Escaping free-energy minima
01 Oct 2002-Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences)-Vol. 99, Iss: 20, pp 12562-12566
TL;DR: A powerful method for exploring the properties of the multidimensional free energy surfaces of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates is introduced.
Abstract: We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the FES, allowing the efficient exploration and accurate determination of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.
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TL;DR: The implementation of various DFT functionals and many‐body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures are discussed.
Abstract: During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science—promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008
2,364 citations
TL;DR: This work presents PLUMED 2 here—a complete rewrite of the code in an object-oriented programming language (C++), which introduces greater flexibility and greater modularity, which both extends its core capabilities and makes it far easier to add new methods and CVs.
2,256 citations
TL;DR: A method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias and the formalism provides a unified description which has metadynamics and canonical sampling as limiting cases.
Abstract: We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape.
2,174 citations
TL;DR: To model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region and an MM treatment for the surroundings, enabling the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.
Abstract: Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.
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TL;DR: The main capabilities of cp2k are summarized, and with recent applications the science cp2K has enabled in the field of atomistic simulation are illustrated.
Abstract: cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation.
2,114 citations
References
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
41,772 citations
TL;DR: A new Monte Carlo algorithm is presented that permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions.
Abstract: We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions. It should also be useful for the study of complex systems with a rough energy landscape.
2,639 citations
TL;DR: In this article, a general method for accelerating the molecular-dynamics (MD) simulation of infrequent events in solids is derived, and the diffusion mechanism of a 10-atom Ag cluster on the Ag(111) surface using a $220\ensuremath{\mu}\mathrm{s}$ hyper-MD simulation.
Abstract: I derive a general method for accelerating the molecular-dynamics (MD) simulation of infrequent events in solids. A bias potential ( $\ensuremath{\Delta}{V}_{b}$) raises the energy in regions other than the transition states between potential basins. Transitions occur at an accelerated rate and the elapsed time becomes a statistical property of the system. $\ensuremath{\Delta}{V}_{b}$ can be constructed without knowing the location of the transition states and implementation requires only first derivatives. I examine the diffusion mechanisms of a 10-atom Ag cluster on the Ag(111) surface using a $220\ensuremath{\mu}\mathrm{s}$ hyper-MD simulation.
887 citations
TL;DR: In this article, a computationally efficient molecular dynamics method for estimating the rates of rare events that occur by activated processes is described, where the system is constrained at bottleneck regions on a general many-body reaction coordinate in order to generate a biased configurational distribution.
835 citations
TL;DR: In this article, the blue-moon ensemble method was used to compute the potential of mean force and transmission coefficient of a given reaction coordinate in the case of an arbitrary reaction coordinate.
Abstract: Activated processes can be studied in the molecular dynamics (MD) approach by imposing a mechanical constraint on the corresponding reaction coordinate and by performing a kind of thermodynamic integration. The blue-moon ensemble method provides us with the correct algorithm for computing the potential of mean force and the transmission coefficient. Here we show a procedure for obtaining the mean force directly from the average force of constraint and a geometric correction term which is easy to compute in MD simulations. Previous work on the same problem will be also discussed.
724 citations