Frozen Rotor Approximation in the Mixed Quantum/Classical Theory for Collisional Energy Transfer: Application to Ozone Stabilization

A frozen-rotor approximation is formulated for the mixed quantum/classical theory of collisional energy transfer and ro-vibrational energy flow [M. Ivanov and D. Babikov, J. Chem. Phys.134, 144107 (Year: 2011)]. Numerical tests are conducted to assess its efficiency and accuracy, compared to the original version of the method, where rotation of the molecule in space is treated explicitly and adiabatically. New approach is considerably faster and helps blocking the artificial ro-vibrational transitions at the pre- and post-collisional stages of the process. Although molecular orientation in space is fixed, the energy exchange between rotational, vibrational, and translational digresses of freedom still occurs, allowing to compute ro-vibrational excitation and quenching. Behavior of the energy transfer function through eight orders of magnitude range of values and in a broad range of ΔE is reproduced well. In the range of moderate −500 ⩽ ΔE ⩽ +500 cm−1 the approximate method is rather accurate. The absolute values of stabilization cross sections for scattering resonances trapped behind the centrifugal threshold are a factor 2-to-3 smaller (compared to the explicit-rotation approach). This performance is acceptable and similar to the well-known sudden-rotation approximation in the time-independent inelastic scattering methods

Mixed Quantum/Classical Theory of Rotationally and Vibrationally Inelastic Scattering in Space-fixed and Body-fixed Reference Frames

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 complex-valued 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 real-valued 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 body-fixed 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

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

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 + H2 and Na + N2. 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

Mapping quantum-classical Liouville equation: projectors and trajectories

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.Comment: 4 figure

Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory

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

Accelerator Design for the CHESS-U Upgrade

During the summer and fall of 2018 the Cornell High Energy Synchrotron Source (CHESS) is undergoing an upgrade to increase high-energy flux for x-ray users. The upgrade requires replacing one-sixth of the Cornell Electron Storage Ring (CESR), inverting the polarity of half of the CHESS beam lines, and switching to single-beam on-axis operation. The new sextant is comprised of six double-bend achromats (DBAs) with combined-function dipole-quadrupoles. Although the DBA design is widely utilized and well understood, the constraints for the CESR modifications make the CHESS-U lattice unique. This paper describes the design objectives, constraints, and implementation for the CESR accelerator upgrade for CHESS-U