Quantum calculations for rotational energy transfer in nitrogen molecule collisions

The H2 + H2 system has long been considered a benchmark system for ro-vibrational energy transfer in bimolecular collisions. However, most studies thus far have focused on collisions involving H2 molecules in the ground vibrational level or in the first excited vibrational state. While H2 + H2/HD collisions have received wide attention due to the important role they play in astrophysics, D2 + D2 collisions have received much less attention. Recently, Zhou et al. [ Nat. Chem. 2022, 14, 658-663, DOI: 10.1038/s41557-022-00926-z] examined stereodynamic aspects of rotational energy transfer in collisions of two aligned D2 molecules prepared in the v = 2 vibrational level and j = 2 rotational level. Here, we report quantum calculations of rotational and vibrational energy transfer in collisions of two D2 molecules prepared in vibrational levels up to v = 2 and identify key resonance features that contribute to the angular distribution in the experimental results of Zhou et al. The quantum scattering calculations were performed in full dimensionality and using the rigid-rotor approximation using a recently developed highly accurate six-dimensional potential energy surface for the H4 system that allows descriptions of collisions involving highly vibrationally excited H2 and its isotopologues.

Total and state-to-state rate coefficients for rotational energy transfer in collisions between NO(X 2Π) and He at temperatures down to 15 K

The distorted wave infinite order sudden (DWIOS) approximation for the calculation of vibrationally inelastic molecular collision cross sections

Test of the infinite-order sudden approximation for electron scattering at intermediate energy

The semiclassical S-matrix theory of Miller and Marcus is utilized to derive an exact classical mechanical expression for the effective cross sections governing collisional depolarization and rotational relaxation in open-shell molecules with Σ electronic symmetry. These cross sections are expressed as a sum of products of classical dynamical terms (which may be evaluated by conventional Monte Carlo techniques) and geometrical terms that describe the quantum mechanical coupling of the angular momentum vectors in the open-shell molecule. All effects on rotational transitions due to the nonzero electronic spin angular momentum in the open-shell molecule are accounted for through the geometrical terms. Recently, sophisticated molecular beam and laser double resonance techniques have allowed the state-resolved study of rotational energy transfer in collisions involving open-shell molecules in their ground electronic state. The present extension of classical scattering theory provides the theoretical framework for an exact classical mechanical calculation of the collision dynamics in such experiments.

Charge transfer due to collisions of ground state ${\mathrm{O}}^{3+}(2{s}^{2}2p{\phantom{\rule{0.2em}{0ex}}}^{2}{P}^{o})$ ions with molecular hydrogen are investigated using the quantum-mechanical molecular-orbital (QMO) coupled-channel method. The QMO calculations utilize $ab$ initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach for a representative range of orientation angles and diatom internuclear separations. Vibrationally resolved cross sections for nondissociative single electron capture are obtained for energies between 0.1 eV∕u and 10 keV∕u for ${\mathrm{H}}_{2}$ in its ground vibrational level using the infinite order sudden approximation (IOSA). Two further approximations are considered in which the electronic radial couplings are assumed to be independent of the diatom stretching. In the first case, vibrational motion is taken into account by multiplying the electronic radial couplings by Franck-Condon (FC) ionization factors while in the second, vibrational motion is completely neglected. We refer to these two approaches as the vibrational sudden approximation (VSA) and the electronic approximation (EA), respectively. In the latter, the resulting cross sections for electronic transitions are multiplied by FC factors to obtain relative vibrationally resolved cross sections which are independent of the collision energy (the centroid approximation). Comparison with existing experimental data for total and electronic state-selective cross sections shows best agreement with IOSA and VSA, but discrepancies for EA. The triplet-singlet electronic cross section ratio reveals a departure at low collision energies from the statistical value.

We have recorded time-domain coherence decay and population decay signals for the pure rotational OCS J=0–1 transition broadened by argon and by helium using pulse methods based on Stark switching of the molecular resonance frequency. The signals have been analyzed to yield the pressure dependence of the two decay rates (1/T2 and 1/T1) and their dependence on the absorber (OCS) speed. For comparison, using a potential which has been used several times in the literature for these systems, IOS (infinite order sudden approximation) scattering results are given. These calculations give substantial agreement on the ratio of the speed dependence of the relaxation rate to the rate itself, but fail to predict the rates quantitatively, especially for helium, or the relationship between the argon and the helium results. Because the IOS is expected to be accurate for these systems, the helium potential is ruled out by these data.

Accurate quantum mechanical close coupling (CC) integral cross sections are reported for rotationally inelastic Ar–N2 collisions at room temperature using an empirical intermolecular potential. These cross sections are used to test the infinite order sudden (IOS) approximation and the results of several methods [classical trajectories (CT), full sudden (SA), generalized phase shift (GPS), and classical limit generalized phase shift (CGPS)] as reported in the preceding paper by Pattengill. The IOS approximation works very well for cross sections involving low rotational states. The CT method works well for all the cross sections examined, justifying the popular belief that the rotational motion of N2 is essentially classical at room temperature.

