Polarizability tensor invariants of H2, HD, and D2

Abstract

We report an exhaustive compilation of wavelength-dependent matrix elements over the mean polarizability (α¯) and polarizability anisotropy (γ) operators for the rovibrational states of the H, HD, and D molecules together with an accompanying computer program for their evaluation. The matrix elements can be readily evaluated using the provided codes for rovibrational states with J = 0-15 and v = 0-4 and for any laser wavelengths in the interval 182.25-1320.6 nm corresponding to popular, commercially available lasers. The presented results substantially extend the scope of the data available in the literature, both in respect of the rovibrational transitions analyzed and the range of covered laser frequencies. The presented detailed tabulation of accurate polarizability tensor invariants is essential for successful realization of our main long-term goal: developing a universal standard for determining absolute Raman cross sections and absolute Raman intensities in experimental Rayleigh and Raman scattering studies of molecules.

Laboratory Study of Rate Coefficients for H2:H2 Inelastic Collisions between 295 and 20 K

“…Uncertainty is twice as much for g J J 0 1 | | , but their weight is far smaller. The moments agree well with recent high-level ab initio calculations (Raj et al 2018); C(J) is a very nearly constant factor fixed a posteriori by the normalization of the populations. From Equations (26) and (27)…”

Toward standardization of Raman spectroscopy: Accurate wavenumber and intensity calibration using rotational Raman spectra of H2, HD, D2, and vibration–rotation spectrum of O2

“…This spectral region is available for measurement using the second harmonic of Nd:YAG as well as argon ion lasers, thus enabling measurement of calibrated Raman spectra falling within −1,036 to 1,700 cm −1 using 532‐nm excitation, ~600–3,330 cm −1 using 488‐nm excitation, and ~1,950–4,685 cm −1 using 457.9‐nm excitation. Previously reported results on theoretical wavelength‐dependent polarizability anisotropy [ 24,58 ] for H 2 , HD, and D 2 enable intensity calibration procedure reported here to be applied also to other wavelength excitations.…”

“…Furthermore, Raman intensities from molecular hydrogen and its isotopologues serve as high accuracy independent standards, which can be compared with accurate theoretical Raman intensities determined using ab initio wavelength-dependent polarizability invariants and rovibrational wavefunctions. [19,24,25] Thus, high accuracy in wavenumber and intensity calibration can be realized due to the particularly simple quantum structure of H 2 .…”

“…We calculated the wavelength‐dependent matrix elements of polarizability anisotropy for H 2 , HD, and D 2 with high accuracy (error < 0.1%) in our previous work. [ 24,25 ] In the present experiment, we utilize 13 pairs of pure rotational Raman bands from H 2 , HD, and D 2 (in the range from −1,034 to 1,447 cm −1 ), for which the required ratios of square of polarizability anisotropy are available. For O 2 , we use the vibration–rotation Raman bands (O1‐ and S1‐branches) accompanying the fundamental in the 1,400–1,700 cm −1 region, for which the corresponding ratio of polarizability anisotropy matrix elements has been reported by Buldakov et al [ 26 ] This inclusion of vibration–rotation bands from O 2 helps us to extend the calibration region while improving accuracy for both wavenumber and intensity calibration on the Stokes end of the Raman spectra where bands from H 2 , HD, and D 2 are weak.…”

“…For wavenumber calibration, theoretical and experimental wavenumbers accurately determined for H 2 and D 2 , [ 21 ] HD, [ 22 ] and O 2 [ 23 ] are used as standards. For intensity calibration, accurate polarizability anisotropy calculated by us previously [ 24,25 ] is used to determine the intensities of the rotational Raman bands of H 2 , HD, and D 2 as intensity standards. Vibration–rotation Raman intensities of O 2 corrected for vibration–rotation interactions [ 26 ] are also used as additional intensity standards.…”