Molecular dynamics (MD) is a form of computer simulation wherein atoms and molecules are allowed to interact for a period of time under known laws of physics, giving a view of the motion of the atoms. Because molecular systems generally consist of a vast number of particles, it is impossible to find the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. It represents an interface between laboratory experiments and theory, and can be understood as a "virtual experiment". In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. ... It has been suggested that simulation software be merged into this article or section. ... Complex systems have a number of properties, some of which are listed below. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Virtual reality (VR) is a technology which allows a user to interact with a computer-simulated environment, be it a real or imagined one. ...

Example of a molecular dynamics simulation in a simple system: deposition of a single Cu atom on a Cu (001) surface. Each circle illustrates the position of a single atom; note that the actual atomic interactions used in the simulations are more complex than those of hard spheres.

Although it has been known since Boltzmann's discoveries in the 19th century that matter consists of interacting particles in motion, many people still think of molecules as rigid museum models. Richard Feynman said in 1963 that "everything that living things do can be understood in terms of the jiggling and wiggling of atoms." ^[1] One of MD's key contributions is creating awareness that molecules like proteins and DNA are machines in motion. ^[2] MD probes the relationship between molecular structure, movement and function. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... CU may stand for: Cervecerias Unidas, SA, NYSE ticker symbol Champaign-Urbana Metropolitan Area Christian Union, a political party in the Netherlands College University, an animated Internet-based comedy series Control unit credit union CU (Powerline), a HVDC-powerline in the USA Cuba, ISO 3166, FIPS Pub 10-4 and... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... CU may stand for: Cervecerias Unidas, SA, NYSE ticker symbol Champaign-Urbana Metropolitan Area Christian Union, a political party in the Netherlands College University, an animated Internet-based comedy series Control unit credit union CU (Powerline), a HVDC-powerline in the USA Cuba, ISO 3166, FIPS Pub 10-4 and... Examples of directions Miller indices are a notation used to describe lattice planes and directions in a crystal. ... Surface science is the study of physical and chemical phenomena that occur at the interface of two phases, including solid-liquid interfaces, solid-gas interfaces, solid-vacuum interfaces, and liquid-gas interfaces. ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... Ludwig Eduard Boltzmann (Vienna, Austrian Empire, February 20, 1844 – Duino near Trieste, September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. ... Richard Phillips Feynman (May 11, 1918 – February 15, 1988; IPA: ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ...

Molecular dynamics is a multidisciplinary method. Its laws and theories stem from mathematics, physics, and chemistry, and it employs algorithms from computer science and information theory. It was originally conceived within theoretical physics in the late 1950's^[3], but is applied today mostly in materials science and biomolecules. In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ... A bundle of optical fiber. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... ...

Before it became possible to simulate molecular dynamics with computers, some undertook the hard work of trying it with physical models such as macroscopic spheres. The idea was to arrange them to replicate the properties of a liquid. J.D. Bernal said, in 1962: "... I took a number of rubber balls and stuck them together with rods of a selection of different lengths ranging from 2.75 to 4 inches. I tried to do this in the first place as casually as possible, working in my own office, being interrupted every five minutes or so and not remembering what I had done before the interruption." ^[4] Fortunately, now computers keep track of bonds during a simulation. John Desmond Bernal (1901-1971) was an Irish-born scientist (from Nenagh, County Tipperary), known for pioneering X-ray crystallography. ...

Molecular dynamics is a specialized discipline of molecular modeling and computer simulation based on statistical mechanics; the main justification of the MD method is that statistical ensemble averages are equal to time averages of the system, known as the ergodic hypothesis. MD has also been termed "statistical mechanics by numbers" and "Laplace's vision of Newtonian mechanics" of predicting the future by animating nature's forces ^{[5] [6]} and allowing insight into molecular motion on an atomic scale. However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated entirely. Furthermore, current potential functions are, in many cases, not sufficiently accurate to reproduce the dynamics of molecular systems. Nevertheless, molecular dynamics techniques allow detailed time and space resolution into representative behavior in phase space. Molecular modelling is a collection of techniques to model or mimic the behaviour of molecules. ... It has been suggested that simulation software be merged into this article or section. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... In physics, a statistical ensemble is a very large set of similar systems, considered all at once. ... In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i. ... Pierre-Simon Laplace Pierre-Simon Laplace (March 23, 1749 – March 5, 1827) was a French mathematician and astronomer, the discoverer of the Laplace transform and Laplaces equation. ... In numerical analysis, the condition number associated with a numerical problem is a measure of that quantitys amenability to digital computation, that is, how well-posed the problem is. ... Numerical Integration with the Monte Carlo method: Nodes are random equally distributed. ... Phase space of a dynamical system with focal stability. ...

Areas of Application

There is a significant difference between the focus and methods used by chemists and physicists, and this is reflected in differences in the jargon used by the different fields. In chemistry and biophysics, the interaction between the particles is either described by a "force field" (classical MD), a quantum chemical model, or a mix between the two. These terms are not used in physics, where the interactions are usually described by the name of the theory or approximation being used and called the potential energy, or just "potential". A force field is used to minimize the bond stretching energy of this ethane molecule. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ...

