The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H 2 and Na + N 2 . This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory.

The interaction between molecular (atomic) electron(s) and the vacuum field of a reflective cavity generates a significant interest thanks to the rapid developments in nanophotonics. Such interaction which lies within the realm of cavity quantum electrodynamic can substantially affect transport properties of molecular systems. In this work we consider non-adiabatic electron transfer process in the presence of a cavity mode. We present a generalized framework for the interaction between a charged molecular system and a quantized electromagnetic field of a cavity and apply it to the problem of electron transfer between a donor and an acceptor placed in a confined vacuum electromagnetic field. The effective system Hamiltonian corresponds to a unified Rabi and spinboson model which includes a self-dipole energy term. Two limiting cases are considered: one where the electron is assumed much faster than the cavity mode and another in which the electron tunneling time is significantly larger than the mode period. In both cases a significant rate enhancement can be produced by coupling to the cavity mode in the Marcus inverted region. The results of this work offer new possibilities for controlling electron transfer processes using visible and infrared plasmonics.

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complexvalued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by realvalued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the bodyfixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

The mixed quantum/classical approach is applied to the problem of ro-vibrational energy transfer in the inelastic collisions of CO(v = 1) with He atom, in order to predict the quenching rate coefficient in a broad range of temperatures 5 < T < 2500 K. Scattering calculations are done in two different ways: direct calculations of quenching cross sections and, alternatively, calculations of the excitation cross sections plus microscopic reversibility. In addition, a symmetrized averagevelocity method of Billing is tried. Combination of these methods allows reproducing experiment in a broad range of temperatures. Excellent agreement with experiment is obtained at 400 < T < 2500 K (within 10%), good agreement in the range 100 < T < 400 K (within 25%), and semiquantitative agreement at 40 < T < 100 K(within a factor of 2). This study provides a stringent test of the mixed quantum/classical theory, because the vibrational quantum in CO molecule is rather large and the quencher is very light (He atom). For heavier quenchers and closer to dissociation limit of the molecule, the mixed quantum/classical theory is expected to work even better. © 2013 AIP Publishing LLC. [http://dx

For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.

The mixed quantum/classical theory (MQCT) for inelastic molecule-atom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetric-top-rotor molecule in the body-fixed reference frame. This complements a similar theory formulated in the space-fixed reference-frame [M. Ivanov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H 2 O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm −1 the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm −1 the errors are consistently in the range of 1%-2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fully-coupled MQCT calculations scales as n 2 , where n is the number of channels. This is more favorable than the full-quantum inelastic scattering calculations that scale as n 3 . Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages. © 2014 AIP Publishing LLC.

A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies.

The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.