Kinetic Isotope Effect in Low-Energy Collisions between Hydrogen Isotopologues and Metastable Helium Atoms: Theoretical Calculations Including the Vibrational Excitation of the Molecule

Abstract

We present very accurate theoretical results of Penning ionization rate coefficients of the excited metastable helium atoms (⁴He(2³S) and ³He(2³S)) colliding with the hydrogen isotopologues (H₂, HD, D₂) in the ground and first excited rotational and vibrational states at subkelvin regime. The calculations are performed using the current best ab initio interaction energy surface, which takes into account the nonrigidity effects of the molecule. The results confirm a recently observed substantial quantum kinetic isotope effect (Nat. Chem. 2014, 6, 332-335) and reveal that the change of the rotational or vibrational state of the molecule can strongly enhance or suppress the reaction. Moreover, we demonstrate the mechanism of the appearance and disappearance of resonances in Penning ionization. The additional model computations, with the morphed interaction energy surface and mass, give better insight into the behavior of the resonances and thereby the reaction dynamics under study. Our theoretical findings are compared with all available measurements, and comprehensive data for prospective experiments are provided.

Figure 1

Interaction energy of He* + H₂/HD/D₂, where the molecule is in the ground rotational state (j = 0) and in the ground or first excited vibrational state (v = 0 or 1). Two angular orientations are chosen: the linear one (θ = 0; the batch of lower curves) and the T-shaped one (θ = π/2; the batch of upper curves).

Figure 2

Isotropic (V₀) and anisotropic (V₁ and V₂) radial interaction potential terms of He* + H₂/HD/D₂, where the molecule is in the ground rotational state (j = 0) and in the ground or first excited vibrational state (v = 0 or 1).

Figure 3

Theoretical and experimental reaction rate coefficients of the H₂/HD/D₂ molecules in the ground and excited rotational (j = 0/1) and vibrational (v = 0/1) states, with ⁴He(2³S) [left panels] or ³He(2³S) [right panels]. The theoretical results have been convoluted with the experimental energy resolution. No matching and scaling have been performed to fit the experimental data. The points with error bars are experimental values: the purple ones are for j = 0, and the green ones are for j = 1 (both taken from ref (6)), whereas the black ones are for the mixture of para and ortho molecules (taken from ref (2)). Note that the experimental data are burdened with systematic normalization error greater than the vertical discrepancy with respect to our results. The arrows schematically indicate the evolution of some resonances, caused by the isotopic substitution with respect to the molecule (dashed) or by the vibrational excitation of the molecule (dotted).

Figure 4

Reaction rate coefficients of ⁴He(2³S) with the rovibrational ground-state hydrogen molecule, where the mass of one of the atoms in H₂ is morphed from the H-atom mass to the D-atom one and simultaneously the interaction energy is morphed from the ⁴He* + H₂ form to the ⁴He* + HD one, according to the transformation presented in eqs 3 and 4. Only the curves indicated by the values of λ equal to 0 and 1 correspond to the physical ⁴He* + para-H₂(j = 0, v = 0) [the a₀ panel of Figure 3] and ⁴He* + HD(j = 0, v = 0) [the b₀ panel of Figure 3] resonances, whereas the rest of the curves are to show the evolution from the former case into the latter one. The theoretical results have been convoluted with the experimental energy resolution.

Figure 5

Theoretical reaction rate coefficients of the ³He* + D₂(j, v) collisions, for various values of j and v, corresponding to the data from the f₀ and f₁ panels of Figure 3, but without the convolution.

Figure 6

Effective adiabatic potentials (adiabats) as a function of intermolecular separation R for the ³He(2³S) atom colliding with ortho/para-D₂(j = 0/1) in the vibrational ground (v = 0; top panel) and excited (v = 1; bottom panel) states. All adiabats here are characterized by the partial wave l = 4. They support the low-energy resonances. J denotes the total angular momentum, |l – j| ≤ J ≤ l + j. For pragmatic reasons, all adiabats are moved to achieve asymptotes at zero.

Figure 7

Reaction rate coefficients of ³He(2³S) + para-D₂(j = 1) with the interaction energy morphed from the v = 0 vibrational form to the v = 1 one, according to the following transformation: Ṽ^morph = (1 – λ)⟨V⟩_j=1,v=0 + λ⟨V⟩_j=1,v=1, where λ ∈ [0, 1], see eq 5. The theoretical results have been convoluted with the experimental energy resolution.