Beginning in theoretical physics, the method of MD gained popularity in materials science and since the 1970s also in biochemistry and biophysics. In chemistry, MD serves as an important tool in protein structure determination and refinement using experimental tools such as X-ray crystallography and NMR. It has also been applied with limited success as a method of refining protein structure predictions. In physics, MD is used to examine the dynamics of atomic-level phenomena that cannot be observed directly, such as thin film growth and ion-subplantation. It is also used to examine the physical properties of nanotechnological devices that have not or cannot yet be created. This article needs additional references or sources for verification. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... The 1970s decade refers to the years from 1970 to 1979, also called The Seventies. ... Biochemistry is the study of the chemical processes and transformations in living organisms. ... Biophysics (also biological physics) is an interdisciplinary science that applies the theories and methods of physics, to questions of biology. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... X-ray crystallography, also known as single-crystal X-ray diffraction, is the oldest and most common crystallographic method for determining the structure of molecules. ... NMR may refer to: Nuclear magnetic resonance, a phenomenon involving the interaction of atomic nuclei and external magnetic fields Nielsen Media Research, a U.S. company which measures TV, radio and newspaper audiences This is a disambiguation page — a navigational aid which lists other pages that might otherwise share... Protein structure prediction is one of the most significant technologies pursued by computational structural biology and theoretical chemistry. ... Buckminsterfullerene C60, also known as the buckyball, is the simplest of the carbon structures known as fullerenes. ...

In applied mathematics and theoretical physics, molecular dynamics is a part of the research realm of dynamical systems, ergodic theory and statistical mechanics in general. The concepts of energy conservation and molecular entropy come from thermodynamics. Some techniques to calculate conformational entropy such as principal components analysis come from information theory. Mathematical techniques such as the transfer operator become applicable when MD is seen as a Markov chain. Also, there is a large community of mathematicians working on volume preserving, symplectic integrators for more computationally efficient MD simulations. In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Conformational entropy is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular state in solution. ... It has been suggested that this article or section be merged with Proper orthogonal decomposition. ... This article or section is in need of attention from an expert on the subject. ... In mathematics, the transfer operator encodes information about an iterated map and is frequently used to study the behavior of dynamical systems, statistical mechanics, quantum chaos and fractals. ... In mathematics, a Markov chain, named after Andrey Markov, is a discrete-time stochastic process with the Markov property. ... In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics. ...

MD can also be seen as a special case of the discrete element method (DEM) in which the particles have spherical shape (e.g. with the size of their van der Waals radii.) Some authors in the DEM community employ the term MD rather loosely, even when their simulations do not model actual molecules. The term discrete element method (DEM) is a family of numerical methods for computing the motion of a large number of particles like molecules or grains of sand. ... The van der Waals radius of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. ...

Design Constraints

Design of a molecular dynamics simulation should account for the available computational power. Simulation size (n=number of particles), timestep and total time duration must be selected so that the calculation can finish within a reasonable time period. However, the simulations should be long enough to be relevant to the time scales of the natural processes being studied. Most scientific publications about the dynamics of proteins and DNA use data from simulations spanning nanoseconds (1E-9 s) to microseconds (1E-6 s). To obtain these simulations, several CPU-days to CPU-years are needed. Parallel algorithms allow the load to be distributed among CPUs; an example is the spatial decomposition in LAMMPS. The pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). ... To help compare orders of magnitude of different times this page lists times between 10-9 seconds and 10-8 seconds (1 nanosecond and 10 nanoseconds) See also times of other orders of magnitude. ... To help compare orders of magnitude of different times this page lists times between 10-6 seconds and 10-5 seconds (1. ... LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is a molecular dynamics program from Sandia National Laboratories. ...

During a classical MD simulation, the most CPU intensive task is the evaluation of the potential (force field) as a function of the particles' internal coordinates. Within that energy evaluation, the most expensive one is the non-bonded or non-covalent part. In Big O notation, common molecular dynamics simulations scale by O(n²) if all pair-wise electrostatic and van der Waals interactions must be accounted for explicitly. This computational cost can be reduced by employing electrostatics methods such as Particle Mesh Ewald ( O(nlog(n)) ) or good spherical cutoff techniques ( O(n) ). A force field is used to minimize the bond stretching energy of this ethane molecule. ... Big O notation is often used to describe how the size of the input data affects an algorithms running time. ... To analyze an algorithm is to determine the amount of resources (such as time and storage) necessary to execute it. ... Electrostatics is the branch of physics that deals with the force exerted by a static (i. ... The title given to this article is incorrect due to technical limitations. ... Ewald summation is a method for computing the interaction energies of crystals, particularly electrostatic energies. ...

Another factor that impacts total CPU time required by a simulation is the size of the integration timestep. This is the time length between evaluations of the potential. The timestep must be chosen small enough to avoid discretization errors (i.e. smaller than the fastest vibrational frequency in the system). Typical timesteps for classical MD are in the order of 1 femtosecond (1E-15 s). This value may be extended by using algorithms such as SHAKE, which fix the vibrations of the fastest atoms (e.g. hydrogens) into place. Multiple time scale methods have also been developed, which allow for extended times between updates of slower long-range forces.^[7][8][9] Discretization concerns the process of transferring continuous models and equations into discrete counterparts. ... To help compare orders of magnitude of different times this page lists times between 10−15 seconds and 10−12 seconds (1 femtosecond and 1 picosecond). ... In mechanics, a constraint algorithm is a method for satisfying constraints for bodies that obey Newtons equations of motion. ...

For simulating molecules in a solvent, a choice should be made between explicit solvent and implicit solvent. Explicit solvent particles (such as the TIP3P and SPC/E water models) must be calculated expensively by the force field, while implicit solvents use a mean-field approach. The impact of explicit solvents on CPU-time can be 10-fold or more. But the granularity and viscosity of explicit solvent is essential to reproduce certain properties of the solute molecules. Implicit solvation (sometimes known as continuum solvation) is a method of representing solvent in molecular dynamics simulations and molecular mechanics (e. ... In computational chemistry, classical water models are used for the simulation of liquid water and aqueous solutions. ...

