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Zerbetto, Mirco; Piserchia, Andrea; Frezzato, Diego

doi:10.1002/jcc.23701

Cited by 12 publications

(34 citation statements)

References 65 publications

(96 reference statements)

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“…At the molecular scale, this is translated into a broadening of the distribution of work values, p(w), which is characteristic of the system under inspection, of the transformation protocol, and of the stochastic dynamics over the uncontrolled degrees of freedom. 18 The calculations here performed for the gaseous methane passed these checks. This implies that an excellent sampling of the low-work wing of p(w) is required to get a very accurate result; on the other hand, the tail of any distribution is hardly sampled unless an extremely large number of measures (calculations, here) is performed.…”

Section: Uncertainties On the Outcomementioning

confidence: 98%

“…Since the energy landscape is initially ''flat'', this operation is nothing but a trivial unbiased drawing of 3N values À1/2 r x i,a r +1/2. As stated in the Introduction, up to now the efficiency of the morphing route has been proved by us on archetype systems like alkyl chains, 18 but also on more complex systems like aliphatic coatings of gold surfaces (up to about 150 internal degrees of freedom with a coarse-grained representation). In routine applications of the JE, in fact, the initial configuration is drawn from the effective equilibrium distribution at fixed controlled parameters.…”

Section: Morphing/steering Of the Gaseous Statementioning

confidence: 99%

“…18 For technicalities, the interested reader is referred to such a publication and to the documentation that accompanies the software. 18 For technicalities, the interested reader is referred to such a publication and to the documentation that accompanies the software.…”

Section: Computational Details (Essentials)mentioning

confidence: 99%

“…1 By looking at eqn (27), it is intuitive that the lower values of the work amount dominate the outcome of the calculation, because of the exponential character of the average. 18, we assess the statistical uncertainty by splitting the ensemble of N tr outcomes into M blocks formed by N tr /M results from consecutive trajectories (taken as they are generated); for each block we evaluate the argument of the logarithm in eqn (27) and get the statistical uncertainty dF on such a ''morphing factor'' F simply by taking one standard deviation of these partial outcomes from the average (computed from all trajectories). This means that for any finite number of repetitions, N tr , an unavoidable bias (systematic error), (dDA transf ) bias , due to poor sampling of the low-work wing, will affect to some extent the outcome from eqn (27).…”

Section: Uncertainties On the Outcomementioning

confidence: 99%

“…18,19 The strategy, termed by us as ''total energy morphing'', consists of making a sort of drastic ''alchemical transformation'' where the whole energetics of the chemical system grows from a flat state in which all the interactions are absent, while possible constraints (e.g., chemical bonds) amongst the constituting moieties are set and kept from the beginning. 18,19 The strategy, termed by us as ''total energy morphing'', consists of making a sort of drastic ''alchemical transformation'' where the whole energetics of the chemical system grows from a flat state in which all the interactions are absent, while possible constraints (e.g., chemical bonds) amongst the constituting moieties are set and kept from the beginning.…”

Section: Introductionmentioning

confidence: 99%

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Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

Zerbetto

Frezzato

2015

Phys. Chem. Chem. Phys.

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We illustrate how the Jarzynski equality (JE), which is the progenitor of non-equilibrium methods aimed at constructing free energy landscapes for molecular-sized fluctuating systems subjected to steered transformations, can be applied to derive equations of state for bulk systems. The key-step consists of physically framing the computational strategy of "total energy morphing", recently presented by us as an efficient implementation of the JE [M. Zerbetto, A. Piserchia, D. Frezzato, J. Comput. Chem., 2014, 35, 1865-1881], in terms of build-up of the real thermodynamic state of a bulk material from the corresponding ideal state, in which the particles are non-interacting. In this context, the JE machinery yields the excess free energy versus suitably chosen controlled state variables, whose thermodynamic derivatives eventually lead to the equation of state. As an explanatory case study, we apply the methodology to derive the equation of state of gaseous methane by constructing the Helmholtz free energy versus the particle density (at fixed temperature) and then evaluating the thermodynamic derivative with respect to the volume. In our intent, this "old-style" work on gaseous methane should open the way for the investigation of thermodynamics of extended systems via non-equilibrium methods.

