Journal of Atomic, Molecular, and Optical Physics
Volume 2011 (2011), Article ID 470530, 3 pages
Comparison of the Calculated Collision-Induced Absorption Spectra by Dense Hydrogen-Helium, Deuterium-Helium, and Tritium-Helium Gas Mixtures
1Department of Physics, The University of Texas at Austin, Austin, TX 78712-1081, USA
2Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA
Received 10 June 2011; Accepted 7 August 2011
Academic Editor: Klaus R. Bartschat
Copyright © 2011 Martin Abel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We have recently determined the induced dipole surface (IDS) and potential energy surface (PES) of collisional H2-He complexes. We have used these surfaces to compute the binary collision-induced absorption spectra of H2 molecules interacting with He atoms and of D2 molecules interacting with He atoms. Here we extend these calculations to the case of T2 molecules interacting with He atoms. Whereas the electronic structure of X2-He is virtually the same for all hydrogen isotopes X = H, D, or T, the collisional dynamics and molecular scattering wave functions are different for the different collisional pairs. We have calculated spectra up to a temperature of 9000 K and frequencies up to 20,000 cm−1. Here we compare the calculated collision-induced absorption spectra for the different hydrogen isotopes. While we have observed reasonable agreement between our calculations and laboratory measurements for the collisional H2-He and D2-He complexes, there are no laboratory measurements for T2-He collisional complexes, and one must rely on the fundamental theory, supported by the agreement between theory and experiment for the other isotopes.
It is an interesting fact that even the so-called infrared-inactive gases, such as hydrogen and its homonuclear isotopes, absorb infrared radiation, if sufficiently high gas densities are encountered [1–4]. This absorption can be traced back to transient electric dipole moments that are induced during collisions of two or more molecules by the same mechanisms that result in the intermolecular forces, that is, by exchange, dispersion forces, and multipolar induction. Modulation of these induced dipole moments due to vibration, rotation, and relative translational motion leads to collision-induced absorption (CIA) of radiation from applied electromagnetic fields. Collision-induced absorption is omnipresent in dense media—it has been observed in dense gases, liquids, and solids [1, 5, 6].
Laboratory measurements of CIA are performed at a very limited range of selected temperatures and frequencies. In contrast to that, the fundamental theory  makes it possible to compute collision-induced absorption spectra reliably, over a wide range of temperatures and frequencies, thereby providing numerical values for the absorption intensities even where laboratory measurements do not exist. To compute the binary collision-induced absorption spectra from the fundamental theory, the induced dipole surfaces (IDSs) and potential energy surfaces (PESs) of the binary van der Waals complexes under consideration have to be known. These surfaces have been obtained using quantum chemical methods [7, 8]. The thus computed collision-induced absorption spectra have been compared to laboratory measurements at infrared and microwave frequencies [7–9]. Close agreement between theory and experiment has been observed . We have recently determined the IDS and PES of H2 molecules interacting with helium atoms, allowing for high rotovibrational excitation of H2 [7, 8]. We have used these surfaces to compute the CIA spectra of H2 interacting with He  and of D2 interacting with He  over a wide range of temperatures. Here we use the same surfaces to compute the CIA spectrum of T2 interacting with He.
While the electronic structure of X2-He is virtually the same for all hydrogen isotopes X = H, D, or T, the collisional dynamics and molecular scattering wave functions are different for the different species [9, 10]. Whereas numerous laboratory measurements of collision-induced absorption spectra of H2-H2 and H2-He exist, far fewer laboratory measurements of the CIA of D2-He exist, and no laboratory measurements of the CIA of gaseous mixtures of T2-He are available thus far. Theoretical calculations therefore provide the only knowledge of the collision-induced absorption of T2-He. The reliability of these calculations is supported by the good agreement between the calculations for H2-He  and D2-He  collisional complexes and existing laboratory measurements.
The reader can find a detailed description of the computational procedures elsewhere [1, 7, 11]. We have obtained the absorption coefficient , a function of frequency , and temperature , normalized by the gas densities of tritium molecules and of helium, by a state-to-state quantum scattering calculation, which accounts for the interaction of the collisional complex with the radiation field. This quantity is shown in Figure 1 for the temperatures 150 K, 600 K, 2000 K, and 9000 K, for frequencies from 0 to 20,000 cm−1. It is remarkable that the normalized absorption intensity varies over several orders of magnitude. From left to right, the peaks in Figure 1 correspond roughly to the rotational band, the fundamental band, and the first through eighth overtone bands of T2. The absorption minima that appear between the peaks are quite deep at the lowest temperatures, but with increasing temperature the peaks merge. It should be pointed out here that for all calculations we have employed the isotropic potential approximation, an approach that has been found to be quite reasonable in previous studies of collision-induced absorption . In particular, in  for collision-induced absorption by H2-He mixtures, at frequencies in the fundamental band of H2, the differences between calculations with isotropic and anisotropic potentials were found to amount to less than 10% for H2-He at K, and even less at lower temperatures . Further evidence of the applicability of the isotropic potential approximation in H2-He comes from computational studies by Gianturco et al.  of a weakly bound “halo” state of He interacting with para-H2, observed by Kalinin et al. , in molecular beams produced by cryogenic free-jet expansion. Gianturco et al.  compared the binding energies, average H2-He distances, and peak positions of the radial distribution functions as computed with the potential of Boothroyd et al.  versus the values obtained with the isotropic component of that potential, averaged over the ground rotovibrational state. They concluded that “the isotropic approximation provides a very good description of the H2 interaction with the helium partner.” They also observed that the orientational anisotropy of the ground state probability density is very slight, for H2-He . We believe that the isotropic potential approximation is useful for the heavier species as well although we note that the separation of the zeroth-order vibration-rotation states is smaller for D2-He and T2-He than for H2-He. Inclusion of the potential anisotropy in quantum close-coupled scattering calculations is impractical currently because the anisotropy causes coupling of a very large number of channels.