In all kinds of molecular dynamics simulations, the simulation box size must be large enough to avoid boundary condition artifacts. Boundary conditions are often treated by choosing fixed values at the edges, or by employing periodic boundary conditions in which one side of the simulation loops back to the opposite side, mimicking a bulk phase. In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ...

Physical Principles

Microcanonical ensemble (NVE)

In the microcanonical, or NVE ensemble, the system is isolated from changes in moles (N), volume (V) and energy (E). It corresponds to an adiabatic process with no heat exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved. For a system of N particles with coordinates X and velocities V, the following pair of first order differential equations may be written in Newton's notation as In thermodynamics, an adiabatic process or an isocaloric process is a process in which no heat is transferred to or from the working fluid. ... Newtons notation for differentiation involved placing a dash/dot over the function name, which he termed the fluxion. ...

The potential energy function U(X) of the system is a function of the particle coordinates X. It is referred to simply as the "potential" in Physics, or the "force field" in Chemistry. The first equation comes from Newton's laws; the force F acting on each particle in the system can be calculated as the negative gradient of U(X). Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ...

For every timestep, each particle's position X and velocity V may be integrated with a symplectic method such as Verlet. The time evolution of X and V is called a trajectory. Given the initial positions (e.g. from theoretical knowledge) and velocities (e.g. randomized Gaussian), we can calculate all future (or past) positions and velocities. In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics. ... Verlet integration is a method for calculating the trajectories of particles in molecular dynamics simulations. ...

One frequent source of confusion is the meaning of temperature in MD. Commonly we have experience with macroscopic temperatures, which involve a huge number of particles. But temperature is a statistical quantity. If there is a large enough number of atoms, statistical temperature can be estimated from the instantaneous temperature, which is found by equating the kinetic energy of the system to nk_BT/2 where n is the number of degrees of freedom of the system. This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ...

A temperature-related phenomenon arises due to the small number of atoms that are used in MD simulations. For example, consider simulating the growth of a copper film starting with a substrate containing 500 atoms and a deposition energy of 100 eV. In the real world, the 100 eV from the deposited atom would rapidly be transported through and shared among a large number of atoms (10¹⁰ or more) with no big change in temperature. When there are only 500 atoms, however, the substrate is almost immediately vaporized by the deposition. Something similar happens in biophysical simulations. The temperature of the system in NVE is naturally raised when macromolecules such as proteins undergo exothermic conformational changes and binding.

Canonical ensemble (NVT)

In the canonical ensemble, moles (N), volume (V) and temperature (T) are conserved. It is also sometimes called constant temperature molecular dynamics (CTMD). In NVT, the energy of endothermic and exothermic processes is exchanged with a thermostat. A canonical ensemble in statistical mechanics is an ensemble of dynamically similar systems, each of which can share its energy with a large heat reservoir, or heat bath. ...

A variety of thermostat methods are required to add and remove energy from the boundaries of an MD system in a realistic way, approximating the canonical ensemble. Popular techniques to control temperature include the Nosé-Hoover thermostat and Langevin dynamics. A canonical ensemble in statistical mechanics is an ensemble of dynamically similar systems, each of which can share its energy with a large heat reservoir, or heat bath. ... Langevin dynamics is an approach to mechanics using simplified models and using stochastic differential equations to account for omitted degrees of freedom. ...

Isothermal-Isobaric (NPT) ensemble

In the isothermal-isobaric ensemble, moles (N), pressure (P) and temperature (T) are conserved. In addition to a thermostat, a barostat is needed. It corresponds most closely to laboratory conditions with a flask open to ambient temperature and pressure. The isothermal-isobaric ensemble is an statistical mechanical ensemble where the partition function is given as The characteristic state function of this ensemble is the Gibbs free energy since Categories: | ...

In the simulation of biological membranes, isotropic pressure control is not appropriate. For lipid bilayers, pressure control occurs under constant membrane area (NPAT) or constant surface tension "gamma" (NPγT). Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ...

Generalized ensembles

The replica exchange method is a generalized ensemble. It was originally created to deal with the slow dynamics of disordered spin systems. It is also called parallel tempering. The replica exchange MD (REMD) formulation ^[10] tries to overcome the multiple-minima problem by exchanging the temperature of non-interacting replicas of the system running at several temperatures.

Potentials in MD simulations

A molecular dynamics simulation requires the definition of a potential function, or a description of the terms by which the particles in the simulation will interact. In chemistry and biology this is usually referred to as a force field. Potentials may be defined at many levels of physical accuracy; those most commonly used in chemistry are based on molecular mechanics and embody a classical treatment of particle-particle interactions that can reproduce structural and conformational changes but usually cannot reproduce chemical reactions. When finer levels of detail are required, potentials based on quantum mechanics are used; some techniques attempt to create hybrid classical/quantum potentials where the bulk of the system is treated classically but a small region is treated as a quantum system, usually undergoing a chemical transformation. The term potential function can mean more than one thing. ... A force field is used to minimize the bond stretching energy of this ethane molecule. ... The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ... Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... In molecular biology, a protein may change its shape in order to undertake a new function; each possible shape is called a conformation, and a transition between them is called a conformational change. ... Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ... Fig. ...

Empirical potentials

Empirical potentials used in chemistry are frequently called force fields, while those used in materials physics are called just empirical or analytical potentials.

