Special Issue "Molecular Dynamics Simulation"
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (30 September 2013)
Prof. Dr. Giovanni Ciccotti
Department of Physics, University of Roma “La Sapienza”, La Sapienza,00185 Roma, Italy
Interests: methods in molecular dynamics simulation of systems of statistical mechanical interest, equilibrium and non equilibrium molecular dynamics, rare events, computer simulation of complex molecular systems
Prof. Dr. Mauro Ferrario
Department of Physics, University of Modena and Reggio Emilia, Via G. Campi 213, A 41100 Modena Italy
Interests: molecular dynamics simulation of condensed matter systems; solvation in h-bonded liquids; friction at the nanoscale
Prof. Dr. Christof Schuette
Freie Universitaet Berlin, Institute of Mathematics, Arnimallee 6, 14195 Berlin, Germany
Interests: rare events statistics in molecular dynamics, coarse graining in molecular dynamics, conformation dynamics
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.
Entropy 2013, 15(4), 1232-1246; doi:10.3390/e15041232
Received: 6 January 2013; in revised form: 18 March 2013 / Accepted: 18 March 2013 / Published: 8 April 2013| Download PDF Full-text (1122 KB)
Entropy 2013, 15(8), 3249-3264; doi:10.3390/e15083339
Received: 30 June 2013; in revised form: 5 August 2013 / Accepted: 7 August 2013 / Published: 13 August 2013| Download PDF Full-text (240 KB)
Article: SpaGrOW—A Derivative-Free Optimization Scheme for Intermolecular Force Field Parameters Based on Sparse Grid Methods
Entropy 2013, 15(9), 3640-3687; doi:10.3390/e15093640
Received: 16 February 2013; in revised form: 15 July 2013 / Accepted: 28 August 2013 / Published: 6 September 2013| Download PDF Full-text (1468 KB)
Entropy 2013, 15(9), 3734-3745; doi:10.3390/e15093734
Received: 21 July 2013; in revised form: 2 September 2013 / Accepted: 3 September 2013 / Published: 6 September 2013| Download PDF Full-text (2804 KB)
Review: Molecular Dynamics at Constant Pressure: Allowing the System to Control Volume Fluctuations via a “Shell” Particle
Entropy 2013, 15(9), 3941-3969; doi:10.3390/e15093941
Received: 29 July 2013; in revised form: 6 September 2013 / Accepted: 16 September 2013 / Published: 23 September 2013| Download PDF Full-text (1039 KB)
Entropy 2013, 15(10), 4300-4309; doi:10.3390/e15104300
Received: 26 June 2013; Accepted: 6 October 2013 / Published: 10 October 2013| Download PDF Full-text (275 KB)
Entropy 2013, 15(11), 4569-4588; doi:10.3390/e15114569
Received: 6 August 2013; in revised form: 15 October 2013 / Accepted: 18 October 2013 / Published: 24 October 2013| Download PDF Full-text (2680 KB)
Entropy 2013, 15(11), 4802-4821; doi:10.3390/e15114802
Received: 13 August 2013; in revised form: 28 October 2013 / Accepted: 31 October 2013 / Published: 5 November 2013| Download PDF Full-text (5960 KB)
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Title: Modelling potential energy surfaces: from first-principle approaches to empirical force fields
Authors: Pietro Ballone
Affiliation: Department of Physics, Università di Roma “La Sapienza”, 00185 Roma, Italy; E-Mail: firstname.lastname@example.org
Abstract: Explicit or implicit expressions of potential energy surfaces (PES) represent the basis of our ability to simulate condensed matter systems, possibly understanding and sometimes predicting their properties by purely computational methods. The paper provides an outline of the major approaches currently used to approximate and represent PES’s, and contains a brief discussion of what still needs to be achieved. The paper also analyses the relative role of empirical and ab-initio methods, that represents a crucial issue affecting the future of modelling in chemical physics and materials science.
Title: Analysis of Time-Reversible Born-Oppenheimer Molecular Dynamics
Authors: Lin Lin1, Jianfeng Lu2 and Sihong Shao3
Affiliations: 1 Lawrence Berkeley National Laboratory, USA; E-Mail: email@example.com
2 Duke University, USA; E-Mail: firstname.lastname@example.org
3 Peking University, China; E-Mail: email@example.com
Abstract: We analyze the time reversible Born-Oppenheimer molecular dynamics (TR-BOMD) scheme, which preserves the time reversibility of the Born-Oppenheimer molecular dynamics even with non-convergent self-consistent field iteration. In the linear response regime, we derive the stability condition as well as the accuracy of TRBOMD for computing physical properties such as the phonon frequency obtained from the molecular dynamic simulation. We connect and compare TRBOMD with the Car-Parrinello molecular dynamics in terms of accuracy and stability. We further discuss the accuracy of TRBOMD beyond the linear response regime for non-equilibrium dynamics of nuclei. Our results are demonstrated through numerical experiments using a simplified one dimensional model for Kohn-Sham density functional theory.
