Nancy Makri of the University of Illinois at Urbana-Champaign is supported by an award from the Chemical Theory, Models and Computational Methods program for research in the development of simulation methods for dynamical processes in quantum clusters and liquids. Fully quantum mechanical calculations of such systems present a major challenge because the numerical effort required increases very rapidly with system size. Makri and her research group are developing an iterative Monte Carlo (IMC) methodology that combines the precision of iterative grid-based propagation algorithms with the advantageous scaling of Metropolis Monte Carlo. The use of lattice representations and grid sampling techniques motivated from the high-temperature and semiclassical limit will further increase efficiency, while maintaining the fully quantum mechanical nature of IMC.
The IMC methodology will enable for the first time fully quantum mechanical simulation of the dynamics of quantum clusters, fluids and doped helium nano-droplets, offering new physical insights. The work will also impact a broader scientific community by offering researchers the ability to generate much needed benchmarks for the assessment of approximate simulation methods. Makri's work is also having a further broader impact through the training of graduate students and postdoctoral researchers.
Many chemical and biological processes are dominated by quantum mechanical effects. Unfortunately, simulating such processes by performing accurate quantum mechanical calculations is practically impossible in most cases, as the difficulty of such calculations increases very rapidly with the number of atoms. Even though the majority of atoms could be treated by inexpensive classical trajectories, the presence of a few highly quantum mechanical degrees of freedom (e.g., an electron or transferring proton) makes purely classical simulations tools unsuitable. We have introduced a rigorous and very accurate methodology for studying dynamical processes in the condensed phase, which treats important degrees of freedom by full quantum mechanics, while retaining a simple and efficient classical trajectory treatment for the majority of the atoms comprising the system of interest and its environment. This quantum-classical path integral (QCPI) methodology is free of commonly employed assumptions. While path integral calculations typically require astronomical numbers of terms, QCPI exploits decoherence mechanisms that occur naturally in condensed-phase to minimize the required number of terms, leading to an efficient and practical tool for large-scale simulation. To our knowledge, QCPI is currently the most accurate quantum-classical methodology that is suitable for condensed phase simulations. We have presented preliminary evidence that shows that QCPI converges sufficiently rapidly, such that it can be used to investigate the dynamics of charge- or proton-transfer reactions in solution and in biological environments. Further developments and applications of QCPI are in progress.