Most force fields in chemistry are empirical and consist of a summation of bonded forces associated with chemical bonds, bond angles, and bond dihedrals, and non-bonded forces associated with van der Waals forces and electrostatic charge. Empirical potentials represent quantum-mechanical effects in a limited way through ad-hoc functional approximations. These potentials contain free parameters such as atomic charge, van der Waals parameters reflecting estimates of atomic radius, and equilibrium bond length, angle, and dihedral; these are obtained by fitting against detailed electronic calculations (quantum chemical simulations) or experimental physical properties such as elastic constants, lattice parameters and spectroscopic measurements. A force field is used to minimize the bond stretching energy of this ethane molecule. ... A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ... In Aerospace engineering, the dihedral is the angle that the two wings make with each other. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Johannes Diderik van der Waals, a 1910 Nobel Prize winner, was responsible for a number of advances in physical chemistry which are named after him. ... In molecular geometry, bond length or bond distance is the distance between two bonded atoms in a molecule. ... Extremely high resolution spectrogram of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter. ...

Chemistry force fields commonly employ preset bonding arrangements (an exception being ab-initio dynamics), and thus are unable to model the process of chemical bond breaking and reactions explicitly. On the other hand, many of the potentials used in physics, such as those based on the bond order formalism can describe several different coordinations of a system and bond breaking. Examples of such potentials include the Brenner potential^[11] for hydrocarbons and its further developments for the C-Si-H and C-O-H systems. The ReaxFF potential^[12] can be considered a fully reactive hybrid between bond order potentials and chemistry force fields. Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. ... Bond order potentials are a class of empirical (analytical) potentials used e. ... Bond order potentials are a class of empirical (analytical) potentials used e. ... ReaxFF (for “reactive force field”) is a force field developed by Adri van Duin, William A. Goddard, III and co- workers at the California Institute of Technology. ...

The potential functions representing the non-bonded interactions are usually "pair potentials", in which the total potential energy of a system can be calculated from the sum of energy contributions from pairs of atoms. These non-bonded interactions, because they are nonlocal and involve at least weak interactions between every pair of particles in the system, are normally the bottleneck in the speed of MD simulations. In electrostatic interactions, solving the Poisson equation for complete systems is usually prohibitively slow; instead numerical approximations are used such as shifted cutoff radii, reaction field algorithms, particle mesh Ewald summation, or the newer Particle-Particle Particle Mesh (P3M). Poissons equation is the partial differential equation: Or alternately: or i. ... Ewald summation is a method for computing the interaction energies of periodic systems (e. ... Particle-Particle Particle Mesh (P3M) is a specilized hybrid algorithm in computing electrostatic potential among N point charges in computer simulations i. ...

An example of a calculated pair potential is the non-bonded Lennard-Jones potential (also known as the 6-12 potential), used for calculating van der Waals forces. Neutral atoms and molecules are subject to two distinct forces in the limit of large distance, and short distance: an attractive van der Waals force, or dispersion force, at long ranges, and a repulsion force, the result of overlapping electron orbitals, referred to as Pauli repulsion (from Pauli exclusion principle). ...

Another example is the Born (ionic) model of the ionic lattice. The first term in the next equation is Coulomb's law for a pair of ions, the second term is the short-range repulsion explained by Pauli's exclusion principle and the final term is the dispersion interaction term. Usually, a simulation only includes the dipolar term, although sometimes the quadrupolar term is included as well. Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ...

Empirical potentials can be subcategorized into pair potentials and many-body potentials. In many-body potentials, the potential energy cannot be found by a sum over pairs of atoms. For example, the Tersoff potential^[13], which was originally used to simulate carbon, silicon and germanium and has since been used for a wide range of other materials, involves a sum over groups of three atoms, with the angles between the atoms being an important factor in the potential. Other examples are the Embedded-Atom method (EAM)^[14] and the Tight-Binding Second Moment Approximation (TBSMA) potentials ^[15], where the electron density of states in the region of an atom is calculated from a sum of contributions from surrounding atoms, and the potential energy contribution is then a function of this sum. Bond order potentials are a class of empirical (analytical) potentials used e. ... General Name, Symbol, Number carbon, C, 6 Chemical series nonmetals Group, Period, Block 14, 2, p Appearance black (graphite) colorless (diamond) Standard atomic weight 12. ... General Name, Symbol, Number silicon, Si, 14 Chemical series metalloids Group, Period, Block 14, 3, p Appearance as coarse powder, dark grey with bluish tinge Standard atomic weight 28. ... General Name, Symbol, Number germanium, Ge, 32 Chemical series metalloids Group, Period, Block 14, 4, p Appearance grayish white Atomic mass 72. ...

Semi-empirical potentials

Semi-empirical potentials make use of the matrix representation from quantum mechanics. However, the values of the matrix elements are found through empirical formulae that estimate the degree of overlap of specific atomic orbitals. The matrix is then diagonalized to determine the occupancy of the different atomic orbitals, and empirical formulae are used once again to determine the energy contributions of the orbitals. Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. ...

There are a wide variety of semi-empirical potentials, known as tight-binding potentials, which vary according to the atoms being modeled.

Ab-initio methods

Ab-initio quantum-mechanical formula to calculate the potential energy of a system of atoms or molecules. Compared to classical potential function, which is represented by empirical functions, the properties of the system in ab-intio calculations are calculating the wave-functions for electrons moving around the nucleus of atoms. This calculation is usually made "locally", i.e., for nuclei in the close neighborhood of the reaction coordinate. Although various approximations may be used, these are based on theoretical considerations, not on empirical fitting. Ab-Initio produce a large amount of information that is not available from the empirical methods, such as density of states information. Of course, the computational price paid is high. A significant advantage of using ab-initio methods is the ability to study reactions that involved breakage or formation of covalent bonds, this would correspond to multiple electronic states. Classical molecular dynamics is unable to simulate breakage and formation of covalent bonds, However, in recent years techniques such as thermodynamic integration and ghost particles have been introduced to overcome these limitations. The success however remains limited. Ab Initio Software Corporation was founded in the mid 1990s by the former CEO, Sheryl Handler, and several other former employees of Thinking Machines Corporation, after the bankruptcy of that company. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. ... The nucleus (atomic nucleus) is the center of an atom. ... In chemistry, a reaction coordinate is an abstract one-dimensional coordinate system which represents progress along a reaction pathway. ...

