We consider the problem of free energy estimation from the general perspective of regularization ... more We consider the problem of free energy estimation from the general perspective of regularization and Bayes estimation theory. We try to take advantage of an assumed a priori knowledge of the free energy. We reformulate the original Bennett acceptance ratio method, in this perspective, devise a numerical algorithm to solve it, and give a closed formula to estimate the confidence in the prior. Finally, we test the derived estimators by applying them to a toy model.
Mathematical relations concerning particle systems require knowledge of the applicability conditi... more Mathematical relations concerning particle systems require knowledge of the applicability conditions to become physically relevant and not merely formal. We illustrate this fact through the analysis of the Jarzynski equality (JE), whose derivation for Hamiltonian systems suggests that the equilibrium free-energy variations can be computational or experimentally determined in almost any kind of non-equilibrium processes. This apparent generality is surprising in a mechanical theory. Analytically, we show that the quantity called “work” in the Hamiltonian derivation of the JE is neither a thermodynamic quantity nor mechanical work, except in special circumstances to be singularly assessed. Through molecular dynamics simulations of elastic and plastic deformations induced via nano-indentation of crystalline surfaces that fall within the formal framework of the JE, we illustrate that the JE cannot be verified and that the results of this verification are process dependent.
Clathrate hydrates are crystalline inclusion compounds wherein a water framework encages small gu... more Clathrate hydrates are crystalline inclusion compounds wherein a water framework encages small guest atoms/molecules within its cavities. Among the others, methane clathrates are the largest fossil fuel resource still available. They can also be used to safely transport gases and can also form spontaneously under suitable conditions plugging pipelines. Understanding the crystallization mechanism is very important, and given the impossibility of experimentally identifying the atomistic path, simulations played an important role in this field. Given the large computational cost of these simulations, in addition to all-atom force fields, scientists considered coarse-grained water models. Here, we have investigated the effect of coarse-graining, as implemented in the water model mW, on the crystallization characteristics of methane clathrate in comparison with the all-atom TIP4P force field. Our analyses revealed that although the characteristics directly depending on the energetics of the water models are well reproduced, dynamical properties are off by the orders of magnitude. Being crystallization a non-equilibrium process, the altered kinetics of the process results in different characteristics of crystalline nuclei. Both TIP4P and mW water models produce methane clathrate nuclei with some amount of the less stable (in the given thermodynamic conditions) structure II phase and an excess of pentagonal dodecahedral cages over the tetrakaidecahedral ones regarding the ideal ratio in structure I. However, the dependence of this excess on the methane concentration in solution is higher with the former water model, whereas with the latter, the methane concentration in solution dependence is reduced and within the statistical error.
.The school that was held at the Ettore Majorana Foundation and Center for Scientific Culture (EM... more .The school that was held at the Ettore Majorana Foundation and Center for Scientific Culture (EMFCSC), Erice (Sicily), in July 2005, aimed to provide an up-to-date overview of almost all technical advances of computer simulation in statistical mechanics, giving a fair glimpse of the domains of interesting appli- cations. Full details on the school programme and participants, plus some ad- ditional material, are available at its Web site, http://cscm2005.unimore.it Computer simulation is now a very well established and active field, and its applications are far too numerous and widespread to be covered in a single school lasting less than 2 weeks. Thus, a selection of topics was required, and it was decided to focus on perspectives in the celebration of the 65th birthday of Mike Klein, whose research has significantly pushed forward the frontiers of computer simulation applications in a broad range, from materials science to chemical biology. Prof. M. L. Klein (Dept. Chem., Univ. Pennsylvania, Philadelphia, USA) is internationally recognized as a pioneer in this field; he is the winner of both the prestigious Aneesur Rahman Prize for Computa- tional Physics awarded by the American Physical Society, and its European counterpart, the Berni J. Alder CECAM Prize, given jointly with the Euro- pean Physical Society. The festive session held on July 23rd, 2005, highlighting these achievements, has been a particular focus in this school. In the frame- work of the EMFCSC International School of Solid State Physics Series, the present school was the 34th course of its kind. However, this school can be considered as being the third (and perhaps last?) event in a series of comprehensive schools on computer simulation, 10 years after the COMO Euroconference on \u201cMonte Carlo and Molecular Dy- namics of Condensed Matter systems,\u201d and 20 years after the VARENNA Enrico Fermi Summer School on \u201cMolecular Dynamics of Statistical Mechan- ical Systems.