### Gas phase dynamics

Much of our research in the last twenty years has focused on the quantum mechanical description of elementary chemical reactions in the gas phase. We have learned a great deal during this time about the interpretation of transition state spectroscopy experiments, the role of quantum mechanical resonances in hydrogen atom transfer reactions, the significance of the non-adiabatic effects caused by electronic and spin-orbit couplings, the effect of van der Waals forces on chemical reaction dynamics, and the statistical nature of insertion reactions that proceed via deep potential energy wells.

### Condensed phase dynamics

In a new line of research that began around ten years ago, we have shown how the standard path integral molecular dynamics (PIMD) method, which has been used since the mid 1980s to compute the exact static equilibrium properties of quantum mechanical systems, can be generalized to calculate approximate real-time quantum correlation functions, and so used to study the role of quantum mechanical (zero point energy and tunnelling) effects in condensed phase chemical dynamics. The resulting ring-polymer molecular dynamics (RPMD) method has already been used to study the diffusion in and the inelastic neutron scattering from liquid para-hydrogen, various dynamical processes in ice and water, and chemical reaction rates in the gas phase and in solution. We are now continuing to use PIMD and RPMD to study a wide variety of structural, thermodynamic, and dynamical properties of condensed phase systems containing hydrogen atoms.

### Spin dynamics

Most recently, we have become interested in the theory of radical (and polaron) pair recombination reactions, in a collaboration with the group of Peter Hore. These reactions are relevant to a wide variety of problems, ranging from how the electroluminescence of organic light emitting diodes (OLEDs) changes in the presence of an applied magnetic field to how migratory birds detect the direction of the Earth's magnetic field. The quantum mechanical Hamiltonian of a radical pair is straightforward to write down in terms of a sum of Zeeman, hyperfine, and dipolar and exchange coupling interactions. However, the resulting Schrodinger equation is extremely difficult to solve for a radical pair containing a realistic number of nuclear spins. We have therefore developed a more feasible semiclassical theory of radical pair recombination reactions, improving on earlier work in this area by bringing it into line with Newton's third law of motion. Our semiclassical theory is good enough to give reliable predictions for many interesting spin dynamics problems, as we have recently illustrated in an application to a carotenoid-porphyrin-fullerene triad molecule that provides a "proof of principle" for the operation of a chemical compass.

Spectroscopic observation of resonances in the F+H2 reaction. J. B. Kim, M. L. Weichmann, T. F. Sjolander, D. M. Neumark, J. Klos, M. H. Alexander and D. E. Manolopoulos, Science 349, 510 (2015).

Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions. A. M. Lewis, D. E. Manolopoulos and P. J. Hore, J. Chem. Phys. 141, 044111 (2014).

Ring polymer molecular dynamics: Quantum effects in chemical dynamics from classical trajectories in an extended phase space. S. Habershon, D. E. Manolopoulos, T. E. Markland and T. F. Miller, Ann. Rev. Phys. Chem. 64, 387-413 (2013).

The inefficiency of re-weighted sampling and the curse of system size in high-order path integration. M. Ceriotti, G. A. R. Brain, O. Riordan and D. E. Manolopoulos, Proc. Roy. Soc. A 468, 2 (2012).

Bimolecular reaction rates from ring polymer molecular dynamics: Application to H+CH4 to H2+CH3. Y. V. Suleimanov, R. Collepardo-Guevara and D. E. Manolopoulos, J. Chem. Phys. 134, 044131 (2011).

Efficient stochastic thermostatting of path integral molecular dynamics. M. Ceriotti, M. Parrinello, T. E. Markland and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010).

Competing quantum effects in the dynamics of a flexible water model. S. Habershon, T. E. Markland and D. E. Manolopoulos, J. Chem. Phys. 131, 024501 (2009).