A multiple time step algorithm compatible with a large number of distance classes and an arbitrary distance dependence of the time step size for the fast evaluation of nonbonded interactions in molecular simulations

Methods for Classical-Mechanical Molecular Simulation in Chemistry: Achievements, Limitations, Perspectives

More than a half century ago it became feasible to simulate, using classical-mechanical equations of motion, the dynamics of molecular systems on a computer. Since then classical-physical molecular simulation has become an integral part of chemical research. It is widely applied in a variety of branches of chemistry and has significantly contributed to the development of chemical knowledge. It offers understanding and interpretation of experimental results, semiquantitative predictions for measurable and nonmeasurable properties of substances, and allows the calculation of properties of molecular systems under conditions that are experimentally inaccessible. Yet, molecular simulation is built on a number of assumptions, approximations, and simplifications which limit its range of applicability and its accuracy. These concern the potential-energy function used, adequate sampling of the vast statistical-mechanical configurational space of a molecular system and the methods used to compute particular properties of chemical systems from statistical-mechanical ensembles. During the past half century various methodological ideas to improve the efficiency and accuracy of classical-physical molecular simulation have been proposed, investigated, evaluated, implemented in general simulation software or were abandoned. The latter because of fundamental flaws or, while being physically sound, computational inefficiency. Some of these methodological ideas are briefly reviewed and the most effective methods are highlighted. Limitations of classical-physical simulation are discussed and perspectives are sketched.

On the use of multiple-time-step algorithms to save computing effort in molecular dynamics simulations of proteins

Computer simulation of proteins in aqueous solution at the atomic level of resolution is still limited in time span and system size due to limited computing power available and thus employs a variety of time-saving techniques that trade some accuracy against computational effort. Examples of such time-saving techniques are the application of constraints to particular degrees of freedom or the use of a multiple-time-step (MTS) algorithm distinguishing between particular forces when integrating Newton's equations of motion. The application of two types of MTS algorithms to bond-stretching forces versus the remaining forces in molecular dynamics (MD) simulations of a protein in aqueous solution or of liquid water is investigated and the results in terms of total energy conservation and the influence on various other properties are compared to those of MD simulations of the same systems using bond-length, and for water bond-angle, constraints. At comparable computational effort, the use of bond-length constraints in proteins leads to better energy conservation and less distorted properties than the two MTS algorithms investigated.

On the Effect of the Various Assumptions and Approximations used in Molecular Simulations on the Properties of Bio-Molecular Systems: Overview and Perspective on Issues

Computer simulations of molecular systems enable structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic or supra-molecular level and plays an increasingly important role in chemistry, biology and physics. To interpret the results of such simulations appropriately, the degree of uncertainty and potential errors affecting the calculated properties must be considered. Uncertainty and errors arise from (1) assumptions underlying the molecular model, force field and simulation algorithms, (2) approximations implicit in the interatomic interaction function (force field), or when integrating the equations of motion, (3) the chosen values of the parameters that determine the accuracy of the approximations used, and (4) the nature of the system and the property of interest. In this overview, advantages and shortcomings of assumptions and approximations commonly used when simulating bio-molecular systems are considered. What the developers of bio-molecular force fields and simulation software can do to facilitate and broaden research involving bio-molecular simulations is also discussed.

Multiple-Time Step Ab Initio Molecular Dynamics Based on Two-Electron Integral Screening

A multiple-timestep ab initio molecular dynamics scheme based on varying the two-electron integral screening method used in Hartree-Fock or density functional theory calculations is presented. Although screening is motivated by numerical considerations, it is also related to separations in the length- and timescales characterizing forces in a molecular system: Loose thresholds are sufficient to describe fast motions over short distances, while tight thresholds may be employed for larger length scales and longer times, leading to a practical acceleration of ab initio molecular dynamics simulations. Standard screening approaches can lead, however, to significant discontinuities in (and inconsistencies between) the energy and gradient when the screening threshold is loose, making them inappropriate for use in dynamics. To remedy this problem, a consistent window-screening method that smooths these discontinuities is devised. Further algorithmic improvements reuse electronic-structure information within the dynamics step and enhance efficiency relative to a naı̈ve multiple-timestepping protocol. The resulting scheme is shown to realize meaningful reductions in the cost of Hartree-Fock and B3LYP simulations of a moderately large system, the protonated sarcosine/glycine dipeptide embedded in a 19-water cluster.

On searching in, sampling of, and dynamically moving through conformational space of biomolecular systems: A review

Methods to search for low-energy conformations, to generate a Boltzmann-weighted ensemble of configurations, or to generate classical-dynamical trajectories for molecular systems in the condensed liquid phase are briefly reviewed with an eye to application to biomolecular systems. After having chosen the degrees of freedom and method to generate molecular configurations, the efficiency of the search or sampling can be enhanced in various ways: (i) efficient calculation of the energy function and forces, (ii) application of a plethora of search enhancement techniques, (iii) use of a biasing potential energy term, and (iv) guiding the sampling using a reaction or transition pathway. The overview of the available methods should help the reader to choose the combination that is most suitable for the biomolecular system, degrees of freedom, interaction function, and molecular or thermodynamic properties of interest.