A popular package for ab-initio molecular dynamics is the Car-Parrinello Molecular Dynamics (CPMD) package based on the density functional theory. The Car-Parrinello method in computational chemistry is a type of ab initio (first principles) molecular dynamics, usually employing periodic boundary conditions, planewave basis sets, and DFT. In slight contrast to Born-Oppenheimer molecular dynamics wherein the nuclear (ions) and electronic degrees of freedom are separated and conventional matrix diagonalization... Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ...

Hybrid QM/MM

QM (quantum-mechanical) methods are very powerful however they are computationally expensive, while the MM (classical or molecular mechanics) methods are fast but suffer from several limitations (require extensive parameterization; energy estimates obtained are not very accurate; cannot be used to simulate reactions where covalent bonds are broken/formed; and are limited in their abilities for providing accurate details regarding the chemical environment). A new class of method has emerged that combines the good points of QM (accuracy) and MM (speed) calculations. These methods are known as mixed or hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM). The methodology for such techniques was introduced by Warshel and coworkers. In the recent years have been pioneered by several groups including: Arieh Warshel (University of Southern California), Weitao Yang (Duke University), Sharon Hammes-Schiffer (The Pennsylvania State University), Donald Truhlar and Jiali Gao (University of Minnesota) and Kenneth Merz (University of Florida). The Trojan Shrine, better known as Tommy Trojan located in the center of University of Southern California campus. ... Duke University is a private coeducational research university located in Durham, North Carolina, USA. Founded by Methodists and Quakers in the present-day town of Trinity in 1838, the school moved to Durham in 1892. ... The Pennsylvania State University The Pennsylvania State University (commonly known as Penn State) is a state-related land-grant university in Pennsylvania, with over 80,000 students at 24 campuses throughout the state. ... Washington Avenue Bridge at night The University of Minnesota, Twin Cities, almost always abbreviated U of M, and sometimes referred to as The U by locals, is the oldest and largest part of the University of Minnesota system. ... The University of Florida (commonly referred to as Florida or UF) is a public land-grant, space-grant, research university located in Gainesville, Florida. ...

The most important advantage of hybrid QM/MM methods is the speed. The cost of doing classical molecular dynamics (MM) in the most straight forward case scales O(n²), where N is the number of atoms in the system. This is mainly due to electrostatic interactions term (every particle interacts with everything else). However, use of cutoff radius, periodic pair-list updates and more recently the variations of the particle-mesh Ewald's (PME) method has reduced this between O(N) to O(n²). In other words, if a system with twice many atoms is simulated then it would take between twice to four times as much computing power. On the other hand the simplest ab-initio calculations typically scale O(n³) or worse (Restricted Hartree-Fock calculations have been suggested to scale ~O(n^2.7)). To overcome the limitation, a small part of the system is treated quantum-mechanically (typically active-site of an enzyme) and the remaining system is treated classically. In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...

In more sophisticated implementations, QM/MM methods exist to treat both light nuclei susceptible to quantum effects (such as hydrogens) and electronic states. This allows generation of hydrogen wave-functions (similar to electronic wave-functions). This methodology has been useful in investigating phenomenon such as hydrogen tunneling. One example where QM/MM methods have provided new discoveries is the calculation of hydride transfer in the enzyme liver alcohol dehydrogenase. In this case, tunneling is important for the hydrogen, as it determines the reaction rate. ^[16] The word tunneling (also spelled tunnelling) has more than one meaning. ...

Coarse-graining and reduced representations

At the other end of the detail scale are coarse-grained and lattice models. Instead of explicitly representing every atom of the system, one uses "pseudo-atoms" to represent groups of atoms. MD simulations on very large systems may require such large computer resources that they cannot easily be studied by traditional all-atom methods. Similarly, simulations of processes on long timescales (beyond about 1 microsecond) are prohibitively expensive, because they require so many timesteps. In these cases, one can sometimes tackle the problem by using reduced representations, which are also called coarse-grained models.

Examples for coarse graining (CG) methods are discontinuous molecular dynamics (CG-DMD) ^[17] and Go-models ^[18]. Coarse-graining is done sometimes taking larger pseudo-atoms. Such united atom approximations have been used in MD simulations of biological membranes. The aliphatic tails of lipids are represented by a few pseudo-atoms by gathering 2-4 methylene groups into each pseudo-atom.

The parameterization of these very coarse-grained models must be done empirically, by matching the behavior of the model to appropriate experimental data or all-atom simulations. Ideally, these parameters should account for both enthalpic and entropic contributions to free energy in an implicit way. When coarse-graining is done at higher levels, the accuracy of the dynamic description may be less reliable. But very coarse-grained models have been used successfully to examine a wide range of questions in structural biology.

Examples of applications of coarse-graining in biophysics:

• protein folding studies are often carried out using a single (or a few) pseudo-atoms per amino acid;
• DNA supercoiling has been investigated using 1-3 pseudo-atoms per basepair, and at even lower resolution;
• Packaging of double-helical DNA into bacteriophage has been investigated with models where one pseudo-atom represents one turn (about 10 basepairs) of the double helix;
• RNA structure in the ribosome and other large systems has been modeled with one pseudo-atom per nucleotide.