Title: First-Principle Methods: a Perspective from Quantum Monte Carlo
Authors: Miguel A. Morales1, Raymond Clay2, Carlo Pierleoni3,4 and David M. Ceperley2
Affiliations: 1 Lawrence Livermore National Lab, Livermore, USA; E-Mail: firstname.lastname@example.org
2 Department of Physics, University of Illinois, Urbana-Champaign, USA; E-Mail: email@example.com (RC); firstname.lastname@example.org (DC)
3 Dipartimento Di Scienze Fisiche e Chimiche, Università de L'Aquila, Italy; E-Mail: email@example.com
4 Department of Physics, University of Roma “La Sapienza”, La Sapienza,00185 Roma, Italy
Abstract: Quantum Monte Carlo methods are the most accurate algorithms for predicting properties of general quantum systems. We briefly introduce ground state, path integral at finite temperature and coupled-electron Monte Carlo methods, their merits and limitations. We then discuss recent calculations using these methods for dense liquid hydrogen as in undergoes a molecular atomic (metal/insulator) transition. We then discuss a procedure that can be used to assess electronic density functionals, which in turn can be used on a larger scale for first principles calculations and apply this technique to dense hydrogen and liquid water.
Title: On Metropolis Integrators for Molecular Dynamics
Author: Nawaf Bou-Rabee
Affiliation: Rutgers University-Camden, Camden, New Jersey, USA; E-Mail: firstname.lastname@example.org
Abstract : This paper invites the reader to experiment with an easy-to-use MATLAB  implementation of Metropolis integrators for Molecular Dynamics (MD) simulation [N. Bou-Rabee and E. Vanden-Eijnden, Comm Pure and Appl Math, 63:655–696, 2010]. These integrators are analysis-based, in the sense that they can rigorously simulate dynamics along an infinitely long MD trajectory. Among explicit integrators for MD, they seem to be the only ones that satisfy the fundamental requirement of stability. The schemes can handle stiff or hard-core potentials, and are straightforward to set up, apply and extend to new situations. Potential pitfalls in high dimension are discussed, and tricks for mitigation are given.
Title: Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-exchange, and Temperature-acceleration
Authors: Cameron F Abrams1 and Giovanni Bussi2
Affiliations: 1 Department of Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104 USA; E-Mail: email@example.com
2 Statistical and Biological Physics Sector, SISSA, Trieste, Italy; E-Mail: firstname.lastname@example.org
Abstract: We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration that use mean force biasing, including the adaptive biasing force algorithm and temperature acceleration. We then turn to methods that use bias potentials, including umbrella sampling and metadynamics. We next consider parallel tempering and replica-exchange methods. We conclude with a brief presentation of some combination methods.
Title: Free Energies from Non-Equilibrium MD Simulations
Author: Christoph Dellago1 and Gerhard Hummer2
Affiliation: 1 Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria; E-Mail:email@example.com
2 Dept. Theoretical Biophysics, Max Planck Institute of Biophysics, Frankfurt, Germany; E-Mail:gerhard.hummer(at)biophys.mpg.de
Abstract: As shown by Jarzynski, free energy difference between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crook fluctuation theorem, provide the basis for the computation of free energy differences from fast switching molecular dynamics simulations, in which an external parameter is changed at a finite rate driving the system away from equilibrium. In this article we first briefly review the Jarzynski identity and the Crooks theorem and then survey various algorithms building on these relations. We pay particular attention on the statistical efficiency of these methods and discuss practical issue arising in their implementation.
Title: Dynamical Non-Equilibrium Molecular Dynamics
Authors: Giovanni Ciccotti1 and Mauro Ferrario2
Affiliations: 1 Department of Physics, University of Roma “La Sapienza”, La Sapienza,00185 Roma, Italy; E-Mail: firstname.lastname@example.org
2 Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio E., 41125 Modena, Italy; E-Mail: email@example.com
Abstract: In this paper we discuss the dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD) which extends NEMD to time dependent situations, be them responses or relaxations. Based on the original Onsager regression hypothesis, implemented by Ciccotti, Jacucci and MacDonald [J. Stat. Phys. 21, 1 (1979)], the approach permits to separate the problem of the dynamical evolution from the problem of sampling the initial condition. D-NEMD provides the theoretical framework to compute time dependent macroscopic dynamical behaviors by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions generated from a suitable initial (equilibrium or non-equilibrium) distribution. We also discuss how to generate a large class of initial distributions. The same approach applies also to the calculation of the rate constants of activated processes. The range of problems treatable by this method is illustrated by applying it to a couple of hydrodynamic processes (the formation of convective cells and the relaxation of an interface between two immiscible liquids).
Title: Malliavin Weight Sampling: a Practical Guide
Authors: Patrick B. Warren1 and Rosalind J. Allen2
Affiliations: 1 Unilever R&D Port Sunlight , UK; E-Mail: firstname.lastname@example.org
2 School of Physics and Astronomy, University of Edinburgh, UK; E-Mail: email@example.com
Abstract: Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system’s dynamics. It applies to systems in or out of equilibrium, in steady state or time-dependent situations, and has applications in the calculation of response coefficients, parameter sensitivities, and Jacobian matrices for gradient-based parameter optimisation algorithms. The implementation of MWS has been described in the specific contexts of kinetic Monte Carlo and Brownian dynamics simulation algorithms. Here, we present a general theoretical framework for deriving the appropriate MWS update rule for any stochastic simulation algorithm. We also provide pedagogical information on its practical implementation.