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Section: Uncertainties On the Outcomementioning

confidence: 98%

Section: Morphing/steering Of the Gaseous Statementioning

confidence: 99%

Section: Computational Details (Essentials)mentioning

confidence: 99%

Section: Uncertainties On the Outcomementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

Zerbetto

Frezzato

2015

Phys. Chem. Chem. Phys.

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On the accurate estimation of free energies using the jarzynski equality

et al. 2018

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The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so‐called Jarzynski estimator, normalΔFfalse^J. Alternatively, the second‐order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation‐Dissipation estimator normalΔFfalse^FD. Here we derive the parametric maximum‐likelihood estimator (MLE) of the free energy normalΔFfalse^ML considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to normalΔFfalse^J. We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional normalΔFfalse^italicML∗ to the Bennett acceptance ratio (normalΔFfalse^BAR) estimator. We show that, for Gaussian unidirectional work distributions, normalΔFfalse^FD is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that normalΔFfalse^ML and normalΔFfalse^italicML∗ perform better than normalΔFfalse^J and normalΔFfalse^BAR, for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc.

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Multiscale modeling for interpreting nuclear magnetic resonance relaxation in flexible molecules

Zerbetto

Polimeno

2016

Int J of Quantum Chemistry

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In this tutorial review, we provide a comprehensive description of a multiscale methodology tailored to the calculation of nuclear magnetic resonance (NMR) relaxation data of flexible molecules, based on the definition, parametrization, and solution of a Smoluchowski equation defined for a set of relevant molecular coordinates. While the method is applicable in principle to any collection of internal degrees of freedom, here we focus on flexibility described in terms of torsion angles under the paradigm of what we call the diffusive chain model. The theoretical basis of the multiscale stochastic approach to NMR spectroscopy is provided in detail. Computational aspects are discussed, pointing at a suggested set of specific software packages. To give to this contribution a hands-on component, a self-contained tutorial is made available as Supporting Information with the discussion of some examples taken from recently published studies.diffusive chain model, integrated computational approach, nuclear magnetic resonance, stochastic methods | I N T R O D U C T I O NIn this contribution, we present a general overview of a multiscale modeling approach to the interpretation of spectroscopic observables that are highly sensitive to molecular flexibility. In particular, we discuss a stochastic approach for the calculation of nuclear magnetic resonance (NMR) relaxation data of flexible molecules. In a multiscale spirit, all parameters entering the basic stochastic equation are calculated (or evaluated) using a proper level of description of the molecule, which can be quantum mechanical (QM), classical, or hybrid quantumclassical, depending on the type of the required parameter. After a short general review of the connection between molecular dynamics (MD) and spectroscopic observables, the discussion will be focused on NMR studies of molecules in solution, where the fast motional regime can be invoked.Our target is the description of the structural dynamics of a given flexible molecular system. MD is a fundamental ingredient, together with structural properties, that needs to be taken into account when interpreting, understanding, and predicting both single-molecule and bulk properties of matter. Just to mention a few important examples, dynamics affects proteins properties in a number of different ways, from tuning the binding properties of folded proteins to regulating pathways of folding and binding, from modulating allosteric regulation to controlling function in disordered/unstructured proteins or domains. [1,2] MD is also at the basis of function of molecular machines [3] and it can modulate charge transfer in molecular electronic devices. [4] Having access to molecular motions is, thus, of primary importance and a number of experimental (spectroscopic) techniques are at present available, which are split in two main branches: bulk and single-molecule experiments.NMR is the selected bulk technique to be described in this tutorial review. It is widely used in studying structure and dynamics of biomolecules, es...

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Looking for some free energy? Call JEFREE (…)

Cited by 12 publications

References 65 publications

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

On the accurate estimation of free energies using the jarzynski equality

Multiscale modeling for interpreting nuclear magnetic resonance relaxation in flexible molecules

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