Non-Adiabatic Molecular Dynamics Simulations of Non-Charge-Transfer and Charge-Transfer Scattering in H^++CO2 at ELab=30 eV

The H^++CO2 reaction at high energies is relevant in atmospheric chemistry,astrophysics,and proton cancer therapy research.Therefore,we present herein a complete investigation of H^++CO2 at ELab=30 eV with the simplest-level electron nuclear dynamics(SLEND)method.SLEND describes nuclei via classical mechanics and electrons with a singledeterminantal Thouless wavefunction.The 3402 SLEND conducted simulations from 42 independent CO2 target orientations provide a full description of all the reactive processes and their mechanisms in this system:non-charge-transfer scattering(NCTS),charge-transfer scattering(CTS),and single C=O bond dissociation;all this valuable information about reactivity is not accessible experimentally.Numerous details of the projectile scattering patterns are provided,including the appearance and coalescence of primary and secondary rainbow angles as a function of the target orientation.SLEND NCTS and CTS differential cross sections(DCSs)are evaluated in conjunction with advanced semi-classical techniques.SLEND NCTS DCS agrees well with its experimental counterpart at all the measured scattering angles,whereas SLEND CTS DCS agrees well at high scattering angles but less satisfactorily at lower ones.Remarkably,both NCTS and CTS SLEND DCSs predict the primary rainbow angle signatures in agreement with the experiment.

Stochastic description of quantum Brownian dynamics

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-t）ath model has been developed and found many applications in chemical dynamics, spectroscopy, quantmn transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Ito calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition （Toulouse limit） at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems such as the dynamical description of quantum phase transition （localization） and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.