Quantum Metadynamics

Many physical phenomena take place on a time scale that far exceeds what can be reached in atomistic simulations, strongly limiting the scope of an otherwise very powerful method. The vast literature on the subject is evidence of the relevance of this problem. In the last decade our group has been actively involved in developing methods that speed up sampling and calculate rates of transition between metastable states separated by large barriers. In particular we have introduced a method called Metadynamics and more recently a variationally enhanced sampling (VES) approach that have proven to be extremely effective. When properly engineered both methods allow also the calculation of rates. Thus far this effort has been mostly focused on classical systems. One of the aims of this project is to extend these sampling methods to quantum systems and calculate quantum rates. We shall use the Feynman’s Path Integral formulation of quantum statistical systems to map the quantum system into an isomorphic classical system. Neglecting quantum exchanges, each particle is mapped into a ring polymer of P beads. As P ? 8 the exact quantum limit is reached while the P = 1 case corresponds to the purely classical case. While in principle a quantum system is expected to surmount high barriers thanks to effects like zero point motion and tunneling, still in the presence of high barriers sampling remains severely hindered. The few methods that have been proposed for quantum systems presume conditions and or knowledge of the system that in complex situations are not available. Here we propose to develop a number of specifically designed methods to sample quantum systems that can be applied blindly to very generic systems. In preliminary investigations we have shown that this is possible. On the one hand we have been able to enhance sampling in quantum systems on the other we have shown that sampling quantum systems can be profitably used to sample classical systems. We plan to extend this approach in various directions including the introduction of Bose exchange processes. The resulting software will be made available to the community. We want also to calculate rates for quantum transitions. We will follow two approaches: the first one at variance with previous efforts does not contain any approximation, the second one will be more approximated but computationally more expedite and capable of overcoming barriers where other methods fail. The project duration is scheduled for 3 years and it will involve one post-doctoral researcher and a doctoral student with a total working load of 180%.