Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Dellago, Christoph; Hummer, Gerhard

doi:10.3390/e16010041

Cited by 82 publications

(93 citation statements)

References 83 publications

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“…For further background on equilibrium and NEW methods to compute free energies we refer the reader to Refs. [ ], respectively. The reader should further keep in mind that we are focusing on the calculation of

Δ A_{}^{low \to high}

in connection with indirect cycles, not arbitrary alchemical free energy differences.…”

Section: Methodsmentioning

confidence: 99%

“…. The switching simulations are started from coordinates/velocities saved during an equilibrium simulation in the canonical ensemble, the actual switch can then be carried out during dynamics in the microcanonical or canonical ensemble, including Langevin dynamics (LD) …”

Section: Methodsmentioning

confidence: 99%

“…The switching simulations are started from coordinates/velocities saved during an equilibrium simulation in the canonical ensemble, the actual switch can then be carried out during dynamics in the microcanonical or canonical ensemble, including Langevin dynamics (LD). [53] Bennett's acceptance ratio (BAR) method, [55] a two-sided extension to FEP, has become increasingly popular in the arena of classical FES. [52,[56][57][58][59][60][61] In contrast to FEP, one needs simulations at both states to compute DA 0!1 ,…”

Section: Methodology Free Energy Methodsmentioning

confidence: 99%

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Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

et al. 2017

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We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.

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Δ A_{}^{low \to high}

in connection with indirect cycles, not arbitrary alchemical free energy differences.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodology Free Energy Methodsmentioning

confidence: 99%

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Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

et al. 2017

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“…In general, it relates the probability to observe variations of a certain fluctuating variable proceding forward in time to that of observing its change in a time-reversed process [15][16][17][18][19][20][21][22][23] and permits to comprehend how irreversibility emerges from the reversible dynamics [24][25][26]. The correctness of the different variants of the fluctuation theorem have been verified in the case of many experimental protocols [27][28][29][30][31][32], as well as theoretical models [33][34][35][36][37][38][39][40][41][42][43][44][45][46], for the systems that operate on the mesoscopic scales. Here, we use the method of numerical simulations and argue that the stationary distributions of the probability fluxes converge to the Gaussian function.…”

Section: Introductionmentioning

confidence: 99%

Steady-state distributions of probability fluxes on complex networks

Chelminiak

Kurzynski

2017

Physica A: Statistical Mechanics and its Applications

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The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a complex network extended by the additional transition, called hereafter the gate. The random skips through the gate, driven by the external constant force, violate the detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge, regardless of the network topology, to the normal distribution. This result, combined with the stationary fluctuation theorem, permits to show that its standard deviation depends directly on the square root of the average flux. In turn, the central result of our paper relates this quantity to the external constant force and the two parameters that entirely characterize the normal distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of the computer simulations are widely discussed in terms of the rigorous theoretical predictions.

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“…Such so-called fluctuation theorems have now been derived for several quantities, such as heat, work and entropy [5,6], shedding new light on the significance of irreversibility and the second law at the nanoscale [7,8]. Besides their fundamental importance, fluctuation theorems also provide the basis for the interpretation of single-molecule experiments [9][10][11] as well as for the development of novel nonequilibrium computer simulation methods [12].…”

Section: Introductionmentioning

confidence: 99%

Non-equilibrium steady state of a driven levitated particle with feedback cooling

et al. 2015

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Laser trapped nanoparticles have been recently used as model systems to study fundamental relations holding far from equilibrium. Here we study a nanoscale silica sphere levitated by a laser in a low density gas. The center of mass motion of the particle is subjected, at the same time, to feedback cooling and a parametric modulation driving the system into a non-equilibrium steady state. Based on the Langevin equation of motion of the particle, we derive an analytical expression for the energy distribution of this steady state showing that the average and variance of the energy distribution can be controlled separately by appropriate choice of the friction, cooling and modulation parameters. Energy distributions determined in computer simulations and measured in a laboratory experiment agree well with the analytical predictions. We analyze the particle motion also in terms of the quadratures and find thermal squeezing depending on the degree of detuning.

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Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Cited by 82 publications

References 83 publications

Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

Steady-state distributions of probability fluxes on complex networks

Non-equilibrium steady state of a driven levitated particle with feedback cooling

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