Quantum Nuclear Dynamics in the Condensed Phase

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The quantum properties of nuclei are determined by the Schroedinger equation, but this equation is much more difficult to solve for nuclei than electrons, with the result that exact quantum dynamics can be obtained from it only for small gas-phase molecules. This project aims to develop approximate methods which will allow quantum dynamics to be simulated in condensed phase systems, such as ice and liquid water. The key idea is that most of the quantum effects in such systems (i.e. zero-point energy and tunnelling) are the result mainly of quantum effects in the Boltzmann statistics; real-time quantum coherences mostly average out. This project will build on a recently developed mixed quantum statistics-classical dynamics method knowns as the 'planetary model', whereby the quantum Boltzmann delocalisation of atomic nuclei is approximated by means of a supplementary 'planet' particle which orbits another particle at the centre of mass of the Boltzmann distribution. This technique allows observable properties such as infrared spectra and neutron-scattering cross sections to be simulated relatively cheaply, and has given very promising results in tests on the infrared spectra of liquid water. This project will focus on extending this methodology to treat non-linear spectra.