\u201d Comparing the topics emphasized upon in these schools, both the progress in achieving pioneering applications to problems of increasing complexity, and the impressive number of new methodological developments are evident. While the focus of the Varenna School was mostly on Molecular Dynamics (MD) and its applications from simple to complex fluids, the Como school included both Monte Carlo (MC) simulations of lattice systems (from quantum problems to the advanced analysis of critical phenomena in classi- cal systems like the simple Ising model), and the density functional theory of electronic structure up to the Car-Parrinello ab initio Molecular Dynamics techniques (CPMD). At the Erice school, a new focus was put on the para- digma of \u201cMultiscale Simulation\u201d, i.e. the idea to combine different methods of simulation on different scales of length and time in a coherent fashion. This method allow us to clarify the properties of complex materials or biosystems where a single technique (like CPMD or MD or MC etc.) due to excessive needs of computer resources is bound to fail. Good examples presented at this school for such multiscale simulation approaches included MD studies of polymers coupled with a solvent, which is described only in a coarse-grained fashion by the lattice Boltzmann technique and hybrid quantum mechanical/molecular mechanics (QM/MM) methods for CPMD simulations of biomolecules, etc. As a second \u201cleitmotif,\u201d emphasis has been put on rapidly emerging novel simulation techniques. Techniques that have been dealt with at this school in- clude the methods of \u201ctransition path sampling\u201d (i.e. a Monte Carlo sampling not intending to clarify the properties of a state in the space of thermodynamic variables, but the properties of the dominating paths that lead \u201cin the course of a transition\u201d from one stable state to another), density of state methods (like Wang-Landau sampling and multicanonical Monte Carlo, allowing an elegant assessment of free energy differences and free energy barriers, etc.) and so on. These techniques promise substantial progress with famous \u201cgrand challenge problems\u201d like the kinetics of protein folding, as well as with classi- cal ubiquitous problems like the theory of nucleation phenomena. Other sub- jects where significant progress in methodological aspects was made included cluster algorithms for off-lattice systems, evolutionary design in biomedical physics, construction of coarse-grained models describing the self-assembly and properties of lipid layers or of liquid crystals under confinement and/or shear, glass simulations, novel approaches to quantum chemistry, formulation of models to correctly describe the essence of dry friction and lubrication, rare event sampling, quantum Monte Carlo methods, etc. The diversity of this list vividly illustrates the breadth and impact that simulation methods have today. While the most simple MC and MD methods have been invented about 50…
... 1: Fundamental techniques & approaches (Lecture notes in physics, Vol. ... Large Scale Co... more ... 1: Fundamental techniques & approaches (Lecture notes in physics, Vol. ... Large Scale CondensedMatter Calculations Using The Gaussian Augmented Plane Waves Method ... Biomelecular Conformations as Metastable States.Transport Coefficients of Quantum-Classical Systems ...
Multiscale molecular dynamics of open systems represents a powerful tool of investigation in soft... more Multiscale molecular dynamics of open systems represents a powerful tool of investigation in soft matter.
Some time ago, Ciccotti and Jacucci [Phys. Rev. Lett. 1975;35:789-792] – on the basis of Onsager ... more Some time ago, Ciccotti and Jacucci [Phys. Rev. Lett. 1975;35:789-792] – on the basis of Onsager regression hypothesis as explained by Kubo – suggested and implemented an original approach to study both stationary and time-dependent situations in non-equilibrium systems. The key idea of their approach was to tackle separately the dynamical evolution from the problem of sampling the initial condition. In this review, we discuss the evolution of this approach dubbed D-NEMD, the dynamical approach to non-equilibrium molecular dynamics, to differentiate it from the stationary NEMD methods. We will go through the D-NEMD theoretical framework and illustrate how it allows to compute time-dependent macroscopic dynamical behaviours by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions associated to a suitable distribution (either equilibrium or non-equilibrium) at time zero. We discuss a few case studies where the D-NEMD method is illustrated: first for ‘historical’ applications, like the study of transport properties in the linear and non-linear regimes, including a divertissement on the calculation of time correlation functions in the Gran Canonical ensemble. We finally briefly illustrate D-NEMD applications to the study of problems arising in key hydrodynamic processes such as the formation of convective cells and the relaxation of a non-uniform density profile in a fluid, giving attention to the problem of sampling the conditional probability density ensemble associated with the initial states.
This comment presents few reflections, inspired by various contributions in this special issue, t... more This comment presents few reflections, inspired by various contributions in this special issue, that address the issue of how to interpret and use molecular dynamics (MD). It is argued that, in spite of what its name seems to suggest, MD is not a tool to predict deter- ministic behaviors but a device to sample both time-independent and time-dependent statistical mechanics properties of molecular systems. Therefore MD simulations must be used in concert with tools from stochastic processes theory and a big challenge is how to develop these tools to make them appropriate both conceptually and practically in the context of these simulations.
