Semi-classical surface hopping trajectories

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.

The surface hopping study was rather expensive in terms of CPU time, and consequently large numbers of trajectories could not be run. This is important to obtain statistically converged dynamical properties. The main goal of the surface hopping study was thus not to obtain such information but to provide mechanistic insight into the photodissociation and subsequent relaxation processes. The semi-classical work in the full space of nuclear coordinates provides the important vibrational degrees of freedom that one needs to include in any quantum model of the nuclear motion. This will now be described. 

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... 

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,... 

Dynamics Method Fully Quantum Quasi-Classical Trajectory Surface Hop Semi-Classical (Ehrenfest) Molecular Mechanics... 

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... 

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... 

---