Tully s surface hopping

In Fig. 3, the simulation results for the same model problem are presented using the QCLE, the master equation, Tully s surface-hopping approach, the mean field approach, and adiabatic dynamics. The algorithmic details of each approach can be found elsewhere [2,40,79]. 

Fig. 3 Forward rate coefficient kAB(t) as a function of time for f3 = 1.0. The upper (blue) curve is the adiabatic rate, the purple curve is the result obtained by Tully s surface-hopping algorithm, the middle (black) curve is the quantum master equation result, the green curve is the QCL result, and the lowest dashed line (grey) is the result using mean-field dynamics.

A further complexity in the simulation of photochemistry and more in general of excited state photoinduced dynamics is that they are intrinsically nonadiabatic processes, in which the coupling between the nuclear and electronic motion leads to nonradialive transitions between electronic states. A generally applicable approach for this purpose is the mixed quantum-classical dynamics in which the nuclear motion is described by classical trajectories obtained in the framework of molecular dynamics on the fly combined with Tully s surface hopping (TSH) procedure... 

In this context, one of the most efficient approaches is based on mixed quantum-classical dynamics in which the nonadiabatic effects are simulated using Tully s surface hopping (TSH) method [13, 14]. It is applicable to a large variety of systems ranging from isolated molecules and clusters to complex nanostructures... 

In this section we briefly outline our formulation of the nonadiabatic dynamics in the framework of TDDFT using localized Gaussian basis sets combined with Tully s surface hopping (TSH) method [13]. Within the TSH procedure, nonadiabatic... 

If only a small part of the system needs to be treated quantum mechanically, one attractive approach is the semiclassical surface-hopping methodology, developed by Tully and co-workers in the early 1970s [3-6], Here the quantum subsystem is treated with basis-set methods of some sort while the remainder of the system is described classically, evolving under Newton s equations in the field of the subsystem. The tricky aspect of this method is the coupling between the classical and quantum parts of the system. This can be accomplished either via a formalism worked out by Pechukas [5,7-9] or by methods developed by... 

Tully s fewest switch surface hopping method and its variants... 

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