We consider the problem of free energy estimation from the general perspective of regularization ... more We consider the problem of free energy estimation from the general perspective of regularization and Bayes estimation theory. We try to take advantage of an assumed a priori knowledge of the free energy. We reformulate the original Bennett acceptance ratio method, in this perspective, devise a numerical algorithm to solve it, and give a closed formula to estimate the confidence in the prior. Finally, we test the derived estimators by applying them to a toy model.
Mathematical relations concerning particle systems require knowledge of the applicability conditi... more Mathematical relations concerning particle systems require knowledge of the applicability conditions to become physically relevant and not merely formal. We illustrate this fact through the analysis of the Jarzynski equality (JE), whose derivation for Hamiltonian systems suggests that the equilibrium free-energy variations can be computational or experimentally determined in almost any kind of non-equilibrium processes. This apparent generality is surprising in a mechanical theory. Analytically, we show that the quantity called “work” in the Hamiltonian derivation of the JE is neither a thermodynamic quantity nor mechanical work, except in special circumstances to be singularly assessed. Through molecular dynamics simulations of elastic and plastic deformations induced via nano-indentation of crystalline surfaces that fall within the formal framework of the JE, we illustrate that the JE cannot be verified and that the results of this verification are process dependent.
Clathrate hydrates are crystalline inclusion compounds wherein a water framework encages small gu... more Clathrate hydrates are crystalline inclusion compounds wherein a water framework encages small guest atoms/molecules within its cavities. Among the others, methane clathrates are the largest fossil fuel resource still available. They can also be used to safely transport gases and can also form spontaneously under suitable conditions plugging pipelines. Understanding the crystallization mechanism is very important, and given the impossibility of experimentally identifying the atomistic path, simulations played an important role in this field. Given the large computational cost of these simulations, in addition to all-atom force fields, scientists considered coarse-grained water models. Here, we have investigated the effect of coarse-graining, as implemented in the water model mW, on the crystallization characteristics of methane clathrate in comparison with the all-atom TIP4P force field. Our analyses revealed that although the characteristics directly depending on the energetics of the water models are well reproduced, dynamical properties are off by the orders of magnitude. Being crystallization a non-equilibrium process, the altered kinetics of the process results in different characteristics of crystalline nuclei. Both TIP4P and mW water models produce methane clathrate nuclei with some amount of the less stable (in the given thermodynamic conditions) structure II phase and an excess of pentagonal dodecahedral cages over the tetrakaidecahedral ones regarding the ideal ratio in structure I. However, the dependence of this excess on the methane concentration in solution is higher with the former water model, whereas with the latter, the methane concentration in solution dependence is reduced and within the statistical error.
.The school that was held at the Ettore Majorana Foundation and Center for Scientific Culture (EM... more .The school that was held at the Ettore Majorana Foundation and Center for Scientific Culture (EMFCSC), Erice (Sicily), in July 2005, aimed to provide an up-to-date overview of almost all technical advances of computer simulation in statistical mechanics, giving a fair glimpse of the domains of interesting appli- cations. Full details on the school programme and participants, plus some ad- ditional material, are available at its Web site, http://cscm2005.unimore.it Computer simulation is now a very well established and active field, and its applications are far too numerous and widespread to be covered in a single school lasting less than 2 weeks. Thus, a selection of topics was required, and it was decided to focus on perspectives in the celebration of the 65th birthday of Mike Klein, whose research has significantly pushed forward the frontiers of computer simulation applications in a broad range, from materials science to chemical biology. Prof. M. L. Klein (Dept. Chem., Univ. Pennsylvania, Philadelphia, USA) is internationally recognized as a pioneer in this field; he is the winner of both the prestigious Aneesur Rahman Prize for Computa- tional Physics awarded by the American Physical Society, and its European counterpart, the Berni J. Alder CECAM Prize, given jointly with the Euro- pean Physical Society. The festive session held on July 23rd, 2005, highlighting these achievements, has been a particular focus in this school. In the frame- work of the EMFCSC International School of Solid State Physics Series, the present school was the 34th course of its kind. However, this school can be considered as being the third (and perhaps last?) event in a series of comprehensive schools on computer simulation, 10 years after the COMO Euroconference on \u201cMonte Carlo and Molecular Dy- namics of Condensed Matter systems,\u201d and 20 years after the VARENNA Enrico Fermi Summer School on \u201cMolecular Dynamics of Statistical Mechan- ical Systems.