Bibliography¶
Bastiaan J Braams and David E Manolopoulos. On the short-time limit of ring polymer molecular dynamics. J. Chem. Phys., 125:124105, 2006.
Jianshu Cao and Gregory A Voth. A new perspective on quantum time correlation functions. J. Chem. Phys., 99:10070–10073, 1993.
Jianshu Cao and Gregory A Voth. The formulation of quantum statistical mechanics based on the Feynman path centroid density. IV. Algorithms for centroid molecular dynamics. J. Chem. Phys., 101:6168–6183, 1994.
Michele Ceriotti, Guy A. R. Brain, Oliver Riordan, and David E. Manolopoulos. The inefficiency of re-weighted sampling and the curse of system size in high order path integration. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468:2–17, 2011.
Michele Ceriotti, David E Manolopoulos, and Michele Parrinello. Accelerating the convergence of path integral dynamics with a generalized Langevin equation. J. Chem. Phys., 134:84104, 2011.
Michele Ceriotti, Joshua More, and David E. Manolopoulos. i-PI: A Python interface for ab initio path integral molecular dynamics simulations. Comp. Phys. Comm., 185:1019–1026, 2014.
Michele Ceriotti, Michele Parrinello, Thomas E Markland, and David E Manolopoulos. Efficient stochastic thermostatting of path integral molecular dynamics. J. Chem. Phys., 133:124104, 2010.
Siu A. Chin. Symplectic integrators from composite operator factorizations. Phys. Lett. A, 226:344–348, 1997.
I R Craig and D E Manolopoulos. Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics. J. Chem. Phys., 121:3368, 2004.
R P Feynman and A R Hibbs. Quantum Mechanics and Path Integrals. McGraw-Hill, New York, 1964.
Scott Habershon, David E Manolopoulos, Thomas E Markland, and Thomas F Miller. Ring-polymer molecular dynamics: quantum effects in chemical dynamics from classical trajectories in an extended phase space. Annual review of physical chemistry, 64:387–413, 2013.
Venkat Kapil, Mariana Rossi, Ondrej Marsalek, Riccardo Petraglia, Yair Litman, Thomas Spura, Bingqing Cheng, Alice Cuzzocrea, Robert H Meißner, David M Wilkins, Benjamin A Helfrecht, Przemysław Juda, Sébastien P Bienvenue, Wei Fang, Jan Kessler, Igor Poltavsky, Steven Vandenbrande, Jelle Wieme, Clemence Corminboeuf, Thomas D Kühne, David E Manolopoulos, Thomas E Markland, Jeremy O Richardson, Alexandre Tkatchenko, Gareth A Tribello, Veronique Van Speybroeck, and Michele Ceriotti. i-PI 2.0: A universal force engine for advanced molecular simulations. Computer Physics Communications, 236:214–223, March 2019.
Thomas E Markland and David E Manolopoulos. An efficient ring polymer contraction scheme for imaginary time path integral simulations. J. Chem. Phys., 129:024105, 2008.
Glenn J Martyna, Adam Hughes, and Mark E Tuckerman. Molecular dynamics algorithms for path integrals at constant pressure. J. Chem. Phys., 110:3275, 1999.
Thomas F Miller and David E Manolopoulos. Quantum diffusion in liquid para-hydrogen from ring-polymer molecular dynamics. J. Chem. Phys., 122:184503, 2005.
Alejandro Pérez and Mark E Tuckerman. Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes. J. Chem. Phys., 135:064104, 2011.
Isaac F. Silvera and Victor V. Goldman. The isotropic intermolecular potential for H2 and D2 in the solid and gas phases. J. Chem. Phys., 69:4209, 1978.
M Suzuki. Hybrid exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations. Phys. Lett. A, 201:425–428, 1995.