(Funded by the National Science Foundation)

Inelastic scattering processes play important roles in a broad variety of chemical and physical phenomena. For example, they are crucial for quantitative interpretation of molecular spectra observed in astrochemical environments, modeling atmospheric chemistry, development of cooling and trapping techniques at ultracold temperatures and description of thermalization of enthalpy released by chemical bonds in combustion. Calculations of inelastic cross sections are usually carried out using quantum scattering codes such as MOLSCAT but the full-quantum scattering calculations, physically indispensable and computationally affordable at low temperatures, become prohibitively demanding at higher temperatures and/or for heavier (polyatomic) molecules and quenchers. It is important to realize that at such conditions the intermolecular degrees of freedom can be treated classically. Computationally powerful and physically appropriate method for description of inelastic scattering can be formulated if the classical trajectory treatment of scattering is interfaced with quantum treatment of rotation (and/or vibration) in a self-consistent way, which allows energy exchange between external and internal degrees of freedom, but keeps total energy conserved.

The idea of such mixed quantum/classical theory (MQCT) is not entirely new, but it has never been fully developed to the level of a predictive computational tool. In a series of recent papers we presented and tested, using a model system and several real molecules, the general and fully-coupled version of MQCT, formulated in both laboratory-fixed and body-fixed reference frames. The level of agreement between MQCT and full-quantum calculations is very encouraging, if not to say exciting. We want to stress that MQCT was applied without any adjustments which makes this general theory an excellent candidate for the “black box” utilization in a broad spectrum of applications, even by non-expert users. The computer code is simple and calculations are highly affordable. Furthermore, calculations with different impact parameters are entirely independent, which makes this method intrinsically parallel: one can easily spread MQCT trajectories onto hundreds of processors with zero communication overlap. The results obtained so far indicate that MQCT is more accurate for heavier masses, at higher collision energies and smaller spacings between quantized states (energy quanta). Importantly, in this regime the full-quantum method becomes computationally costly, while the MQCT calculations become very affordable.


Figure 11: Schematic of MQCT calculations for Na + N2 in the BF reference frame. The quencher atom (treated classically) scatters off the ro-vibrational wave function of the molecule.  Coordinates are defined in the text. Initial position of the quencher is on polar axis. Incident direction of its momentum vector P is determined by impact parameter.

Relevant Publications:

  1. M. Ivanov, M.-L. Dubernet and D. Babikov, "Rotational Quenching of H20 by He: Mixed Quantum/Classical Theory and Comparison with Quantum Results," J. Chem. Phys. 140, 134301 (2014).
  2. A. Semenov and D. Babikov, "Mixed quantum/classical calculations of total and differential elastic and rotationally inelastic scattering cross sections for light and heavy reduced masses in a broad range of collision energies," J. Chem. Phys. 140, 044306 (2014).
  3. A. Semenov and D. Babikov, "Accurate calculations of rotationally inelastic scattering cross sections using mixed quantum/classical theory," J. Phys. Chem. Lett. 5, 275 (2014).
  4. A. Semenov and D. Babikov, "Mixed quantum/classical theory of inelastic scattering in space-fixed and body-fixed reference frames," J. Chem. Phys. 139, 174108 (2013). J. Chem. Phys. 139, 174108 (2013).
  5. A. Semenov, M. Ivanov and D. Babikov, "Ro-vibrational quenching of CO(v =1) by He impact in a broad range of temperatures: A benchmark study using mixed quantum/classical inelastic scattering theory," J. Chem. Phys. 139, 74306 (2013).
  6. A. Semenov and D. Babikov, "Equivalence of the Ehrenfest theorem and the fluid-rotor model for mixed quantum/classical theory of collisonal energy transfer," J. Chem. Phys. 138, 164110 (2013).


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