The simplest form of coarse-graining is the "united atom" (sometimes called "extended atom") and was used in most early MD simulations of proteins, lipids and nucleic acids. For example, instead of treating all four atoms of a CH3 methyl group explicitly (or all three atoms of CH2 methylene group), one represents the whole group with a single pseudo-atom. This pseudo-atom must, of course, be properly parameterized so that its van der Waals interactions with other groups have the proper distance-dependence. Similar considerations apply to the bonds, angles, and torsions in which the pseudo-atom participates. In this kind of united atom representation, one typically eliminates all explicit hydrogen atoms except those that have the capability to participate in hydrogen bonds ("polar hydrogens"). An example of this is the Charmm 19 force-field. Protein folding is the process by which a protein assumes its characteristic functional shape or tertiary structure, also known as the native state. ... It has been suggested that this article or section be merged with Superhelix. ... The structure of part of a DNA double helix Deoxyribonucleic acid, or DNA, is a nucleic acid molecule that contains the genetic instructions used in the development and functioning of all known living organisms. ... A bacteriophage (from bacteria and Greek phagein, to eat) is a virus that infects bacteria. ... Figure 1: Ribosome structure indicating small subunit (A) and large subunit (B). ... CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. ...

The polar hydrogens are usually retained in the model, because proper treatment of hydrogen bonds requires a reasonably accurate description of the directionality and the electrostatic interactions between the donor and acceptor groups. A hydroxyl group, for example, can be both a hydrogen bond donor and a hydrogen bond acceptor, and it would be impossible to treat this with a single OH pseudo-atom. Note that about half the atoms in a protein or nucleic acid are nonpolar hydrogens, so the use of united atoms can provide a substantial savings in computer time.

Examples of applications

Molecular dynamics is used in many fields of science.

• First macromolecular MD simulation published (1977, Size: 500 atoms, Simulation Time: 9.2 ps=0.0092 ns, Program: CHARMM precursor) Protein: Bovine Pancreatic Trypsine Inhibitor. This is one of the best studied proteins in terms of folding and kinetics. Its simulation published in Nature magazine paved the way for understanding protein motion as essential in function and not just accessory. ^[19]

The following two biophysical examples are not run-of-the-mill MD simulations. They illustrate almost heroic efforts to produce simulations of a system of very large size (a complete virus) and very long simulation times (500 microseconds): CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. ...

• MD simulation of the complete satellite tobacco mosaic virus (STMV) (2006, Size: 1 million atoms, Simulation time: 50 ns, program: NAMD) This virus is a small, icosahedral plant virus which worsens the symptoms of infection by Tobacco Mosaic Virus (TMV). Molecular dynamics simulations were used to probe the mechanisms of viral assembly. The entire STMV particle consists of 60 identical copies of a single protein that make up the viral capsid (coating), and a 1063 nucleotide single stranded RNA genome. One key finding is that the capsid is very unstable when there is no RNA inside. The simulation would take a single 2006 desktop computer around 35 years to complete. It was thus done in many processors in parallel with continuous communication between them. ^[20]

• Folding Simulations of the Villin Headpiece in All-Atom Detail (2006, Size: 20,000 atoms; Simulation time: 500 µs = 500,000 ns, Program: folding@home) This simulation was run in 200,000 CPU's of participating personal computers around the world. These computers had the folding@home program installed, a large-scale distributed computing effort coordinated by Vijay Pande at Stanford University. The kinetic properties of the Villin Headpiece protein were probed by using many independent, short trajectories run by CPU's without continuous real-time communication. One technique employed was the Pfold value analysis, which measures the probability of folding before unfolding of a specific starting conformation. Pfold gives information about transition state structures and an ordering of conformations along the folding pathway. Each trajectory in a Pfold calculation can be relatively short, but many independent trajectories are needed. ^[21]

The Satellite Tobacco Mosaic Virus or Tobacco mosaic satellivirus was first reported in Nicotiana glauca from southern California, U.S.A. by Valverde and Dodds. ... NAMD is an open-source molecular dynamics simulation package developed in the University of Illinois. ... Groups I: dsDNA viruses II: ssDNA viruses III: dsRNA viruses IV: (+)ssRNA viruses V: (-)ssRNA viruses VI: ssRNA-RT viruses VII: dsDNA-RT viruses A virus (from the Latin noun virus, meaning toxin or poison) is a microscopic particle (ranging in size from 20 - 300 nm) that can infect the... A capsid is the outer shell of a virus. ... In biology the genome of an organism is the whole hereditary information of an organism that is encoded in the DNA (or, for some viruses, RNA). ... Villin is an actin-binding protein that contains gelsolin domains capped by a headpiece consisting of a fast- and independently-folding three-helix bundle that is stabilized by hydrophobic interactions. ... Folding@home (also known as FAH or F@H) is a distributed computing project designed to perform computationally intensive simulations of protein folding and other molecular dynamics simulations. ... Vijay S. Pande is currently an Associate Professor in the Chemistry Department at Stanford University. ... Phi value analysis is an experimental protein engineering method used to study the structure of the folding transition state in small protein domains that fold in a two-state manner. ... Protein folding is the process by which a protein assumes its characteristic functional shape or tertiary structure, also known as the native state. ...

Molecular dynamics algorithms

Integrators

• Verlet integration
• Constraint algorithms (for constrained systems)
• Symplectic integrator

Verlet integration is a method for calculating the trajectories of particles in molecular dynamics simulations. ... In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics. ...

Short-range interaction algorithms

• Cell lists
• Verlet list
• Bonded interactions

Cell lists (also sometimes referred to as Cell linked-lists) are a tool for finding all atom pairs within a given cut-off distance of each other in Molecular dynamics simulations. ... Verlet lists are a device in Molecular dynamics simulations to efficiently maintain a list of all particles within a given cut-off distance of each other. ...

