Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamics Brownian dynamics Quantum simulations Some applications Appendix A: Computers and computer simulation Appendix B: Reduced units Appendix C: Calculation of forces and torques Appendix D: Fourier transforms Appendix E: The gear predictor - corrector Appendix F: Programs on microfiche Appendix G: Random numbers References Index.

Computer Simulation of Liquids

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

A smooth particle mesh Ewald method

Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case.

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A unified formulation of the constant temperature molecular dynamics methods

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.

/pdf/gromacs-fast-flexible-and-free-15aazpel5u.pdf

GROMACS: Fast, flexible, and free

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

/pdf/gromacs-4-algorithms-for-highly-efficient-load-balanced-and-16xnd83poh.pdf

GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation

Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble at 25 °C and 1 atm using six of the simpler intermolecular potential functions for the water dimer: Bernal–Fowler (BF), SPC, ST2, TIPS2, TIP3P, and TIP4P. Comparisons are made with experimental thermodynamic and structural data including the recent neutron diffraction results of Thiessen and Narten. The computed densities and potential energies are in reasonable accord with experiment except for the original BF model, which yields an 18% overestimate of the density and poor structural results. The TIPS2 and TIP4P potentials yield oxygen–oxygen partial structure functions in good agreement with the neutron diffraction results. The accord with the experimental OH and HH partial structure functions is poorer; however, the computed results for these functions are similar for all the potential functions. Consequently, the discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons are also made for self‐diffusion coefficients obtained from molecular dynamics simulations. Overall, the SPC, ST2, TIPS2, and TIP4P models give reasonable structural and thermodynamic descriptions of liquid water and they should be useful in simulations of aqueous solutions. The simplicity of the SPC, TIPS2, and TIP4P functions is also attractive from a computational standpoint.

Comparison of simple potential functions for simulating liquid water

We present a molecular model for studying the prototypical ferric–ferrous electron transfer process in liquid water, and we discuss its structural implications. Treatment of the nonequilibrium dynamics will be the subject of future work. The elementary constituents in the model are classical water molecules, classical ferric ions (i.e., Fe3+ particles), and a quantal electron. Pair potentials and pseudopotentials describing the interactions between these constituents are presented. These interactions lead to ligand structures of the ferric and ferrous ions that are in good agreement with those observed in nature. The validity of the tight binding model is examined. With umbrella sampling, we have computed the diabatic free energy of activation for electron transfer. The number obtained, roughly 20 kcal/mol, is in reasonable accord with the aqueous ferric–ferrous transfer activation energy of about 15 to 20 kcal/mol estimated from experiment. The Marcus relation for intersecting parabolic diabatic free ene...

Molecular model for aqueous ferrous–ferric electron transfer

The effect of changes in temperature and density on the structure of water has been studied by molecular dynamics using the analytical potential of Matsuoka, Clementi, and Yoshimine. Significant structural changes are found to occur, particularly at high density. Implications for the interpretation of neutron scattering experiments are discussed.

Molecular dynamics studies of the structure of water at high temperatures and density

The elastic constants of a classical nearest-neighbor Lennard-Jones solid are evaluated with the use of molecular-dynamics calculations in order to make comparisons with similar quantities derived from Monte Carlo calculations. Following Parrinello and Rahman, we use both strain fluctuations in the ($p,H,N$) ensemble and uniaxial loading to obtain the adiabatic elastic compliances and hence the elastic constants. While there is broad agreement between the three methods, Monte Carlo evaluation seems to be the most efficient procedure. The relationship between the elastic constants of the fcc and hcp solids is also discussed.

Second-order elastic constants for the Lennard-Jones solid

Molecular dynamics (MD) simulations were performed in order to investigate the molecular origin of the nuclear quadrupole relaxation mechanism for Li+, Na+, and Cl− ions in dilute aqueous solution. Different boundary conditions were investigated in the simulations, but neither the boundary conditions nor the system size have any significant effect on the different time correlation functions (tcf:s) calculated. It is found that the field gradient tcf, determining the NMR relaxation rate for these ions, is almost completely due to the water molecules in the first shell. The calculated field gradient tcf:s show a complex time‐dependence not describable with a mono‐exponential decay. The very rapid decay shown by the field gradient tcf for all three ions can partly be attributed to a correlated water motion in the first hydration shell. The relaxation rates obtained from the simulations are in excellent agreement with experimental data for Na+ and Cl−, while the Li+ relaxation rate is less well produced.

Molecular dynamic simulation of quadrupole relaxation of atomic ions in aqueous solution

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