Algorithms

G. Bussi, D. Donadio and M. Parrinello, Canonical sampling through velocity-rescaling, (note)J. Chem. Phys. 126, 014101 (2007) Preprint: arXiv:0803.4060 G. Bussi and M. Parrinello, Stochastic thermostats: comparison of local and global schemes, Comp. Phys. Comm. 179, 26 (2008)

Preprint: arXiv:0803.4397

G. Bussi, T. Zykova-Timan and M. Parrinello,

Isothermal-isobaric molecular dynamics using stochastic velocity rescaling,

J. Chem. Phys. 130, 074101 (2009) Preprint: arXiv:0901.0779P. Raiteri, J. D. Gale and G. Bussi,Reactive Force Field for Proton Diffusion in BaZrO₃J. Phys.: Condens. Matter 23, 334213 (2011)Preprint: arXiv:1104.0773

In these papers we introduce and discuss an algorithm to perform molecular dynamics simulations in the canonical ensemble, i.e. a thermostat. This thermostat is very efficient, does not suffer of ergodicity problems, minimally perturbs the dynamics, and has a conserved quantity called effective energy.

In the first paper (JCP 2007) we introduce the scheme as a sort of stochastic version of the very popular Berendsen thermostat. Our scheme is as simple to use as the Berendsen one, but with the advantage that it provides the correct ensemble. In the second paper (CPC 2008) we derive the same method in an alternative manner, i.e. transforming the local Langevin dynamics into a global scheme. We then compare in detail the local and the global approach, showing that the global one (our new thermostat) has a much minor impact on the dynamics. In the third paper (JCP 2009) we show how to combine our scheme with variable-cell methods to control temperature and pressure, and we perform systematic benchmarks against other algorithms. The last paper (JPCM 2011) is not really about thermostats, but it's included here since in that paper we introduce an integrator for flexible cell which, combined with our thermostat, gives a very efficient scheme for sampling the isostress-isothermal ensemble.

As far as I know, our thermostat is available out-of-the-box in the following molecular dynamics packages:

• GROMACS (keyword "v-rescale", thanks to Berk Hess)

• CP2K (keyword "CSVR", thanks to Teodoro Laino)

• TINKER (keyword "BUSSI")

• CAMPARI (keyword TSTAT=4)

• QBOX (keyword "BDP")

• FFX (keyword "BUSSI")

If you want to implement it in another molecular dynamics code, you can download here a couple of useful routines (C and F90 version).

(note) There is a typo in the Bussi, Donadio and Parrinello JCP (2007) paper in the instructions for calculating the sum of Gaussian numbers using a gamma distribution - many thanks to Francois Gygi for pointing it out! If you follow exactly the instructions in the paper you will end up in a wrong implementation. On the other hand, the routines that you can download from this website are working properly. In case you need help, feel free to contact me.

An integration scheme for Langevin equation with tracking of effective energy conservation

G. Bussi and M. Parrinello,

Accurate sampling using Langevin dynamics,

Phys. Rev. E 75, 056707 (2007)

Preprint: arXiv:0803.4083

In this paper we show how it is possible to define an effective energy for Langevin dynamics. This quantity can be proven to be exactly conserved in the limit of small time-step, so that its imperfect conservation can be tracked to check if the choice of the time-step is appropriate. It is extremely useful, especially when dealing with new systems where there is no standard choice for this parameter. Moreover, one can use effective energy to perform hybrid Monte Carlo simulations, where the trial moves are generated by Langevin dynamics.

You can find a reference implementation of this scheme, including effective energy monitoring, in my SimpleMD Lennard-Jones code (note however that the results in the paper were produced using a modified version of DLPOLY).

Colored Langevin equation for molecular dynamics simulations