Long-range interaction algorithms

• Ewald summation
• Particle Mesh Ewald (PME)
• Particle-Particle-Particle-Mesh (P3M)
• Reaction Field Method

Ewald summation is a method for computing the interaction energies of crystals, particularly electrostatic energies. ... Ewald summation is a method for computing the interaction energies of periodic systems (e. ... Particle-Particle Particle Mesh (P3M) is a specilized hybrid algorithm in computing electrostatic potential among N point charges in computer simulations i. ...

Parallelization strategies

• Domain decomposition method (Distribution of system data for parallel computing)
• Molecular Dynamics - Parallel Algorithms

In mathematics, numerical analysis and numerical partial differential equations, the domain decomposition method solves a boundary value problem by splitting it into smaller boundary value problems. ... Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain results faster. ...

Major software for MD simulations

• ABINIT (DFT)
• AMBER (classical)
• CASTEP (ab initio)
• CPMD (DFT)
• CHARMM (classical)
• ESPResSo (classical, coarse-grained, parallel, extensible)
• Fireball (ab initio)
• DL_POLY (classical)
• GROMACS (classical)
• GROMOS (classical)
• GULP (classical)
• LAMMPS (classical, large-scale with spatial-decomposition of simulation domain for parallelism)
• MOLDY (classical)
• MOSCITO (classical)
• NAMD
• PWscf
• SIESTA (DFT)
• VASP (Ab-initio)
• TINKER (classical)
• YASARA (classical)
• ORAC (classical)

What is ABINIT ? ABINIT is a package whose main program allows one to find the total energy, charge density and electronic structure of systems made of electrons and nuclei (molecules and periodic solids) within Density Functional Theory (DFT), using pseudopotentials and a planewave basis. ... This article or section is in need of attention from an expert on the subject. ... CASTEP is a commercial software package which uses density functional theory with a plane wave basis set to calculate electronic properties of solids from first principles. ... The Car-Parrinello Molecular Dynamics, better known as CPMD, is a package for performing ab-initio quantum mechanical molecular dynamics (MD) using pseudopotentials and a plane wave basis set. ... CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. ... GROMACS (GROningen MAchine for Chemical Simulations) is a molecular dynamics simulation package originally developed in the University of Groningen, now maintained and extended at different places, including the University of Uppsala, University of Stockholm and the Max Planck Institute for Polymer Research. ... LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is a molecular dynamics program from Sandia National Laboratories. ... Moscito is a simulation software package for molecular dynamics (MD) simulation, originally developed at the University of Dortmund. ... NAMD is an open-source molecular dynamics simulation package developed in the University of Illinois. ... PWscf (Plane-Wave Self-Consistent Field) is a set of programs for electronic structure calculations within density functional theory and density functional perturbation theory, using plane wave basis sets and pseudopotentials. ... SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) is an original method and a software implementation for performing electronic structure calculations and ab initio molecular dynamics simulations of molecules and solids. ... The Vienna Ab-initio Simulation Package, better known as VASP (or alternatively VAMP), is a package for performing ab-initio quantum mechanical molecular dynamics (MD) using pseudopotentials and a plane wave basis set. ... Tinker may mean: Tinker (profession), the profession of metalsmith To tinker, verb. ...

Related software

• VMD - MD simulation trajectories can be loaded and visualized
• PyMol - Molecular Modelling software written in python
• Sirius - Molecular modeling, analysis and visualization of MD trajectories
• AGM Build - Molecular builder and conformational editor with proper partial charges and MM atom types association.
• esra - Lightweight molecular modeling and analysis library (Java/Jython/Mathematica).

Screenshot of VMD 1. ... PyMOL is an open-source, user-sponsored, molecular visualization system created by Warren Lyford DeLano and commercialized by DeLano Scientific LLC, which is a private software company dedicated to creating useful tools that become universally accessible to scientific and educational communities. ... Sirius is a molecular modeling and analysis system developed by Oleksandr (Sasha) Buzko at San Diego Supercomputer Center. ...

See also

• Car-Parrinello method
• Computational chemistry
• Dynamical systems
• Force field (chemistry)
• Implicit solvation
• Monte Carlo method
• Quantum chemistry
• Symplectic numerical integration
• Theoretical chemistry
• Statistical mechanics
• Software for molecular mechanics modeling

The Car-Parrinello method in computational chemistry is a type of ab initio (first principles) molecular dynamics, usually employing periodic boundary conditions, planewave basis sets, and DFT. In slight contrast to Born-Oppenheimer molecular dynamics wherein the nuclear (ions) and electronic degrees of freedom are separated and conventional matrix diagonalization... Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to complement the information obtained by actual chemical experiments, predict hitherto unobserved chemical phenomena, and solve related problems. ... In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... A force field is used to minimize the bond stretching energy of this ethane molecule. ... Implicit solvation (sometimes known as continuum solvation) is a method of representing solvent in molecular dynamics simulations and molecular mechanics (e. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics. ... Theoretical chemistry is the use of reasoning to explain or predict chemical phenomena. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Min - Optimization, MD - Molecular Dynamics, MC - Monte Carlo, QM - Quantum mechanics. ...