The quantum state-to-state rotationally inelastic quenching of N2O by colliding with a He atom is studied on an abinitio potential energy surface with N2O lying on its vibrational ground state. The cross sections for collision energies from 10-6-100cm-1 and rate constants from 10-5-10K are calculated employing the fully converged quantum close-coupling method for the quenching of the j = 1-6 rotational states of N2O. Numerous van der Waals shapes or Feshbach resonances are observed; the cross sections of different channels are found to follow the Wigner scaling law in the cold threshold regime and may intersect with each other. In order to interpret the mechanism and estimate the cross sections of the rotational energy transfer, we propose a minimal classical model of collision between an asymmetric double-shell ellipsoid and a point particle. The classical model reproduces the quantum scattering results and points out the attractive interactions and the potential asymmetry can affect the collision process. The resulting insights are expected to expand our interpretations of inelastic scattering and energy transfer in molecular collisions.

A simple, direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given. Connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed. Simple procedures for calculating cross sections for specific transitions are discussed and many older model formulas are given clear derivations. Total (summed over rotation) differential, integral, and transport cross sections, useful in the analysis of many experiments involving nonspherical molecules, are shown to be exceedingly simple: They are just averages over the potential angle of cross sections calculated using simple structureless spherical particle formulas and programs. In the case of vibrationally inelastic scattering, the IOSA, without further approximation, provides a well-defined way to get fully three dimensional cross sections from calculations no more difficult than collinear calculations. Integral, differential, viscosity, and diffusion cross sections for He–CO2 obtained from the IOSA and a realistic intermolecular potential are calculated as an example and compared with experiment. Agreement is good for the complete potential but poor when only its spherical part is used, so that one should never attempt to treat this system with a spherical model. The simplicity and accuracy of the IOSA make it a viable method for routine analysis of experiments involving collisions of nonspherical molecules.

A semiclassical study of vibrational and rotational transition in He+H 2 at suprathermal energies

A simple procedure is developed to correct the infinite-order sudden (IOS) approximation for the finite energy separation between states. A phase-shift matrix 〈i‖Δη‖j〉 is computed using the IOS and multiplied by an energy correction factor Bij and then exponentiated to give the S matrix. The correction factor is obtained by calculating an approximate phase-shift matrix for a finite energy separation and dividing this by the approximate form with no energy separation. A simple procedure is given for choosing the energy at which the IOS phase shifts are calculated. Results for He+H2 and Ar+N2 show good agreement with accurate calculations and a substantial improvement over the IOS.

Classical trajectory calculations of effective cross sections have been carried out for the N2-Ne system using the recent HFD3(N2-Ne) potential surface of McCourt et al. Forty-five such cross sections governing a wide variety of transport and relaxation phenomena in binary gaseous mixtures have been calculated at a number of temperatures ranging from 77K to 1100K. Wherever possible, we have made comparisons with much cheaper infinite-order sudden approximation (IOSA) calculations in order to assess their reliability. For cross sections relating to diffusion and viscosity, IOSA errors are less than 5·4 per cent, but, for cross sections which vanish for isotropic interactions, the IOSA is much less reliable, with possible errors of up to a factor of two. At the same time, we have compared our classical trajectory results for this surface with available experimental results. We find that the HFD3(N2-Ne) surface is too anisotropic, by as much as 20 per cent.

Time-resolved double resonance spectroscopy using infrared pump radiation and millimeter-wave and submillimeter-wave probe radiation (IRMMDR) has been used to study rotational energy transfer (RET) in CH3Cl. A collisional energy transfer model using only five parameters for RET plus those needed for vibrational processes is shown to accurately model 350 IRMMDR time responses for two different pump states and 43 probe transitions covering a wide range of rotational states. Previous studies in this laboratory have revealed that J- and K-changing RET have vastly different characters in CH3F [J. Chem. Phys. 92, 6480 (1990)]. Both J- and K-changing RET were accurately modeled with four parameters—one for dipole–dipole collisions, two for the ΔJ scaling law, and one for the cumulative rate of K-changing collisions. As was found for CH3F, J-changing rotational collision rates in CH3Cl are modeled accurately by both the statistical power gap (SPG) law and the infinite order sudden approximation using a power law expression for the basis rates (IOS-P). However, in contrast to CH3F, where all IRMMDR time responses for K-changing collisions have the same shape, many time responses of CH3Cl states populated by K-changing collisions contain an additional early time feature (ETF) that varies with pump and probe states. Nonetheless, a simple generalization of the previously reported model for K-changing collisions is shown to account for all of the additional features observed in CH3Cl. Rather than observing a fixed temperature for K-changing collisions as was the case for CH3F, the temperature is found to be a function of time for CH3Cl. Moreover, the two new parameters this adds to the RET model are related to known physical quantities. A qualitative argument of K-changing collisions based on a classical picture is offered to explain the difference between the measured J- and K-changing state-to-state rates in CH3Cl.

The infinite order sudden (IOS) approximation is extended to calculate rate constants for rotationally inelastic scattering between two H2O molecules. A modified version of the breathing sphere (BS) approximation, which has previously been shown to work reasonably well for N2+N2 rotationally inelastic scattering, is also extended to H2O+H2O scattering. The rate constants obtained using both approximations are used to determine Raman Q-branch spectral linewidths. In order to calculate such linewidths, it is necessary to sum the rate constants for any initial rotational level over all final inelastic rotational levels. While the IOS linewidths are in reasonable agreement with experiment over a range of temperatures, the IOS-BS linewidths are much too small.