Comparison of the Calculated Collision-Induced Absorption Spectra by Dense Hydrogen-Helium, Deuterium-Helium, and Tritium-Helium Gas Mixtures

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 infraredinactive gases, such as hydrogen and its homonuclear isotopes, absorb infrared radiation, if sufficiently high gas densities are encountered [1][2][3][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 [1] 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 collisioninduced absorption spectra have been compared to laboratory measurements at infrared and microwave frequencies [7][8][9].Close agreement between theory and experiment has been observed [1].We have recently determined the IDS and PES of H 2 molecules interacting with helium atoms, allowing for high rotovibrational excitation of H 2 [7,8].We have used these surfaces to compute the CIA spectra of H 2 interacting with He [8] and of D 2 interacting with He [9] over a wide range of temperatures.Here we use the same surfaces to compute the CIA spectrum of T 2 interacting with He.
While the electronic structure of X 2 -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 H 2 -H 2 and H 2 -He exist, far fewer laboratory measurements of the CIA of D 2 -He exist, and no laboratory measurements of the CIA of gaseous mixtures of T 2 -He are available thus far.Theoretical calculations therefore provide the only knowledge of the collision-induced absorption of T 2 -He.The reliability of these calculations is supported by the good agreement between the calculations for H 2 -He [8] and D 2 -He [9] 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 α(ω, T), a function of frequency ω, and temperature T, normalized by the gas densities ρ T of tritium molecules and ρ He of helium, by a state-tostate 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 T 2 .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 [1].In particular, in [11] for collision-induced absorption by H 2 -He mixtures, at frequencies in the fundamental band of H 2 , the differences between calculations with isotropic and anisotropic potentials were found to amount to less than 10% for H 2 -He at T = 298 K, and even less at lower temperatures [11].Further evidence of the applicability of the isotropic potential approximation in H 2 -He comes from computational studies by Gianturco et al. [12] of a weakly bound "halo" state of He interacting with para-H 2 , observed by Kalinin et al. [13], in molecular beams produced by cryogenic freejet expansion.Gianturco et al. [12] compared the binding energies, average H 2 -He distances, and peak positions of the radial distribution functions as computed with the potential of Boothroyd et al. [14] 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 H 2 interaction with the helium partner."They also observed that the orientational anisotropy of the ground state probability density is very slight, for H 2 -He [12].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 D 2 -He and T 2 -He than for H 2 -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.The collision-induced absorption spectrum of gaseous T 2 -He, normalized by the densities of helium and tritium molecules, at temperatures of 150 K, 600 K, 2000 K, and 9000 K (from bottom to top) for frequencies from 0 to 20,000 cm −1 .From left to right, the peaks correspond roughly to the rotational band, the fundamental band, and the first through eighth overtone bands of T 2 .
For comparison, we show here also the collision-induced absorption spectra of H 2 -He (see Figure 2) and D 2 -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 ν > 0. For H 2 -He we have included initial states up to ν = 5 and j = 27.Final states range up to ν = 14 and j = 35.For D 2 -He we have included initial states up to ν = 9 and j = 32.Final states range up to ν = 14 and j = 32.For T 2 -He we have included initial states up to ν = 11 and j = 32.Final states range up to ν = 14 and j = 32.An interesting feature of the T 2 -He spectrum is the rise in peak intensities of the higher overtones; that is, the fifth, sixth, and seventh T 2 overtones are more intense than the fourth T 2 overtone at the three lower temperatures, and, at the highest temperature shown, there is a highfrequency shoulder in the absorption spectrum.A similar effect is detectable in the D 2 -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 T 2 -He because the lower vibrational frequency makes larger deviations from the equilibrium bond length more accessible thermally, at any given temperature.The collision-induced absorption spectrum of gaseous H 2 -He, normalized by the densities of helium and hydrogen molecules, at temperatures of 150 K, 600 K, 2000 K, and 9000 K (from bottom to top) for frequencies from 0 to 20,000 cm −1 .From left to right, the peaks correspond roughly to the rotational band, the fundamental band, and the first through fourth overtone bands of H 2 ; from [8].

)
Figure 3: The collision-induced absorption spectrum of gaseous D 2 -He, normalized by the densities of helium and deuterium molecules, at temperatures of 150 K, 600 K, 2000 K, and 9000 K (from bottom to top) for frequencies from 0 to 20,000 cm −1 .From left to right, the peaks correspond roughly to the rotational band, the fundamental band, and the first through sixth overtone bands of D 2 ; from [9].

Figure 1 :
Figure1: The collision-induced absorption spectrum of gaseous T 2 -He, normalized by the densities of helium and tritium molecules, at temperatures of 150 K, 600 K, 2000 K, and 9000 K (from bottom to top) for frequencies from 0 to 20,000 cm −1 .From left to right, the peaks correspond roughly to the rotational band, the fundamental band, and the first through eighth overtone bands of T 2 .

Figure 2 :
Figure2: The collision-induced absorption spectrum of gaseous H 2 -He, normalized by the densities of helium and hydrogen molecules, at temperatures of 150 K, 600 K, 2000 K, and 9000 K (from bottom to top) for frequencies from 0 to 20,000 cm −1 .From left to right, the peaks correspond roughly to the rotational band, the fundamental band, and the first through fourth overtone bands of H 2 ; from[8].