Computer Simulation of Molecular Dynamics: Methodology, Applications, and Perspectives in Chemistry By Wilfred E van Gunsteren * and Herman J. C. Berendsen * During recent decades it has become feasible to simulate the dynamics of molecular systems on a computer. The method of molecular dynamics (MD) solves Newton's equations of motion for a molecular system, which results in trajectories for all atoms in the system. From these atomic trajectories a variety of properties can be calculated. The aim of computer simulations of molecular systems is to compute macroscopic behavior from microscopic interactions. The main contributions a microscopic consideration can offer are (1) the understanding and (2) interpretation of experimental results, (3) semiquantitative estimates of experimental re- sults, and (4) the capability to interpolate or extrapolate experimental data into regions that are only difficultly accessible in the laboratory. One of the two basic problems in the field of molecular modeling and simulation is how to efficiently search the vast configuration space which is spanned by all possible molecular conformations for the global low (free) energy regions which will be populated by a molecular system in thermal equilibrium. The other basic problem is the derivation of a sufficiently accurate interaction energy function or force field for the molecular system of interest. An important part of the art of computer simulation is to choose the unavoidable assumptions, approximations and simplifications of the molecular model and computational procedure such that their contributions to the overall inaccuracy are of comparable size, without affecting significantly the property of interest. Methodology and some practical applications of computer simulation in the field of (bio)chemistry will be reviewed. 1. Introduction in terms of interactions at the atomic level. These three basic challenges are listed according to increasing difficulty. The Computational chemistry is a branch of chemistry that first challenge concerns prediction of which state of a system enjoys a growing interest from experimental chemists. In this has the lowest energy. The second challenge goes further; it discipline chemical problems are resolved by computational involves prediction of the relative (free) energy of different methods. A model of the real world is constructed, both states. The third challenge involves prediction of the dynam- measurable and unmeasurable properties are computed, and ic process of change of states. the former are compared with experimentally determined Chemical systems are generally too inhomogeneous and properties. This comparison validates or invalidates the complex to be treated by analytical theoretical methods. This model that is used. In the former case the model may be used is illustrated in Figure 1. The treatment of molecular systems to study relationships between model parameters and as- in the gas phase by quantum mechanical methods is straight- sumptions or to predict unknown or unmeasurable quanti- forward; if a classical statistical mechanical approximation ties. is permitted the problem becomes even trivial. This is due to Since chemistry concerns the study of properties of sub- the possibility of reducing the many-particle problem to a stances or molecular systems in terms of atoms, the basic few-particle one based on the low density of a system in the challenge facing computational chemistry is to describe or gas phase. In the crystalline solid state, treatment by quan- even predict tum mechanical or classical mechanical methods is made 1. the structure and stability of a molecular system, possible by a reduction of the many-particle problem to a 2. the (free) energy of different states of a molecular system, few-(quasi)particle problem based on symmetry properties 3. reaction processes within molecular systems of the solid state. Between these two extremes, that is, for liquids, macromolecules, solutions, amorphous solids, etc., one is faced with an essentially many-particle system. No simple reduction to a few degrees of freedom is possible, and [*I Prof. Dr. W. F. van Gunsteren"' Department of Physical Chemistry a full treatment of many degrees of freedom is required in University of Groningen order to adequately describe the properties of molecular sys- Nijenborgh 16, NL-9747 AG Groningen (The Netherlands) tems in the fluid-like state. This state of affairs has two direct Department of Physics and Aslronomy Free University consequences when treating fluid-like systems. De Boelelaan 1081, NL-1081 HV Amsterdam (The Netherlands) Prof. Dr. H. J. C. Berendsen 1. One has to resort to numerical simulation of the behavior Department of Physical Chemistry of the molecular system on a computer, which University of Groningen 2. produces a statistical ensemble of configurations repre- Nijenborgh 16, NL-9747 AG Groningen (The Netherlands) senting the state of the system. ['I Present address: Eidgenossische Technische Hochschule ETH Zentrum If one is only interested in static equilibrium properties, it Universititstrasse 6, CH-8092 (Switzerland) suffices to generate an ensemble of equilibrium states, which 992 0 VCH Verla~.s~e.