Trajectory-Surface-Hopping

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). 

Stokes theorem, geometric phase theory, eigenvector evolution, 14-17 Stueckelberg oscillations, direct molecular dynamics, trajectory surface hopping, 398-399... 

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.

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... 

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