3-0 band intensities at 273°K of 260, 2.06, and 0.0132 cm −2 atm −1 were then calculated by means of the present theory. The dipole moment expansion was found to be, M ( r ) = −0.112 + 3.10 ( r - r e ) − 0.31 ( r - r e ) 2 − 2.28 ( r - r e ) 3 where r e is the equilibrium internuclear distance in angstroms and M ( r ) is in Debyes. A negative sign was assigned to M 0 on the basis of the good agreement which this sign gave between observed and calculated Herman-Wallis factors. It was concluded that the general expressions obtained in Part I are of good accuracy. Previous analytic expressions obtained for the 2-0 and 3-0 bands are not as accurate primarily because they do not include quadratic and cubic dipole moment terms.

Measurement and Analysis of the ν3 Band of Methane

The ν3 band of CH4 has been recorded with a spectral resolution of 0.016–0.019 cm−1 in the region from 2884 to 3139 cm−1. The manifolds containing the allowed lines were subsequently deconvoluted and 198 allowed and 86 forbidden lines were measured and tabulated. Line frequencies and intensities were calculated using the Hamiltonian as extended by Susskind and are listed for the 284 experimental lines which have been assigned. The rms difference in the measured and calculated frequencies for the 211 allowed transitions with upper state J ≤ 12 is 0.0078 cm−1. The 18 molecular constants used to culate the rotation‐vibration fine structure frequencies are compared with previous values and found to have uncertainties which are generally at least an order of magnitude smaller than those given previously.

Wavenumbers, line strengths, and assignments in the Doppler-limited spectrum of formaldehyde from 2700 to 3000 cm−1

Abstract The spectrum of H 2 CO from 2700 to 3000 cm −1 has been examined at Doppler-limited resolution using a tunable difference frequency laser spectrometer at Lincoln Laboratory. The wavenumbers and strengths of 4350 absorptions have been determined with an accuracy of 0.001 cm −1 and 5%, respectively. These data have been incorporated into the analysis of lower-resolution data from Florida State University to assign 72% of the observed absorptions to one of seven bands: ν 3 + ν 4 (a C -type band at 2655 cm −1 ), ν 3 + ν 6 (a B -type band at 2719.156 cm −1 ), ν 1 (an A -type band at 2782.457 cm −1 ), ν 5 (a B -type band at 2843.326 cm −1 ), ν 2 + ν 4 (a C -type band at 2905 cm −1 ), 2 ν 3 (an A -type band at 2999.5 cm −1 ) and ν 2 + ν 6 (a B -type band at 3000.066 cm −1 ). The band ν 3 + ν 4 has been observed for the first time, and the band center for 2 ν 3 has been corrected from a value of 2972 cm −1 to the value listed above. The effects of strong Fermi and Coriolis resonances on the spectra are discussed.

Rotational constants of the lowest torsional component (0G) of the ground state and lowest torsional component (1G) of the first excited torsional state of hydrogen peroxide

Abstract New high-resolution spectra of hydrogen peroxide has been taken in the OH stretching region and in the overtone-combination region of the OOH bends. Ordinary combination differences in the (0G) and (1G) torsional states and directly obtained energy level differences between these torsional states have been supplemented with combination differences obtained from previously published microwave data and fitted to obtain the rotational constants of the two torsional states and the parameter characterizing the perturbation between them. A simplified notation scheme for the vibrational-torsional-rotational levels, the transitions used to obtain direct energy level differences between levels of the (0G) and (1G) torsional states, and the specific Hamiltonian used are described in the text. A table of rotational and interaction constants is given, and also tables of the actual (perturbed) rotational levels in the (0G) and (1G) torsional states.

High‐Resolution Determination of the Widths of Self‐Broadened Lines of Carbon Monoxide

The half‐widths of self‐broadened lines of carbon monoxide have been measured directly with a resolution of 0.045 cm−1 in the first overtone band at room temperature for | m | values up to 31 and for pressures between 1 and 2 atm. The results, which have an estimated accuracy of ±3.0%, vary from 0.088 cm−1·atm−1 at | m | = 1 to 0.044 cm−1·atm−1 at | m | = 31, and occupy an intermediate position relative to other measurements. The half‐widths have also been determined from peak absorption measurements and previously measured line strengths and these widths agree with the directly measured values to better than 2%.

Measurement of Line Strengths at Low Pressures—Application to the 2–0 Band of CO

The use of low pressures and a high‐resolution spectrometer for the measurement of the absolute line strengths of gases in the near infrared is tested on the first overtone band of carbon monoxide. Measurements are made at pressures from 100 to 500 μ Hg, where the line profile has nearly a pure Doppler contour, and at pressures 2 to 7 cm Hg, where the effects of Doppler and collision broadening are both important. It is found that both wing and base corrections must be made in higher‐pressure measurements, and these corrections are given for lines with combined Doppler and collision‐broadened profiles. It is found that the use of the Doppler profile offers significant advantages for the accurate determination of line strengths, and a discussion of these advantages are included. It is shown that within the accuracy of the measurements, the true line profile at pressures from 100 to 500 μ Hg cannot be distinguished from the assumed Doppler profile. The band strength of the first overtone band of CO is calcu...

Dipole moment matrix elements for the 1-0, 2-0, and 3-0 vibration-rotation bands of diatomic molecules

Abstract Explicit expressions for the matrix elements of the dipole moment have been derived for the 1-0, 2-0, and 3-0 vibration-rotation bands of diatomic molecules. The derivation is based on a cubic dipole moment function and on radial wave functions obtained using a quintic power series expansion of the internuclear potential and third order perturbation theory. The results are given in the form of a rotationless matrix element multiplied by a rotational or Herman-Wallis factor. The expressions for the Herman-Wallis factors include the leading contributions from each dipole moment coefficient and have a reasonably simple form even in the case of the overtone bands. The rotationless matrix elements are similar to results obtained by Herman and Schuler except that their higher order terms are purposely omitted. The reason for this is discussed as are other approaches to the rotational problem which have incorporated a linear dipole moment function. It is pointed out that the results of the present theory for the case of CO are in very good agreement with the numerical treatment of CO by Young and Eachus. The actual comparison is given in a subsequent paper.

Molecular constants for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in 12CH4

Abstract In a previous paper (J.-E. Lolck and A. G. Robiette, J. Mol. Spectrosc. 88 , 14 (1981)) a theoretical model for the interacting upper states of the ν 1 , ν 3 , 2 ν 2 , ν 2 + ν 4 , and 2 ν 4 bands in methane was described. The present paper summarizes the results obtained, using this model, in a comprehensive analysis of the five bands of 12 CH 4 through J ′ = 12. Values of 80 molecular constants, of which 17 correspond to vibrationally off-diagonal operators, are reported. In addition the computed energy levels of the v 3 = 1 state are compared to the experimental ones and to the result of the previous isolated band approach.