Documentation and reviews

This Ph.D. thesis contains a thorough introduction to the GLE thermostat, which includes some background on stochastic differential equations and a number of example applications.

A brief introduction to colored noise sampling for molecular dynamics is given in the February 2014 highlight of the Psi-K newsletter, while the lecture notes for the 2015 Juelich school give a discussion specific to the simulation of nuclear quantum effects. The atomistic cookbook contains several recipes using GLE thermostats, both for use in classical ML and in path integral molecular dynamics.

See also the FAQ page.

References

• “Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei”, Michele Ceriotti and David E. Manolopoulos, Rev. Lett. 109, 100604 (2012) doi: 10.1103/PhysRevLett.109.100604
  The PI+GLE method is extended so as to guarantee that the quantum kinetic energy of nuclei will converge as efficiently as the potential energy. This is done by simultaneously enforcing the correct fluctuations of both individual beads and the centroid, in the harmonic limit. A transient anisotopic Gaussian approximation to the particle momentum distribution is also developed, which makes it easy to estimate the anisotropy of the PMD without using open path integrals.
• “The inefficiency of re-weighted sampling and the curse of system size in high-order path integration”, Michele Ceriotti, Guy A. R. Brain, Oliver Riordan and David E. Manolopoulos, Proc. R. Soc. A 468, 2 (2012) doi: 10.1098/rspa.2011.0413
  The problem of re-weighted sampling is discussed in very general terms, demonstrating the pathological behaviour of the sampling efficiency with increasing variance of the difference Hamiltonian. The implications with respect some recent attempts to make high-order path integration practicable are discussed, and demonstrating that this is a hopeless task and that PI+GLE obtains faster convergence without being affected by sampling problems.
• “Accelerating the convergence of path integral dynamics with a generalized Langevin equation”, M. Ceriotti, D. E. Manolopoulos, and M. Parrinello, J. Chem. Phys. 134, 084104 (2011) doi: 10.1063/1.3556661
  The quantum thermostat can model nuclear quantum effects accurately in quasi-harmonic systems, but becomes less reliable as anharmonicities become more important. Here a non-Markovian GLE dynamics is combined with an imaginary-time path integral dynamics to recover systematic convergence of nuclear quantum effects, at the same time greatly speeding up this convergence.
• “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) doi: 10.1063/1.3518369
  Multiple time step schemes can deliver consistent speed ups to classical molecular dynamics, but can also lead to resonances and instabilities which may affect the reliability of the simulation. Stochastic terms have been used in the past to control resonances, at the expense however of a slowing-down of diffusive motions which ultimately cancels the benefits of MTS. Here a GLE is used to enforce tight control of resonances of high frequency modes, while introducing minimal hindrance to slower, collective dynamics.
• “Efficient stochastic thermostatting of path integral molecular dynamics”, M. Ceriotti, M. Parrinello, T. E. Markland, D. E. Manolopoulos, J. Chem. Phys 133, 124104 (2010) doi: 10.1063/1.3489925
  Thorough comparison of different thermostats applied to the challenging case of path integral molecular dynamics. GLE turns out to be competitive with targeted techniques which exploit explicitly knowledge of the internal modes of the necklace.
“The δ-thermostat: selective normal-modes excitation by colored-noise Langevin dynamics”, M. Ceriotti and M. Parrinello, Proc. Comp. Sci. 1, 1601 (2010) doi: 10.1016/j.procs.2010.04.180
Usage of a non-equilibrium GLE thermostat to freeze all but a narrow range of vibrational modes. Can be used to probe the vibrational spectrum of a solid in a MD framework, or to approximately compute the eigenvalue spectrum of a positive-definite sparse matrix in linear-scaling time.
• “Colored-noise thermostats à la carte”, M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) doi: 10.1021/ct900563s
  Long paper, describing in details the derivation and implementation of the GLE framework. Examples of optimal sampling LE and quantum-thermostat dynamics.
• “Nuclear quantum effects in solids using a colored-noise thermostat”, M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 103, 030603 (2009) doi: 10.1103/PhysRevLett.103.030603
  Description of the quantum thermostat, applications to the calculation of nuclear quantum effects in diamond and liquid water (proton momentum distribution).
• “Langevin equation with colored noise for constant-temperature molecular dynamics simulations”, M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009) doi: 10.1103/PhysRevLett.102.020601
  Introduction to the GLE framework for molecular dynamics. Applications to Car-Parrinello dynamics and to Drude-oscillator polarizable forcefields.

Slides and posters

A few (dated) posters and presentations introducing colored noise and Generalized Langevin Equation thermostats.

	"Nuclear quantum effects the colored way" Poster presented in Lugano for the CECAM workshop "Quantum Monte Carlo meets Quantum Chemistry" (2010). Example application of the "quantum thermostat" to estimate nuclear quantum effects in condensed-phase systems. Download PDF
	"A novel framework for enhanced molecular dynamics based on the generalized Langevin equation" Slides presented for M. Ceriotti's Ph.D. dissertation. General overview of both canonical sampling and non-equilibrium GLE thermostats. Download PDF
	"A tutorial on the Generalized Langevin Thermostat" Slides for a group seminar. Introduction to the GLE, and thorough discussion of thermostat issues in the simulation of liquid water (classical, flexible forcefield). Download PDF
	"A tunable, all-purpose colored-noise thermostat" Poster presented at Jülich, for the winter school "Multiscale simulation methods in molecular sciences" (2009). Applications of GLE thermostat to efficient sampling and to Car-Parrinello dynamics. Download PDF