For comparison, we show here also the collision-induced absorption spectra of H2-He (see Figure 2) and D2-He (see Figure 3). As the figures illustrate, increasing the isotope mass of the hydrogen isotope leads to decreasing absorption intensity and a higher number of overtone bands within the same frequency region. This can easily be explained by the observation that increasing the isotope mass reduces the fundamental vibrational frequency of the molecule and also leads to slower collisions, at the same temperature. We note that at the higher temperatures there is a significant population of the hydrogen isotopes in vibrational states with . For H2-He we have included initial states up to and . Final states range up to and . For D2-He we have included initial states up to and . Final states range up to and . For T2-He we have included initial states up to and . Final states range up to and . An interesting feature of the T2-He spectrum is the rise in peak intensities of the higher overtones; that is, the fifth, sixth, and seventh T2 overtones are more intense than the fourth T2 overtone at the three lower temperatures, and, at the highest temperature shown, there is a high-frequency shoulder in the absorption spectrum. A similar effect is detectable in the D2-He spectrum at intermediate temperatures. This effect might be due to an enhancement of the induced dipoles at larger bond lengths, for any given intermolecular separation, and the increased contributions of larger bond lengths to the transition matrix elements for the higher overtones. It also makes sense to see this for T2-He because the lower vibrational frequency makes larger deviations from the equilibrium bond length more accessible thermally, at any given temperature.
Support by the National Science Foundation, Grants no. AST0709106 (to L. Frommhold) and AST0708496 (to K. L. C. Hunt), is gratefully acknowledged. Furthermore, the authors are thankful for support from the Center for Complex Quantum Systems at the University of Texas.
- L. Frommhold, Collision-Induced Absorption in Gases, Cambridge University Press, New York, NY, USA, 2006.
- W. Meyer and L. Frommhold, “Collision-induced rototranslational spectra of H2-He from an accurate ab initio dipole moment surface,” Physical Review A, vol. 34, no. 4, pp. 2771–2779, 1986.
- L. Frommhold and W. Meyer, “Erratum: Collision-induced rotovibrational spectra of H2-He pairs from first principles,” Physical Review A, vol. 35, no. 2, pp. 632–638, 1987.
- L. Frommhold and W. Meyer, “Collision-induced rotovibrational spectra of H2-He pairs from first principles,” Physical Review A, vol. 41, no. 1, p. 534, 1990.
- G. Birnbaum, Phenomena induced by intermolecular interactions, NATO Advanced Research Workshop Series B127, Plenum Press, New York, NY, USA, 1985.
- G. C. Tabisz and M. N. Neuman, Collision- and Interaction-Induced Spectroscopy, Series C, vol. 452 of NATO Science Series C: Mathematical and Physical Sciences, Kluwer Academic, Dodrecht, The Netherlands, 1st edition, 1995.
- L. Frommhold, M. Abel, F. Wang, M. Gustafsson, X. Li, and K. L. C. Hunt, “Infrared atmospheric emission and absorption by simple molecular complexes, from first principles,” Molecular Physics, vol. 108, no. 17, pp. 2265–2272, 2010.
- X. Li, A. Mandal, E. Miliordos, and K. L. C. Hunt, “Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: A new ab initio dipole surface for high-temperature applications,” Journal of Chemical Physics. In press.
- M. Abel, L. Frommhold, X. Li, and K. L.C. Hunt, “Note: computation of collision-induced absorption by dense deuterium-helium gas mixtures,” Journal of Chemical Physics, vol. 134, no. 7, 2011.
- M. Abel and L. Frommhold, “Note: collision-induced infrared absorption by gaseous deuterium,” Journal of Chemical Physics, vol. 133, no. 14, Article ID 146101, 2 pages, 2010.
- M. Gustafsson, L. Frommhold, and W. Meyer, “Infrared absorption spectra by H2-He collisional complexes: the effect of the anisotropy of the interaction potential,” Journal of Chemical Physics, vol. 113, no. 9, pp. 3641–3650, 2000.
- F. A. Gianturco, T. González-Lezana, G. Delgado-Barrio, and P. Villarreal, “The binding of 4He and 3He to a hydrogen molecule: a computational study for pH2 and oH2,” Journal of Chemical Physics, vol. 122, no. 8, Article ID 084308, 5 pages, 2005.
- A. Kalinin, O. Kornilov, L. Y. Rusin, and J. P. Toennies, “Evidence for a bound HeH2 halo molecule by diffraction from a transmission grating,” Journal of Chemical Physics, vol. 121, no. 2, pp. 625–627, 2004.
- A. I. Boothroyd, P. G. Martin, and M. R. Peterson, “Accurate analytic He-H2 potential energy surface from a greatly expanded set of ab initio energies,” Journal of Chemical Physics, vol. 119, no. 6, pp. 3187–3207, 2003.