Abstract
A multiple time step (MTS) algorithm for trajectory surface hopping molecular dynamics has been developed, implemented, and tested. The MTS scheme is an extension of the ab initio implementation for Born-Oppenheimer molecular dynamics presented in the work of Liberatore et al. [J. Chem. Theory Comput. 14, 2834 (2018)]. In particular, the MTS algorithm has been modified to enable the simulation of non-adiabatic processes with the trajectory surface hopping (TSH) method and Tully's fewest switches algorithm. The specificities of the implementation lie in the combination of Landau-Zener and Tully's transition probabilities during the inner MTS time steps. The new MTS-TSH method is applied successfully to the photorelaxation of protonated formaldimine, showing that the important characteristics of the process are recovered by the MTS algorithm. A computational speed-up between 1.5 and 3 has been obtained compared to standard TSH simulations, which is close to the ideal values that could be obtained with the computational settings considered.
Highlights
Non-adiabatic phenomena such as photo-physical or photo-chemical processes are characterized by a failure of the Born–Oppenheimer (BO) approximation commonly invoked to describe molecular systems
For the reference trajectory surface hopping (TSH) simulations, the nuclear forces and non-adiabatic coupling (NAC) are computed with the PBE0 hybrid functional
We have presented a new algorithm for non-adiabatic molecular dynamics simulations that is based on Tully’s fewest switches (FS)-TSH method combined with an multiple time step (MTS) scheme for the integration of the nuclear classical equations of motion
Summary
Non-adiabatic phenomena such as photo-physical or photo-chemical processes are characterized by a failure of the Born–Oppenheimer (BO) approximation commonly invoked to describe molecular systems. In the TSH method (summarized in section II A), the evolution of the system is represented by a swarm of independent classical nuclear trajectories, which can hop from one electronic state to another in a stochastic way. The forces acting on the nuclei are calculated on-the-fly along each trajectory and transitions between electronic levels are considered simultaneously In this way, the TSH method is able to describe non-adiabatic phenomena such as photo-chemical and photo-physical processes. Solving the electronic Schrodinger equation is very computationally demanding and often have a very steep scaling with the number of electrons considered.5,6 These considerations limit considerably the applications of the TSH method. The strategy investigated in this work, is to reduce the computational requirements of the TSH method by relying on a multiple time step (MTS) algorithm.
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