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arXiv:2603.04465

Full-dimensional quantum scattering calculations of rovibrationally excited HD+HD collisions

Bikramaditya Mandal, Hubert Jóźwiak, Piotr Wcisło, Naduvalath Balakrishnan

physics.atom-phphysics.chem-phquant-phSubmitted Mar 3, 2026• Announced Mar 5, 2026
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Abstract

Full-dimensional quantum scattering calculations are reported for ro-vibrational transitions in HD+HD collisions using a highly accurate interaction potential for the H$_2$-H$_2$ system. Several near-resonant ro-vibrational transitions are identified that conserve the overall rotational angular momentum and nearly conserve the internal energy of the collision partners. Key anisotropic terms that drive the rotational transitions and angular momentum partial waves that contribute to low energy resonant features in the energy dependence of the cross sections are identified. The computed results are in agreement with total cross sections reported in previous experimental results, including resonant features in the energy dependence of the cross section. In particular, low-energy cross sections show a strong resonant feature associated with an $l=3$ partial wave in the incident channel. Rate coefficients for several inelastic rotational and ro-vibrational transitions are reported for temperatures ranging from $0.1$ K to $200$ K and they display a maximum between $1$ K-$10$ K reflecting the important contributions from the $l=3$ shape resonance that occurs around 2.5 K.

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Full-dimensional quantum scattering calculations are reported for ro-vibrational transitions in HD+HD collisions using a highly accurate interaction potential for the H2_22​-H2_22​ system. Several near-resonant ro-vibrational transitions are identified that conserve the overall rotational angular momentum and nearly conserve the internal energy of the collision partners. Key anisotropic terms that drive the rotational transitions and angular momentum partial waves that contribute to low energy resonant features in the energy dependence of the cross sections are identified. The computed results are in agreement with total cross sections reported in previous experimental results, including resonant features in the energy dependence of the cross section. In particular, low-energy cross sections show a strong resonant feature associated with an l=3l=3l=3 partial wave in the incident channel. Rate coefficients for several inelastic rotational and ro-vibrational transitions are reported for temperatures ranging from 0.10.10.1 K to 200200200 K and they display a maximum between 111 K-101010 K reflecting the important contributions from the l=3l=3l=3 shape resonance that occurs around 2.5 K.
A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T\ensuremath{\sim}{10}^{\ensuremath{-}8}$ K. A global six-dimensional H2{}_{2}2​-H2{}_{2}2​ potential-energy surface is adopted from a previous work [Boothroyd et al., J. Chem. Phys. 116, 666 (2002)]. State-resolved integral cross sections ${\ensuremath{\sigma}}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}({\ensuremath{\varepsilon}}_{\text{kin}})$ of different quantum-mechanical rotational transitions $ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}$ in the HD molecules and corresponding state-resolved thermal rate coefficients ${k}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}(T)$ have been computed. Additionally, for comparison, H2{}_{2}2​+H2{}_{2}2​ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.
The close coupling calculation of rotationally inelastic collision of He with Na2 is first performed by employing a recently computed ab initio potential energy surface. The process of rovibrational energy excitation and relaxation of Na2 in collision with He has been studied in detail based on the single and double exitations coupled cluster with a noniterative perturbation treatment of triple excitations CCSD （T） potential energy surface. Our results are in good agreement with the experimental results. Our results show that: （1）The elastic cross section（Δj=0） is much larger than the inelastic cross section. （2）The largest amplitude occurs at small scattering angles. At low Δj transition, the He projectile is predominantly forward scattering. Backward scattering occurs as Δj increases. （3）For inelastic cross section, the most effective transition is that with Δj=2.（4）The fast narrow diffraction oscillations in the cross sections are the obvious characteristics for the low Δj inelastic transitions, which decreases with increasing j. （5）The elastic differential-cross-sections（DCS）provides a useful visualization of rotational rainbows at low translational energy. It is beneficial to reducing the loss in molecular cooling and trapping.
The radiative association processes for Na+{\mathrm{Na}}^{+}Na+ colliding with 87Rb(5s)^{87}\mathrm{Rb}(5s)87Rb(5s) atoms have been investigated by using the quantum-mechanical method. The total and partial cross sections that associate to the specific rovibrational states are calculated rigorously in the energy range of ${10}^{\ensuremath{-}13}\ensuremath{-}1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. The association cross sections display rich resonance structures. The ratios of rotationally resolved cross sections to total association cross sections and the ratios of vibrationally resolved cross sections to rotationally resolved cross sections are calculated and presented. For energies less than ${10}^{\ensuremath{-}9}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, association to $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}$ (J=1J=1J=1) dominates over all other association states. As the energy increases, each resonance of the total cross sections is associated with the given angular component of specific bound states. In the energy range of ${10}^{\ensuremath{-}13}\ensuremath{-}1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, the vibrational states v=27v\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}27v=27 and v=28v\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}28v=28 are the most probable final states. The probability for the formation of molecular ion NaRb+{\mathrm{NaRb}}^{+}NaRb+ in the rovibrational states is discussed. The existence of Cooper minima in the radiative association cross sections is found and illustrated.
A first-principles based quantum dynamics study of the Li + LiNa(v = 0, j = 0) → Li2(v′, j′) + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li2Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.
The role of the geometric phase effect on chemical reaction dynamics is explored by examining the hydrogen exchange process in the fundamental H+HD reaction. Results are presented for vibrationally excited HD molecules in the v = 4 vibrational level and for collision energies ranging from 1 μ K to 100 K. It is found that, for collision energies below 3 K, inclusion of the geometric phase leads to dramatic enhancement or suppression of the reaction rates depending on the final quantum state of the HD molecule. The effect was found to be the most prominent for rotationally resolved integral and differential cross sections but it persists to a lesser extent in the vibrationally resolved and total reaction rate coefficients. However, no significant GP effect is present in the reactive channel leading to the D+H 2 product or in the D+H 2 HD+H reaction. A simple interference mechanism involving inelastic (nonreactive) and exchange scattering amplitudes is invoked to account for the observed GP effects. The computed results also reveal a shape resonance in the H+HD reaction near 1 K and the GP effect is found to influence the magnitude of the resonant part of the cross section. Experimental detection of the resonance may allow a sensitive probe of the GP effect in the H+HD reaction.
The results from electronically non-adiabatic and adiabatic quantum reactive scattering calculations are presented for the H + HD( v = 5–9) → H + HD( v ′, j ′) reaction at ultracold collision energies from 10 nK to 60 K. Several experimentally verifiable signatures of the geometric phase are reported in the total and vibrationally and rotationally resolved rate coefficients. Most notable is the predicted 2 orders of magnitude enhancement of the rotationally resolved ultracold rates of odd symmetry relative to those of even symmetry. Prominent shape resonances appear at higher collision energies (100 mK to 20 K), which could be measured experimentally. Significant geometric phase effects are also reported on the resonance energies and lifetimes. In particular, an enhancement (suppression) of the l = 1 ( l = 2) shape resonances for HD( v = 5, 6) is predicted for even symmetry relative to those of odd symmetry.