Title: Characterization of Rare Events in Molecular Dynamics
Author: Carsten Hartmann1 , Ralf Banisch1, Marco Sarich1, Thomas Badowski1 and Christof Schuette1,2
Affiliation: 1 Institut für Mathematik, Freie Universitaet Berlin, Arnimallee 6, 14195 Berlin, Germany; E-Mails: firstname.lastname@example.org (CH); email@example.com (RB); firstname.lastname@example.org (MS); email@example.com (TB)
2Konrad-Zuse Zentrum, Takustraße 7, 14195 Berlin, Germany; E-Mail: firstname.lastname@example.org
Abstract: A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski’s equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.
Title: Markov State Models for Rare Events in Molecular Dynamics
Authors: Marco Sarich1, Ralf Banisch1, Carsten Hartmann1 and Christof Schuette1,2
Affiliation: 1 Institut für Mathematik, Freie Universitaet Berlin, Arnimallee 6, 14195 Berlin, Germany; E-Mails: email@example.com (MS); firstname.lastname@example.org (RB); email@example.com (CH)
2Konrad-Zuse Zentrum, Takustraße 7, 14195 Berlin, Germany; E-Mail: firstname.lastname@example.org
Abstract: Rare but important transition events between long lived states are a key feature of many molecular systems. In many cases the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible even on the most powerful computers because of the immensely long simulation timescales needed. Recently a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs), has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore we introduce a novel approach to using MSMs for the efficient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls.
Title: What is a Multiscale Problem in Molecular Dynamics ?
Author: Luigi Delle Site
Affiliation: Institut für Mathematik, Freie Universitaet Berlin, Arnimallee 6, 14195 Berlin, Germany; E-Mail: email@example.com
Abstract: In this work we make an attempt to answer the question of what a multiscale problem is in Molecular Dynamics (MD), or more in general in Molecular Simulation (MS). By introducing the criterion of separability of scales we identify three major (reference) categories of multiscale problems and discuss their corresponding computational strategies by making explicit examples of applications.
Title: Correlation Functions in Open QuantumClassical Systems
Authors: Chang-Yu Hsieh and Ray Kapral
Affiliations: 1 Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada; E-Mails: firstname.lastname@example.org (CH); email@example.com (RK)
Abstract: Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators, and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantumclassical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of quantumclassical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation, and connections to other approximate quantum dynamical methods.
Title: Approximating time dependent quantum statistical properties
Authors: Sara Bonella and Giovanni Ciccotti
Affiliations: Department of Physics, University of Roma “La Sapienza”, La Sapienza,00185 Roma, Italy, E-Mails: Sara.Bonella@roma1.infn.it (SB); firstname.lastname@example.org (GC)
Abstract: Computing quantum dynamics in condensed matter systems is an open challenge due to the exponential scaling of exact algorithms with the number of degrees of freedom. Current methods try to reduce the cost of the calculation using classical dynamics as the key ingredient of approximations of the quantum time evolution. Two main approaches exist, quantum classical and semi classical, but they suffer from various difficulties, in particular when trying to go beyond the classical approximation. It may then be useful to reconsider the problem focusing on statistical time dependent averages rather than directly on the dynamics. In this paper, we discuss a recently developed scheme for calculating symmetrized correlation functions. In this scheme, the full (complex time) evolution is broken into segments alternating thermal and real time propagation and the latter is reduced to classical dynamics via a linearization approximation. Increasing the number of segments systematically improves the result with respect to full classical dynamics, but at a cost which is still prohibitive. We conclude by discussing how this method may benefit from incorporating the idea of treating different degrees of freedom with a different degree of quantum approximation.
Title: Nonadiabatic Molecular Dynamics Based on Trajectories.
Authors: Felipe Franco de Carvalho, Marine E. F. Bouduban, Basile Curchod and Ivano Tavernelli
Affiliation: École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Suisse; E-Mails: email@example.com (FF), firstname.lastname@example.org (MB), email@example.com (BC); firstname.lastname@example.org (IT)
Abstract: Performing molecular dynamics in electronically excited states necessitates the inclusion of nonadiabatic effects to properly describe phenomena beyond the Born-Oppenheimer approximation. This article provides a survey of selected nonadiabatic methods based on quantum or classical trajectories. Among these techniques, trajectory surface hopping constitutes an interesting compromise between accuracy and efficiency for the simulation of medium to large scale molecular systems. It is however based on non-rigorous approximations that could compromise, in some cases, the correct description of the nonadiabatic dynamics under consideration, and hamper a systematic improvement of the theory. Herein we review and highlight the implication of these approximations based on the nonadiabatic Bohmian dynamics equations and on simple model systems.
Last update: 23 September 2013