Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes
TL;DR: In this paper, a numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated, and the relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration.
About: This article is published in Journal of Computational Physics.The article was published on 1977-03-01 and is currently open access. It has received 18394 citations till now. The article focuses on the topics: Generalized coordinates & Holonomic constraints.
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TL;DR: In this paper, a method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling, which can be easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints.
Abstract: In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath
25,256 citations
TL;DR: It is demonstrated that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N), which is comparable to that of a simple truncation method of 10 A or less.
Abstract: The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less
17,897 citations
TL;DR: A new implementation of the molecular simulation toolkit GROMACS is presented which now both achieves extremely high performance on single processors from algorithmic optimizations and hand-coded routines and simultaneously scales very well on parallel machines.
Abstract: Molecular simulation is an extremely useful, but computationally very expensive tool for studies of chemical and biomolecular systems Here, we present a new implementation of our molecular simulation toolkit GROMACS which now both achieves extremely high performance on single processors from algorithmic optimizations and hand-coded routines and simultaneously scales very well on parallel machines The code encompasses a minimal-communication domain decomposition algorithm, full dynamic load balancing, a state-of-the-art parallel constraint solver, and efficient virtual site algorithms that allow removal of hydrogen atom degrees of freedom to enable integration time steps up to 5 fs for atomistic simulations also in parallel To improve the scaling properties of the common particle mesh Ewald electrostatics algorithms, we have in addition used a Multiple-Program, Multiple-Data approach, with separate node domains responsible for direct and reciprocal space interactions Not only does this combination of a
14,032 citations
TL;DR: The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in solution and in crystals.
Abstract: New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent−solvent, solvent−solute, and solute−solute interactions. Optimization of the internal parameters used experimental gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the atomic charges, were determined by fitting ab initio interaction energies and geometries of complexes between water and model compounds that represented the backbone and the various side chains. In addition, dipole moments, experimental heats and free energies of vaporization, solvation and sublimation, molecular volume...
13,164 citations
TL;DR: The software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s is described, which is a very fast program for molecular dynamics simulation.
Abstract: This article describes the software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for molecular dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addition, it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequilibrium dynamics and free energy determinations are incorporated. Interfaces with popular quantum-chemical packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and analysis programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.
13,116 citations
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TL;DR: In this article, the equilibrium properties of a system of 864 particles interacting through a Lennard-Jones potential have been integrated for various values of the temperature and density, relative, generally, to a fluid state.
Abstract: The equation of motion of a system of 864 particles interacting through a Lennard-Jones potential has been integrated for various values of the temperature and density, relative, generally, to a fluid state. The equilibrium properties have been calculated and are shown to agree very well with the corresponding properties of argon. It is concluded that, to a good approximation, the equilibrium state of argon can be described through a two-body potential.
7,564 citations
TL;DR: In this paper, a four-charge model for each molecule and a modification of the prior ''BNS'' interaction was proposed to improve the fidelity of the molecular dynamics simulation, leading to a density maximum near 27°C for the liquid in coexistence with its vapor and to molecular distribution functions in better agreement with x-ray scattering experiments.
Abstract: Molecular dynamics calculations on a classical model for liquid water have been carried out at mass density 1 g/cm3 and at four temperatures. The effective pair potential employed is based on a four‐charge model for each molecule and represents a modification of the prior ``BNS'' interaction. Results for molecular structure and thermodynamic properties indicate that the modification improves the fidelity of the molecular dynamics simulation. In particular, the present version leads to a density maximum near 27°C for the liquid in coexistence with its vapor and to molecular distribution functions in better agreement with x‐ray scattering experiments.
1,551 citations
TL;DR: In this paper, a sample of water, consisting of 216 rigid molecules at mass density 1 gm/cm3, has been simulated by computer using the molecular dynamics technique, subject to an effective pair potential that incorporates the principal structural effects of manybody interactions in real water.
Abstract: A sample of water, consisting of 216 rigid molecules at mass density 1 gm/cm3, has been simulated by computer using the molecular dynamics technique. The system evolves in time by the laws of classical dynamics, subject to an effective pair potential that incorporates the principal structural effects of many‐body interactions in real water. Both static structural properties and the kinetic behavior have been examined in considerable detail for a dynamics ``run'' at nominal temperature 34.3°C. In those few cases where direct comparisons with experiment can be made, agreement is moderately good; a simple energy rescaling of the potential (using the factor 1.06) however improves the closeness of agreement considerably. A sequence of stereoscopic pictures of the system's intermediate configurations reinforces conclusions inferred from the various ``run'' averages: (a) The liquid structure consists of a highly strained random hydrogen‐bond network which bears little structural resemblance to known aqueous crys...
1,192 citations
TL;DR: The self-diffusion coefficient of n-butane is approximately 6.0 × 10−5 cm2/s and the corresponding velocity autocorrelation function displays practically no cage effect, differing markedly from argon and other simple fluids.
578 citations
TL;DR: In this paper, the authors used the molecular-dynamic method to simulate a fluid of 500 rigid diatomic homo-nuclear molecules interacting by a double Lennard-Jones potential.
Abstract: The molecular-dynamic method was used to simulate a fluid of 500 rigid diatomic homo-nuclear molecules interacting by a double Lennard-Jones potential. The equilibrium and time-dependent properties are calculated in the liquid phase. The computed pressure and the internal energy agree quantitatively to a few percent with experimental values for nitrogen. The reorientational and the velocity of the center-of-gravity self-correlation functions are also discussed. The memory-function formalism and the extended-diffusion models are used to interpret the reorientational self-correlation functions. The analysis reveals that these self-correlation functions have an exponential behavior for times larger than 5 \ifmmode\times\else\texttimes\fi{} 1${0}^{\ensuremath{-}13}$ sec. In this model, considering present computing precision, there is no observable hydrodynamic-type relaxation in the reorientational self-correlation functions.
222 citations