Trajectory surface hopping methods

G. L. Cui and W. Thiel. Generahzed trajectory surface-hopping method for internal conversion and intersystem crossing, J. Chem. Phys., 141 (2014). 

Almost all the published PESs have been used to perform quasiclassical trajectory (QCT) [71,83] studies of the title reaction. Those calculations have been mainly focused in adiabatic studies in each PES. In addition, the trajectory surface hopping method [56], has been used to study the nonadiabatic effects between the X A and B M PESs. 

Granucci, G., Persico, M., Excited State Dynamics with the Direct Trajectory Surface Hopping Method Azobenzene and Its Derivatives as a Case Study, Theor. Chem. Acc. 2007, 117, 1131 1143. 

The trajectory surface hopping method is an additional extension of the classical trajectory method. Potential energy surfaces are constructed for each electronic state involved in the collision. In addition, a function has to be obtained that defines the locus of points at which hops between surfaces can occur. Still another function is necessary which gives the probability of such jumps as a function of nuclear positions and velocities.28 Diatomics-in-molecules surfaces approximated the two lowest singlet potential surfaces of H3. The surfaces have been shown30 to be in good agreement with accurate ab initio calculations by Conroy.31... 

Theory. Usually we do not solve the fundamental equations directly. We use a theory, for example, Har-tree-Fock theory [3], Moller-Plesset perturbation theory [4], coupled-cluster theory [5], Kohn s [6, 7], Newton s [8], or Schlessinger s [9] variational principle for scattering amplitudes, the quasiclassical trajectory method [10], the trajectory surface hopping method [11], classical S-matrix theory [12], the close-coupling approximation... 

Topaler MS, Hack MD, Allison TC, liu Y-P, Mielke SL, Schwenke DW, Truhlar DJ (1997) Validation of trajectory surface hopping methods against accurate quantum mechanical dynamics and semiclassical analysis of electronic-to-vibrational energy transfer. J Chem Phys... 

Barbatti M (2011) Nonadiabatic dynamics with trajectory surface hopping method. Wiley... 

On the other hand, the state (a or jS) is determined from the propagation of the wavefunction via equation (5) and this forms the basis of the trajectory surface hopping method that we shall presently discuss. 

The goal of this chapter is twofold. First we wish to critically compare—from both a conceptional and a practical point of view—various classical and mixed quantum-classical strategies to describe non-Born-Oppenheimer dynamics. To this end. Section II introduces five multidimensional model problems, each representing a specific challenge for a classical description. Allowing for exact quantum-mechanical reference calculations, aU models have been used as benchmark problems to study approximate descriptions. In what follows, Section III describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Section IV, which discusses various motivations of the ansatz as well as several variants of the implementation. Section V gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. 

The approximation (58) resembles the usual momentum-jump ansatz employed in various surface-hopping methods [55, 57, 58, 61, 66, 67, 82]. In order to determine the momentum shift of a trajectory, however, the latter formulations typically require the conservation of nuclear energy ... 

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