Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations

Hickman, J.

doi:10.1103/physrevb.94.184311

Cited by 31 publications

(15 citation statements)

References 24 publications

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“…Previous simulations of NM after excess ke was added to a central molecule find similar timescales, τ=11.6-13.6 ps, but with β=1 [83]. The two types of response we find for ,0 ( ) suggest that the short-time behavior comes from localized dynamics, similar to , ( ), while slower relaxation involves transfer of ke to the large heat reservoir, similar to the behavior found in simulations of copper [84]. Measurements of temperature as a function of time after shock-induced ignition in PETN (triangles), and other energetic materials analogous to NM [85], also show a crossover from exponential relaxation at short times to nonexponential relaxation at longer times, somewhat similar to our simulations of ,0 ( ).…”

Section: Resultssupporting

confidence: 75%

Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

Chamberlin

Mújica

Izvekov

et al. 2020

Physica A: Statistical Mechanics and its Applications

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Molecular dynamics (MD) simulations of standard systems of interacting particles ("atoms") give excellent agreement with the equipartition theorem for the average energy, but we find that these simulations exhibit finite-size effects in the dynamics that cause local fluctuations in energy to deviate significantly from the analogous energy fluctuation relation (EFR). We have made a detailed analysis of Lennard-Jones atoms to track the origin of such unphysical fluctuations, which must be corrected for an appropriate description of the statistical mechanics of small systems, especially at low temperatures (T). Similar behavior is found in a model of nitromethane at higher T. The main conclusion of our study is that systems separated into nanometer-sized "blocks" inside much larger simulations exhibit excess fluctuations in potential energy (pe) that diverge inversely proportional to T in a manner that is strongly dependent on the range of interaction. Specifically, at low T with long-range interactions pe fluctuations exceed the EFR by at least an order of magnitude, dropping abruptly to below the EFR when interactions include only 1 st -neighbor atoms. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1 stneighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2 nd -neighbor interactions matches the excess fluctuations, but only if the 2 nd -neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2 ndneighbor interactions considerably increases the width of the pe distribution, suggesting that Anderson localization may play a role. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in each block coincide with negative pe correlations between neighboring blocks, whereas reduced pe fluctuations coincide with positive pe correlations. Indeed, anomalous pe fluctuations in small systems can be quantified using a net local energy in Boltzmann's factor that includes pe from the surrounding shell of similarly small systems, or equivalently an effective local temperature. Our results and analysis elucidate the source of non-Boltzmann fluctuations, and the need to include mesoscopic thermal effects from the local environment for a consistent theoretical description of the equilibrium fluctuations in MD simulations of standard models with long-range interactions.

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Section: Resultssupporting

confidence: 75%

Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

Chamberlin

Mújica

Izvekov

et al. 2020

Physica A: Statistical Mechanics and its Applications

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“…In classical thermodynamics, temperature measures the average kinetic energy of the particles in a system, E K = 3 2 k B T . Such a relation has been employed widely in molecular dynamics simulations [252][253][254]. In the framework of DFT, Ayers et al have defined a local kinetic energy,…”

Section: Definitions Based On Thermodynamic Relationsmentioning

confidence: 99%

Local temperatures out of equilibrium

2019

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The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium. Figure 4: (a) The product of the density of states η(E) times the global distribution function ϕ|ρ|ϕ forms a strongly pronounced peak at the expectation value of the global system energyĒ. (b) The logarithm of the local distribution function a|ρ|a (solid line) and the logarithm of a canonical distribution (dashed line) with the same local temperature for a harmonic chain. (a) and (b) are reprinted with permission from [74].

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“…The temperatures for the QM/MM-MD ensemble are clustered around 600 K, although the spread of temperatures is slightly higher than for the 300 K ensemble. This stems from the fact that the reheating step is applied to a very small system only, and temperature fluctuations in MD simulations depend on the number of atoms (Hickman and Mishin, 2016 ). Furthermore, these fluctuations naturally become larger for larger temperatures (Chui et al, 1992 ).…”

Section: Resultsmentioning

confidence: 99%

Novel Molecular-Dynamics-Based Protocols for Phase Space Sampling in Complex Systems

et al. 2018

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The adequate exploration of the phase space of a chromophore is a fundamental necessity for the simulation of their optical and photophysical properties, taking into account the effects of vibrational motion and, most importantly, the coupling with a (non-homogeneous) molecular environment. A representative set of conformational snapshots around the Franck-Condon region is also required to perform non-adiabatic molecular dynamics, for instance in the framework of surface hopping. Indeed, in the latter case one needs to prepare a set of initial conditions providing a meaningful and complete statistical base for the subsequent trajectory propagation. In this contribution, we propose two new protocols for molecular dynamics-based phase space sampling, called “local temperature adjustment” and “individual QM/MM-based relaxation.” These protocols are intended for situations in which the popular Wigner distribution sampling procedure is not applicable—as it is the case when anharmonic or nonlinear vibrations are present—and where regular molecular dynamics sampling might suffer from an inaccurate distribution of internal energy or from inaccurate force fields. The new protocols are applied to the case of phase space sampling of [Re(CO)3(Im)(Phen)]+ (im, imidazole; phen, phenanthroline) in aqueous solution, showing the advantages and limitations of regular Wigner and molecular dynamics sampling as well as the strengths of the new protocols.

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Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations

Cited by 31 publications

References 24 publications

Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

Local temperatures out of equilibrium

Novel Molecular-Dynamics-Based Protocols for Phase Space Sampling in Complex Systems

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