Our research centers on problems at the interface of quantum and statistical mechanics. Particular themes that occur frequently in our research are hydrogen bonding, the interplay between structure and dynamics, systems with multiple time and length-scales and quantum mechanical effects. The applications of our methods are diverse, ranging from chemistry to biology to geology and materials science. Particular current interests include proton and electron transfer in fuel cells and enzymatic systems, atmospheric isotope separation and the control of catalytic chemical reactivity using electric fields.
Treatment of these problems requires a range of analytic techniques as well as molecular mechanics and ab initio simulations. We are particularly interested in developing and applying methods based on the path integral formulation of quantum mechanics to include quantum fluctuations such as zero-point energy and tunneling in the dynamics of liquids and glasses. This formalism, in which a quantum mechanical particle is mapped onto a classical "ring polymer," provides an accurate and physically insightful way to calculate reaction rates, diffusion coefficients and spectra in systems containing light atoms. Our work has already provided intriguing insights in systems ranging from diffusion controlled reactions in liquids to the quantum liquid-glass transition as well as introducing methods to perform path integral calculations at near classical computational cost, expanding our ability to treat large-scale condensed phase systems.
4) "Unraveling quantum mechanical effects in water using isotopic fractionation," T.E. Markland and B.J. Berne, Proc. Natl. Acad. Sci., 109, 7988-7991 (2012)
5) "Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics," T.C. Berkelbach, D.R. Reichman, and T.E. Markland, J. Chem. Phys., 136, 034113 (2012)
6) "Quantum fluctuations can promote or inhibit glass formation,"T.E. Markland, J.A. Morrone, B.J. Berne, K. Miyazaki, E. Rabani, and D.R. Reichman, Nature Phys., 7, 134-137 (2011)
7) "Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances," J.A. Morrone, T.E. Markland, M.Ceriotti, and B.J. Berne, J. Chem. Phys., 134, 014103 (2011)
8) "An efficient ring polymer contraction scheme for imaginary time path integral simulations," T.E. Markland and D.E. Manolopoulos, J. Chem. Phys., 129, 024105 (2008)
9) "Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice," T.E. Markland, S. Habershon, and D.E. Manolopoulos, J. Chem. Phys., 128, 194506 (2008)