~ellschu/tmhH, 0.6940 Weinheim, I990 0570-0833/90/0909-0992 8 3.50+ 2510 Anger,. Chem. lnr. Ed. Engl. 29 (I9901 992-I023 may lack any temporal correlations. To obtain dynamic and tion 3.4), algorithms for integration of the equations of mo- non-equilibrium properties dynamic simulation methods tion (Section 3.9, and finally equilibration and analysis of that produce trajectories in phase space are to be used. The molecular systems (Section 3.6). In Section 4, a number of connection between the microscopic behavior and macro- applications of computer simulation in chemistry are dis- scopic properties of the molecular system is governed by the laws of statistical mechanics. Figure I also shows the broad applicability of computer Flops [Floating Point Operatlons per second 1 simulation methods in chemistry. For any fluid-like, essen- teraflop tially many-particle system, it is the method of choice. slope: / lox per / / 6 years / / 1O'O / CRYSTALLINE LlOUlD STATE GAS PHASE 'o''l / gigaflop /,/NEC sxz SOLID STATE MACROMOLECULES w CRAY X-MP .'.FUJITSU VP200 QUANTUM still 0' CRAY-2 poss/ble possible ..'CY BER-205 MECHANICS impossible ,CRAY-1 CLASSICAL lo7 - AM 360/195 STAT1 STI CA L easy trivial MECHANICS REDUCTION t REDUCTION to few degrees essdntial to few of freedom by - ,,,any-particTparticles by system DILUTION SYMMETRY lo1 - Fig. 1. Classification of molecular systems. Systems in the shaded area are amenable to treatment by computer simulation. 30 Fig. 2. Development of computing power of the most powerful computers. The expanding role of computational methods in chemis- try has been fueled by the steady and rapid increase in com- puting power over the last 40 years, as is illustrated in Figure 2. The ratio of performance to price has increased an order cussed and examples are given. Finally, future developments of magnitude every 5-7 years, and there is no sign of any are considered in Section 5. For other relatively recent weakening in this trend. The introduction of massive paral- monographs on computer simulation the reader is referred lelism in computer architecture will easily maintain the pres- to the literature (see Refs. [l-91). ent growth rate. This means that more complex molecular systems may be simulated over longer periods of time, or that it will be possible to handle more complex interaction functions in the decades to come. 2. Computer Simulation of Molecular Systems The present article is concerned with computer sirnulation of molecular systems. In Section 2 the two basic problems 2.1. Two Basic Problems are formulated, a brief history of dynamic computer simula- tion is presented, the reliability of current simulations is dis- Two basic problems are encountered in the computer sim- cussed, and the usefulness of simulation studies is consid- ulation of fluid-like molecular systems: ered. Section 3 deals with simulation methodology: choice of 1. the size of the configurational space that is accessible to the computational model and atomic interaction function (Sec- molecular system, and tion 3.1), techniques to search configuration space for low 2. the accuracy of the molecular model or atomic interaction energy configurations (Section 3.2), boundary conditions function or force field that is used to model the molecular (Section 3.3), types of dynamical simulation methods (Sec- system. Wilfred E: van Gunsteren was born in 1947 in Wassenaar {The Netherlands). In 1968 he gained a B.Sc. in physics at the Free University of Amsterdam; in 1976 he was awarded a "Meester" in Law, andin 1976 a Ph.D. in nuclearphysics. After postdoc years at the University of Groningen (1976-1978) and at Harvard University (1978-1980) he was, from 1980 until 1987, senior lecturer and, until August 1990, Professor for Physical Chemistry at the University ofcroningen. Since September 1987 he has also been Professor of Computer Physics at the Free University Amsterdam. In 1990 he was offered and accepted a professorship of Computer Chemistry at the ETH Ziirich. He is holder of a gold medal for research of the Royal Netherlands Chemical Society; in 1988 he was Degussa Guest Professor at the University of Frankfurt. His main interests center on the physical fundamentals of the structure and function of biomolecules. Angew. Chem. Inr Ed. Engl. 29 (1990) 992-1023 993 Table 1. Models at different levels