Free energy landscape from path-sampling: application to the structural transition in LJ38

Adjanor, Gilles; Athènes, Manuel; Calvo, F.

doi:10.1140/epjb/e2006-00353-0

Cited by 42 publications

(64 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first term of the rhs comes from the Langevin dynamics (11), the second one from the evolution of the vector (19) and the last one from the birth-death events. The transition current is then given by Eq.…”

Section: A Stochastic Dynamicsmentioning

confidence: 99%

“…19,25,[27][28][29] This system has a complex potential energy landscape organized around two main basins: a deep and narrow funnel contains the global energy minimum, a face-centered-cubic truncated octahedron configuration (FCC), while a separate, wider, funnel leads to a large number of incomplete Mackay icosahedral structures (ICO) of slightly higher energies.…”

Section: A Lj 38 Clustermentioning

confidence: 99%

“…The study of the equilibrium thermodynamics of this system required more elaborate algorithms such as parallel tempering, [28][29][30] basin-sampling techniques, 31 Wang-Landau approaches, 32 or path-sampling methods. 19,33,34 More recently, the dynamical transitions between the two basins have been studied following various approaches. The interconversion rates between the FCC and ICO structures have been computed using discrete path sampling.…”

Section: A Lj 38 Clustermentioning

confidence: 99%

“…Interestingly, this path goes through a faulty FCC basin located around (Q 4 , Q 6 ) = (0.12, 0.45) that has been previously reported in the literature. 19,28 The clones have thus found reaction paths pointing out of their starting funnels. The clones starting from the FCC basins find a reaction path that leads into the icosahedral funnel while the one started from the ICOm basin still remain in the icosahedral funnel.…”

Section: T = 015mentioning

confidence: 99%

See 3 more Smart Citations

Simulating structural transitions by direct transition current sampling: The example of LJ38

Picciani

Athènes

Kurchan

et al. 2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

Reaction paths and probabilities are inferred, in a usual Monte Carlo or molecular dynamic simulation, directly from the evolution of the positions of the particles. The process becomes time-consuming in many interesting cases in which the transition probabilities are small. A radically different approach consists of setting up a computation scheme where the object whose time evolution is simulated is the transition current itself. The relevant timescale for such a computation is the one needed for the transition probability rate to reach a stationary level, and this is usually substantially shorter than the passage time of an individual system. As an example, we show, in the context of the "benchmark" case of 38 particles interacting via the Lennard-Jones potential ("LJ(38)" cluster), how this method may be used to explore the reactions that take place between different phases, recovering efficiently known results, and uncovering new ones with small computational effort.

show abstract

Section: A Stochastic Dynamicsmentioning

confidence: 99%

Section: A Lj 38 Clustermentioning

confidence: 99%

Section: A Lj 38 Clustermentioning

confidence: 99%

Section: T = 015mentioning

confidence: 99%

See 2 more Smart Citations

Simulating structural transitions by direct transition current sampling: The example of LJ38

Picciani

Athènes

Kurchan

et al. 2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…We show that these pathologies arise because discrete-time-step integrators of Langevin dynamics can be viewed as simulations of artificial driven nonequilibrium dynamics. This perspective has the advantage that the complications generated by this unwanted but inevitable breaking of time-reversal symmetry can be understood, and remedied in a controlled and systematic fashion, with insights from nonequilibrium statistical thermodynamics [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Using Nonequilibrium Fluctuation Theorems to Understand and Correct Errors in Equilibrium and Nonequilibrium Simulations of Discrete Langevin Dynamics

2013

View full text Add to dashboard Cite

Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite-time-step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that, even with a time-independent Hamiltonian, finite-time-step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate worklike quantity is defined-here called the shadow work-recently developed nonequilibrium fluctuation theorems can be used to measure or correct for the errors introduced by the use of finite time steps. In particular, we demonstrate that amending estimators based on nonequilibrium work theorems to include this shadow work removes the time-stepdependent error from estimates of free energies. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying sizes. While these deviations can be large, they can be eliminated altogether by Metropolization or greatly diminished by small reductions in the time step. Through this connection with driven processes, further developments in nonequilibrium fluctuation theorems can provide additional analytical tools for dealing with errors in finite-time-step integrators.

show abstract

Thermodynamics of Small Systems

Evans

Williams

Searles

2010

Nonlinear Dynamics of Nanosystems

View full text Add to dashboard Cite

Free energy landscape from path-sampling: application to the structural transition in LJ38

Cited by 42 publications

References 40 publications

Simulating structural transitions by direct transition current sampling: The example of LJ38

Simulating structural transitions by direct transition current sampling: The example of LJ38

Using Nonequilibrium Fluctuation Theorems to Understand and Correct Errors in Equilibrium and Nonequilibrium Simulations of Discrete Langevin Dynamics

Thermodynamics of Small Systems

Contact Info

Product

Resources

About