References

1. ^ Feynman, Richard (1963). "Lectures on Physics" 1: 3-6. 
2. ^ Agarwal, Pratul K (2006). "Enzymes: An integrated view of structure, dynamics and function (OPEN ACCESS)". Microbial Cell Factories 5 (2). 
3. ^ Alder, B. J.; T. E. Wainwright (1959). "Studies in Molecular Dynamics. I. General Method". J. Chem. Phys. 31 (2): 459. 
4. ^ Bernal, J.D. (1964). "The Bakerian lecture, 1962: The structure of liquids". Proc. R. Soc. 280: 299-322. 
5. ^ Schlick, T. (1996). "Pursuing Laplace's Vision on Modern Computers", in J. P. Mesirov, K. Schulten and D. W. Sumners: Mathematical Applications to Biomolecular Structure and Dynamics, IMA Volumes in Mathematics and Its Applications. New York: Springer-Verlag, 218-247. ISBN 978-0387948386. 
6. ^ de Laplace, P. S. (1820). Oeuveres Completes de Laplace, Theorie Analytique des Probabilites (in French). Paris, France: Gauthier-Villars. 
7. ^ Streett WB, Tildesley DJ, Saville G. (1978). Multiple time-step methods in molecular dynamics. Mol Phys 35(3):639-648.
8. ^ Tuckerman ME, Berne BJ, Martyna GJ. (1991). Molecular dynamics algorithm for multiple time scales: Systems with long range forces J Chem Phys 94(10):6811-6815.
9. ^ Tuckerman ME, Berne BJ, Martyna GJ. (1992). Reversible multiple time scale molecular dynamics. J Chem Phys 97(3): 1990-2001.
10. ^ Sugita, Yuji; Yuko Okamoto (1999). "Replica-exchange molecular dynamics method for protein folding". Chem Phys Letters 314: 141-151. 
11. ^ Brenner, D. W. (1990). "Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films". Phys. Rev. B 42 (15): 9458. 
12. ^ van Duin, A.; Siddharth Dasgupta, Francois Lorant and William A. Goddard III (2001). "". J. Phys. Chem. A 105: 9398. 
13. ^ Tersoff, J. (1989). ""Modeling solid-state chemistry: Interatomic potentials for multicomponent systems". Phys. Rev. B 39: 5566. 
14. ^ Daw, M. S.; S. M. Foiles and M. I. Baskes (1993). "The embedded-atom method: a review of theory and applications". Mat. Sci. and Engr. Rep. 9: 251. 
15. ^ Cleri, F.; V. Rosato (1993). "Tight-binding potentials for transition metals and alloys". Phys. Rev. B 48: 22. 
16. ^ Billeter, SR; SP Webb, PK Agarwal, T Iordanov, S Hammes-Schiffer (2001). "Hydride Transfer in Liver Alcohol Dehydrogenase: Quantum Dynamics, Kinetic Isotope Effects, and Role of Enzyme Motion". J Am Chem Soc 123: 11262-11272. 
17. ^ Ding, F; JM Borreguero, SV Buldyrey, HE Stanley, NV Dokholyan (2003). "Mechanism for the alpha-helix to beta-hairpin transition". J Am Chem Soc 53: 220-228. 
18. ^ Paci, E; M Vendruscolo, M Karplus (2002). "Validity of Go Models: Comparison with a Solvent-Shielded Empirical Energy Decomposition". Biophys J 83: 3032-3038. 
19. ^ McCammon, J; JB Gelin, M Karplus (1977). "Dynamics of folded proteins". Nature 267: 585-590. 
20. ^ Molecular dynamics simulation of the Satellite Tobacco Mosaic Virus (STMV) Peter Freddolino, Anton Arkhipov, Steven B. Larson, Alexander McPherson, Klaus Schulten. Theoretical and Computational Biophysics Group, University of Illinois at Urbana Champaign
21. ^ The Folding@Home Project and recent papers published using trajectories from it. Vijay Pande Group. Stanford University

General references

• M. P. Allen, D. J. Tildesley (1989) Computer simulation of liquids. Oxford University Press. ISBN 0-19-855645-4.
• J. A. McCammon, S. C. Harvey (1987) Dynamics of Proteins and Nucleic Acids. Cambridge University Press. ISBN 0521307503 (hardback).
• D. C. Rapaport (1996) The Art of Molecular Dynamics Simulation. ISBN 0-521-44561-2.
• Daan Frenkel, Berend Smit (2001) Understanding Molecular Simulation. Academic Press. ISBN 0-12-267351-4.
• J. M. Haile (2001) Molecular Dynamics Simulation: Elementary Methods. ISBN 0-471-18439-X
• R. J. Sadus, Molecular Simulation of Fluids: Theory, Algorithms and Object-Orientation, 2002, ISBN 0-444-51082-6
• Oren M. Becker, Alexander D. Mackerell Jr, Benoît Roux, Masakatsu Watanabe (2001) Computational Biochemistry and Biophysics. Marcel Dekker. ISBN 0-8247-0455-X.
• Andrew Leach (2001) Molecular Modelling: Principles and Applications. (2nd Edition) Prentice Hall. ISBN 978-0582382107.
• Tamar Schlick (2002) Molecular Modeling and Simulation. Springer. ISBN 0-387-95404-X.

Also see: 2002 (number). ...

External links

• The Blue Gene Project (IBM)
• BioSimGrid, a database for biomolecular simulations
• Towards the Dynome: Adding a 4th Dimension to the Protein Database by Terascale Simulation
• MolMovDB: A database of molecular motions
• VigyaanCD: A free electronic workbench for bioinformatics, computational biology and computational chemistry.
• Molecular Workbench: A free educational tool based on molecular dynamics simulations
• Molecular Physics
• Statistical mechanics of Nonequilibrium Liquids Lecture Notes on non-equilibrium MD
• Introductory Lecture on Classical Molecular Dynamics by Dr. Godehard Sutmann, NIC, Forschungszentrum Jülich, Germany
• Introductory Lecture on Ab Initio Molecular Dynamics and Ab Initio Path Integrals by Mark E. Tuckerman, New York University, USA
• Introductory Lecture on Ab initio molecular dynamics: Theory and Implementation by Dominik Marx, Ruhr-Universität Bochum and Jürg Hutter, Universität Zürich