We re-introduce a semi-classical methodology based on theories developed for the determination of broadening coefficients. We show that this simple and extremely fast methodology provides results that are in good agreement with results obtained using the more sophisticated MQCT approach. This semi-classical methodology could be an alternative approach which allows to provide large sets of collisional data for very complex molecular systems. It saves time both on the determination of potential energy surfaces and on the collisional dynamical calculations. In addition this paper provides more complete sets of rotational de-excitation cross-sections and rate coefficients of H2O perturbed by a thermal average of water molecules. Those data can be used in the radiative transfer modelling of cometary atmospheres.

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A hierarchy of approximate methods is proposed for solving the equations of motion within a framework of the mixed quantum/classical theory (MQCT) of inelastic molecular collisions. Of particular interest is a limiting case: the method in which the classical-like equations of motion for the translational degrees of freedom (scattering) are decoupled from the quantumlike equations for time evolution of the internal molecular states (rotational and vibrational). In practice, trajectories are pre-computed during the first step of calculations with driving forces determined solely by the potential energy surface of the entrance channel, which is an adiabatic trajectory approximation. Quantum state-to-state transition probabilities are computed in the second step of calculations with an expanded basis and very efficient step-size adjustment. Application of this method to H 2 O + H 2 rotationally inelastic scattering shows a significant computational speedup by 2 orders of magnitude. The results of this approximate propagation scheme are still rather accurate, as demonstrated by benchmarking against more rigorous calculations in which the quantum and classical equations of motion are held coupled and against the full-quantum coupled-channel calculations from the literature. It is concluded that the AT-MQCT method (the adiabatic trajectory version of MQCT) represents a promising tool for the computational treatment of molecular collisions and energy exchange.

A new version of the MQCT program is presented, which includes an important addition, adiabatic trajectory approximation (AT-MQCT), in which the equations of motion for the classical and quantum parts of the system are decoupled. This method is much faster, which permits calculations for larger molecular systems and at higher collision energies than was possible before. AT-MQCT is general and can be applied to any molecule + molecule inelastic scattering problem. A benchmark study is presented for H2O + H2O rotational energy transfer, an important asymmetric-top rotor + asymmetric-top rotor collision process, a very difficult problem unamenable to the treatment by other codes that exist in the community. Our results indicate that AT-MQCT represents a reliable computational tool for prediction of collisional energy transfer between the individual rotational states of two molecules, and this is valid for all combinations of state symmetries (such as para and ortho states of each collision partner).

It is shown that the mixed quantum/classical theory (MQCT) for the description of molecular scattering is considerably improved by using integer values of orbital angular momentum l, just like in quantum theory, instead of treating it as a continuous classical variable related to the impact parameter. This conclusion is justified by the excellent accuracy of the modified theory for prediction of the differential cross sections, at various values of collision energy and in both forward and backward scattering regimes. This approach requires fewer trajectories, compared to the random Monte Carlo sampling, and the only convergence parameter is l (maximum orbital angular momentum) similar to J in the full quantum theory (maximum total angular momentum). Calculations of differential and integral cross sections for elastic and inelastic channels are presented, and the role of the scattering phase is discussed. The low-energy range is analyzed in detail to obtain insight into how the mixed quantum/classical treatment works in the scattering regime dominated by resonances. The differential cross section for rotationally inelastic scattering, computed by MQCT approach, is presented for the first time.