Trajectory surface hopping and

Each of the semi-classical trajectory surface hopping and quantum wave packet dynamics simulations has its pros and cons. For the semi-classical trajectory surface hopping, the lack of coherence and phase of the nuclei, and total time per trajectory are cons whereas inclusion of all nuclear degrees of freedom, the use of potentials direct from electronic structure theory, the ease of increasing accuracy by running more trajectories, and the ease of visualization of results are pros. For the quantum wave packet dynamics, the complexity of setting up an appropriate model Hamiltonian, use of approximate fitted potentials, and the... 

M. D. Hack, A. M. Wensmann, D. G. Truhlar, M. Ben-Nun, and T. J. Martinez (2001) Comparison of full multiple spawning, trajectory surface hopping and converged quantum mechanics for electronically nonadiabatic dynamics. J. Chem. Phys. 115, p. 1172... 

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... 

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). 

B. N. Fu, B. C. Shepler, and J. M. Bowman. Three-state trajectory surface hopping studies of the photodissociation dynamics of formaldehyde on ab initio potential energy surfaces, J. Am. Chem. Soc., 133 7957-7968 (2011). 

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

Fig. 4. Cr(CO)s excited state relaxation dynamics comparison of semi-classical trajectory surface hopping (left), and MCTDH wave packet dynamics (right). Trajectory shows molecule passing through TBP Jahn-Teller geometry within 130 fs, then oscillating in SP potential well afterward. Wave packet dynamics plotted for the Si and S0 adiabatic states in the space the symmetric and asymmetric CCrC bending coordinates.

Trajectory surface-hopping (TSH) calculations have been accomplished for H3+ on DIM hypersurfaces.2,498 A surface-hopping mechanism has also been suggested as applicable to several other systems, including various He2+ charge-transfer reactions,495 the H -H2 reaction,499 and the C+-H2 radiative association process.500... 

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. 

Recently, Garth Jones (UNSW) and his co-workers have described a semi-classical molecular dynamics (MD) model, which incorporates the trajectory surface hopping (TSH) method, that shows promise in investigating a number of important problems concerning the effects of molecular vibrations on the dynamics of ET reactions, including formally symmetry-forbidden ones. Essentially,... 

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. 

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. 

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 simplest three atom ion-molecule reactions are those of H+ with molecular hydrogen and its various isotopic variants. This is an interesting reaction not only because of its simplicity but the reaction involves a deep potential well represented by the stable H3 ion and hence one has the interesting possibility that a long-lived collision complex may be involved. Some preliminary work on such reactions as D+(HD, H)D2, D+(HD, D)HD+ and D+(HD, D2)H+ has been reported.25 However, it is only recently that the complete details of the combined theoretical and experimental study of these reactions has become available.26,27 The associated theoretical treatment of these reactions is the trajectory surface hopping TSH technique extended from the classical trajectory method.28... 

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... 

The trajectory surface hopping model of ion-molecule reaction dynamics has realized an impressive agreement between theory and experiment in this reaction, i.e. H+ + H2, and it provides the experimentalist with a realistic and workable theory to use in the comparison with and interpretation of experimental results. As reliable potential energy surfaces become available for other ion-molecule systems, we can expect further tests of this theory and its applicability to more complicated reactions. 

Eaker and Muzyka [39] have performed a trajectory-surface hopping calculation on the D+ — H2 system, but restricted to the two lowest potential energy surfaces. They observed the electron transfer between the two molecules prior to dissociation, but their CID cross section for D+(v = 3) + H2 at 4 eV was only 0.9 A2, about three times smaller than our result. In addition, their calculated ratio for H+ to D+ products was 8 1, whereas our result was 1 1. A possible explanation of the discrepancy [15] is a mechanism in which the second excited state of the [H2H2]+ system is excited during the collision. This state, which was not considered by Eaker, is repulsive for the H2+ moiety, and would give slow (fast) H+ ions if electron transfer did (did not) occur during the first part of the collision. This suggestion remains to be tested by theory. 

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