New Langevin and gradient thermostats for rigid body dynamics

Davidchack, Ruslan L.; Ouldridge, Thomas E.; Tretyakov, Michael V.

doi:10.1063/1.4916312

Cited by 46 publications

(59 citation statements)

References 52 publications

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“…The microcanonical partition function can then be constructed by using the weighted phase space volume [Eq. (23)] and the conserved quantity [Eq. (20)], which produces …”

Section: Nosé-hoover Chainmentioning

confidence: 99%

A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics

Zhang

Liu

Chen

et al. 2017

The Journal of Chemical Physics

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We show a unified second-order scheme for constructing simple, robust and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated.We show that the scheme is also useful for other types of thermostat, such as the Andersen thermostat and Nosé-Hoover chain, regardless of whether the thermostat is deterministic or stochastic. In addition to analytical analysis, two 1-dimensional models and three typical realistic molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accuracy may be increased by an order of magnitude for estimating coordinate-dependent properties in molecular dynamics (when the same time interval is used), irrespective of which type of thermostat is applied. The scheme is especially useful for path integral molecular dynamics, because it consistently improves the efficiency for evaluating all thermodynamic properties for any type of thermostat.4

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“…The microcanonical partition function can then be constructed by using the weighted phase space volume [Eq. (23)] and the conserved quantity [Eq. (20)], which produces …”

Section: Nosé-hoover Chainmentioning

confidence: 99%

A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics

Zhang

Liu

Chen

et al. 2017

The Journal of Chemical Physics

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“…Hence, the following experimental investigations [27,28] considered rotational diffusion only as a factor influencing the measurements of the dynamic scattering coefficient but not the structure of the aggregates. In contrast to previous studies, we find that an explicit implementation of the aggregates' rotational diffusion yields clusters, which are less compact and more anisotropic in shape than those produced by the translational diffusion only.We studied the evolution of the system in a canonical N V T ensemble with temperature controlled by the Langevin thermostat for rigid body dynamics [29], which couples on the translational as well as rotational degrees of freedom. Throughout the paper, all distances are given in units of sphere diameter σ and the time in τ = σ m/k B T with k B being the Boltzmann constant and T the temperature.…”

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confidence: 99%

Diffusion-Limited Cluster Aggregation: Impact of Rotational Diffusion

2018

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Diffusion-limited cluster aggregation (DLCA) is a well established model for the formation of highly porous low-density non-equilibrium structures. One of the main conclusions of the previous studies considering this model is that the rotational diffusion of aggregating clusters does not change their structure characterized by a universal fractal dimension of d f = 1.7 − 1.8. In contradiction to this assumption, we demonstrate that the rotation movement of clusters significantly changes the structure of forming aggregates. The fractal dimension of rotating clusters is lower than the one found in the standard DLCA model and decreases with the increasing ratio of rotational and translational diffusion constants Dr/Dt, which offers a possibility to tune the structures of the aggregates below the conventional DLCA fractal dimension limit. PACS numbers: 82.20.Wt, 61.43.Hv The model of diffusion-limited cluster aggregation (see, e.g., Refs. 1-3 for a review) was introduced more than 30 years ago [4,5]. Together with the closely related reaction-limited cluster aggregation model [6,7], DLCA provides a scenario for the process of non-equilibrium particle aggregation, which universality is widely accepted [8,9]. In this framework, aggregating nanoparticles form networks of variable density determined by the type of inter-particle interaction. The aggregates can be characterized by their fractal (Hausdorff) dimension, which measures how effectively they fill the available space. In the limiting case of non-interacting particles, which are currently assumed to form a structure with the lowest possible density, early Monte Carlo (MC) simulations of the aggregation process [10] provided a value of d f = 1.7 − 1.8 for the fractal dimension of three-dimensional clusters. At the same time, a similar value was found experimentally by the analysis of twodimensional images of the aggregates formed by gold colloidal particles [11,12]. Later on, however, less dense fractal structures were observed by soot aggregation [13][14][15]. An explanation for the formation of aggregates with a fractal dimension below the DLCA limit is still under discussion. For instance, the anisotropic shape of the aggregates was suggested as a possible factor affecting the structure, but a recent study demonstrated that it does not influence the fractal dimension [16]. In addition, there are indications that the analysis of the twodimensional images of experimentally obtained threedimensional aggregates may overestimate their fractal dimension [17,18].In this letter, we demonstrate that the aggregation of rotating clusters results in structures less dense than those obtained within the DLCA scheme. That is, we extend the conventional model of non-reversible DLCA to include the rotational diffusion of aggregates (rDLCA). The bulk of the previous studies concerning DLCA [16,[19][20][21][22][23][24][25][26] modeled Brownian dynamics of the aggre-gates in MC simulations and, in doing so, omitted the orientational diffusion of the clusters. The reason for thi...

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“…Similar behavior is expected for other global thermostats such as the Nosé-Hoover-Langevin method. 27,28 Extension of our approach to massive Langevin-type thermostats, [54][55][56] in which every degree of freedom is acted upon independently, is beyond the scope of this work. Nonetheless, we envision that this would entail using the components of entrywise products between p andṙ [n] , and also between π andq [n] in the case of rigid bodies, instead of the scalar products present in Eq.…”

Section: Correction Of Discretization Effects On Computed Thermodymentioning

confidence: 99%

Refinement of thermostated molecular dynamics using backward error analysis

Silveira

Abreu

2019

The Journal of Chemical Physics

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Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can be easily recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs.

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New Langevin and gradient thermostats for rigid body dynamics

Abstract: A velocity-dependent potential of a rigid body in a rotating frame Am. J. Phys. 76, 1146 (2008)

Cited by 46 publications

References 52 publications

A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics

A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics

Diffusion-Limited Cluster Aggregation: Impact of Rotational Diffusion

Refinement of thermostated molecular dynamics using backward error analysis

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