\u201d Comparing the topics emphasized upon in these schools, both the progress in achieving pioneering applications to problems of increasing complexity, and the impressive number of new methodological developments are evident. While the focus of the Varenna School was mostly on Molecular Dynamics (MD) and its applications from simple to complex fluids, the Como school included both Monte Carlo (MC) simulations of lattice systems (from quantum problems to the advanced analysis of critical phenomena in classi- cal systems like the simple Ising model), and the density functional theory of electronic structure up to the Car-Parrinello ab initio Molecular Dynamics techniques (CPMD). At the Erice school, a new focus was put on the para- digma of \u201cMultiscale Simulation\u201d, i.e. the idea to combine different methods of simulation on different scales of length and time in a coherent fashion. This method allow us to clarify the properties of complex materials or biosystems where a single technique (like CPMD or MD or MC etc.) due to excessive needs of computer resources is bound to fail. Good examples presented at this school for such multiscale simulation approaches included MD studies of polymers coupled with a solvent, which is described only in a coarse-grained fashion by the lattice Boltzmann technique and hybrid quantum mechanical/molecular mechanics (QM/MM) methods for CPMD simulations of biomolecules, etc. As a second \u201cleitmotif,\u201d emphasis has been put on rapidly emerging novel simulation techniques. Techniques that have been dealt with at this school in- clude the methods of \u201ctransition path sampling\u201d (i.e. a Monte Carlo sampling not intending to clarify the properties of a state in the space of thermodynamic variables, but the properties of the dominating paths that lead \u201cin the course of a transition\u201d from one stable state to another), density of state methods (like Wang-Landau sampling and multicanonical Monte Carlo, allowing an elegant assessment of free energy differences and free energy barriers, etc.) and so on. These techniques promise substantial progress with famous \u201cgrand challenge problems\u201d like the kinetics of protein folding, as well as with classi- cal ubiquitous problems like the theory of nucleation phenomena. Other sub- jects where significant progress in methodological aspects was made included cluster algorithms for off-lattice systems, evolutionary design in biomedical physics, construction of coarse-grained models describing the self-assembly and properties of lipid layers or of liquid crystals under confinement and/or shear, glass simulations, novel approaches to quantum chemistry, formulation of models to correctly describe the essence of dry friction and lubrication, rare event sampling, quantum Monte Carlo methods, etc. The diversity of this list vividly illustrates the breadth and impact that simulation methods have today. While the most simple MC and MD methods have been invented about 50…
... 1: Fundamental techniques & approaches (Lecture notes in physics, Vol. ... Large Scale Co... more ... 1: Fundamental techniques & approaches (Lecture notes in physics, Vol. ... Large Scale CondensedMatter Calculations Using The Gaussian Augmented Plane Waves Method ... Biomelecular Conformations as Metastable States.Transport Coefficients of Quantum-Classical Systems ...
Multiscale molecular dynamics of open systems represents a powerful tool of investigation in soft... more Multiscale molecular dynamics of open systems represents a powerful tool of investigation in soft matter.
Some time ago, Ciccotti and Jacucci [Phys. Rev. Lett. 1975;35:789-792] – on the basis of Onsager ... more Some time ago, Ciccotti and Jacucci [Phys. Rev. Lett. 1975;35:789-792] – on the basis of Onsager regression hypothesis as explained by Kubo – suggested and implemented an original approach to study both stationary and time-dependent situations in non-equilibrium systems. The key idea of their approach was to tackle separately the dynamical evolution from the problem of sampling the initial condition. In this review, we discuss the evolution of this approach dubbed D-NEMD, the dynamical approach to non-equilibrium molecular dynamics, to differentiate it from the stationary NEMD methods. We will go through the D-NEMD theoretical framework and illustrate how it allows to compute time-dependent macroscopic dynamical behaviours by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions associated to a suitable distribution (either equilibrium or non-equilibrium) at time zero. We discuss a few case studies where the D-NEMD method is illustrated: first for ‘historical’ applications, like the study of transport properties in the linear and non-linear regimes, including a divertissement on the calculation of time correlation functions in the Gran Canonical ensemble. We finally briefly illustrate D-NEMD applications to the study of problems arising in key hydrodynamic processes such as the formation of convective cells and the relaxation of a non-uniform density profile in a fluid, giving attention to the problem of sampling the conditional probability density ensemble associated with the initial states.
This comment presents few reflections, inspired by various contributions in this special issue, t... more This comment presents few reflections, inspired by various contributions in this special issue, that address the issue of how to interpret and use molecular dynamics (MD). It is argued that, in spite of what its name seems to suggest, MD is not a tool to predict deter- ministic behaviors but a device to sample both time-independent and time-dependent statistical mechanics properties of molecular systems. Therefore MD simulations must be used in concert with tools from stochastic processes theory and a big challenge is how to develop these tools to make them appropriate both conceptually and practically in the context of these simulations.
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Papers by Giovanni Ciccotti