Algorithmic decoherence time for decay-of-mixing non–Born–Oppenheimer dynamics

Abstract

The performance of an analytical expression for algorithmic decoherence time is investigated for non-Born-Oppenheimer molecular dynamics. There are two terms in the function that represents the dependence of the decoherence time on the system parameters; one represents decoherence due to the quantum time-energy uncertainty principle and the other represents a back reaction from the decoherent force on the classical trajectory. We particularly examine the question of whether the first term should dominate. Five one-dimensional two-state model systems that represent limits of multidimensional nonadiabatic dynamics are designed for testing mixed quantum-classical methods and for comparing semiclassical calculations with exact quantum calculations. Simulations are carried out with the semiclassical Ehrenfest method (SE), Tully's fewest switch version (TFS) of the trajectory surface hopping method, and the decay-of-mixing method with natural switching, coherent switching (CSDM), and coherent switching with reinitiation (CSDM-D). The CSDM method is demonstrated to be the most accurate method, and it has several desirable features: (i) It behaves like the representation-independent SE method in the strong nonadiabatic coupling regions; (ii) it behaves physically like the TFS method in noninteractive region; and (iii) the trajectories are continuous with continuous momenta. The CSDM method is also demonstrated to balance coherence well with decoherence, and the results are nearly independent of whether one uses the adiabatic or diabatic representation. The present results provide new insight into the formulation of a physically correct decoherence time to be used with the CSDM method for non-Born-Oppenheimer molecular dynamic simulations.

Nonadiabatic quantum dynamics in O(3P)+H2→OH+H: A revisited study

“…Moreover, we also carried out the nonadiabatic quantum‐classical trajectory calculations to obtain the information on product angular distributions for the title reactive system. This nonadiabatic method is based on the coherent switching with decay of mixing (CSDM) theory of Truhlar and coworkers,43, 44 and the corresponding computational code we used here is developed by Han and coworkers 45, 46. Briefly speaking, in the CSDM theory for a multistate system, the nuclear motion is still governed by the semiclassical Hamilton's motion equation.…”

Ring polymer molecular dynamics with surface hopping

“…We have not attempted to include decoherence corrections in the surface-hopping algorithm. However, there are a number of prescriptions for decoherence corrections [62][63][64][65] to the traditional FSSH algorithm, which, if needed, can be applied to the present method as well.…”

Excited‐state dynamics

“…Related challenges are the following: developing robust diabatization methods for both kinds of quantum dynamics methods (see, e.g., Ref 145); generating active coordinates automatically for photochemical reactions in the context of reduced‐dimensionality techniques146; making second derivatives of the energy available in excited‐state quantum chemistry methods capable of dealing with dynamical correlation; developing less expensive excited‐state quantum chemistry methods such as CAS‐DFT (Complete Active Space Density Functional Theory)147; imbedding semiclassical and direct quantum dynamics in electronic structure codes148,149; developing new direct quantum dynamics approaches such as Bohmian trajectories150 and improving semiclassical treatments78,79,151; investigating larger‐scale problems (environment, complex structures such as chromophores in proteins, or organometal complexes) with hierarchical methods (hybrid quantum chemistry and quantum dynamics, effective coordinates115,152,153, and multilayer MCTDH154). …”

“…These semiclassical simulations give good estimates for the timescale and efficiency of internal conversion processes at conical intersections. However, they do not represent correctly the coherence preservation of the wavepacket44,45,50,79 and are not reliable to describe many recrossings. In addition, they are plagued with the impossibility of systematic improvement due to the ad hoc treatment of the nonadiabatic event.…”

“…Semiclassical methods approximate the wavepacket with a noncoherent beam of trajectories. Several algorithms have been proposed to estimate the probability that a classical trajectory ‘jumps’ between potential energy surfaces 49,78,79. This happens at finite potential energy gap, and preservation of the total energy involves excess kinetic energy given in an ad hoc manner.…”