Trajectory surface hopping approach

Tully J C and Preston R K 1971 Trajectory surface hopping approach to nonadiabatic molecular collisions the reaction of H" with D2 J. Chem. Phys. 55 562... 

J. C. Tully and R. K. Preston, J. Chem. Phys., 55, 562 (1971). Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions The Reaction of H+ with D2. 

S. Chapman, The classical trajectory-surface-hopping approach to charge-transfer processes, State-Selected and State-to-State, Ion-Molecule Reaction Dynamics. Part 2 Theory, Advances in Chemical Physics LXXXII (M. Baer and C. Y. Ng, eds.), Wiley, New York, 1992, p. 423. 

Tully JC, Preston RK (1971) Trajectory surface hopping approach to nonadiabatic molecular collisions—reaction of H - - with D2. J Chem Phys 55 562... 

Chapman S (1992) The classical trajectory-surface-hopping approach to charge-transfer processes. Adv Chem Phys 82(Pt II) 423... 

Finally, some comments on two recent studies on methods for quantum dynamics simulations. In the first study, by Mendive-Tapia et al., the convergence of non-adiabatic direct dynamics in conjunction with frozen-width variational Gaussian product basis functions is evaluated. The simulation of non-adiabatic dynamics can be subdivided into two groups semi-classical methods (like the trajectory surface hopping approach) and wavepacket methods (for example, the... 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

Figure 3. Time-dependent simulations of the nonadiabatic photoisomerization dynamics exhibited by Model III, comparing results of the mean-field-trajectory method (dashed lines), the surface-hopping approach (thin lines), and exact quanmm calculations (full lines). Shown are the population probabilities of the initially prepared (a) adiabatic and (b) diabatic electronic state, respectively, as well as (c) the probability Pdsit) that the sytem remains in the initially prepared cis conformation.

The mapping approach outlined above has been designed to furnish a well-defined classical limit of nonadiabatic quantum dynamics. The formalism applies in the same way at the quantum-mechanical, semiclassical (see Section VIII), and quasiclassical level, respectively. Most important, no additional assumptions but the standard semiclassical and quasi-classical approximations are needed to get from one level to another. Most of the established mixed quantum-classical methods such as the mean-field-trajectory method or the surface-hopping approach do invoke additional assumptions. The comparison of the mapping approach to these formulations may therefore (i) provide insight into the nature of these additional approximation and (ii) indicate whether the conceptual virtues of the mapping approach may be expected to result in practical advantages. 

Craig, C.F., Duncan, W.R. and Prezhdo, O.V. (2005) Trajectory surface hopping in the time-dependent Kohn-Sham approach for electron-nuclear dynamics. Phys. Rev. Lett., 95, 163001-1-163001-4. 

In difference to normal ground state thermal chemistry (ignoring chemiluminescence and bioluminescence), which is usually well described by the Born-Oppenheimer approximation, photochemistry usually require a non-adiabatic description for a qualitative and quantitative model to be possible. A number of techniques have been developed to address this problem. Out of these we find the semi-classical trajectory surface hopping (TSH) approach or more sophisticated approaches based on a nuclear... 

Because of the stochastic nature of the fewest switches surface hopping approach, trajectories starting with the same initial conditions will give rise to different time development. Moreover, the initial conditions should reflect the initial phase space distribution. Therefore, the averages that define the state occupation should in principle be performed over this double ensemble of trajectories starting in different points of the phase space, several times in each one. Because of computational limitations, this procedure is usually reduced to a single ensemble of trajectories starting only once in different points of the phase space. 

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