# Extensive Definition

Molecular dynamics
(MD) is a form of computer
simulation in which 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". MD probes the relationship between molecular
structure, movement and function. 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, but is applied today mostly in materials
science and biomolecules.

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." Fortunately, now computers keep track of bonds
during a simulation.

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 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, so the much more demanding Ab Initio Molecular Dynamics
method must be used. Nevertheless, molecular dynamics techniques
allow detailed time and space resolution into representative
behavior in phase
space.

## 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".

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.

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.

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.

## 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. To make
statistically valid conclusions from the simulations, the time span
simulated should match the kinetics of the natural process.
Otherwise, it is analogous to making conclusions about how a human
walks from less than one footstep. 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.

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(n^2) 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(n \log(n)) ) or good spherical cutoff techniques (
O(n) ).

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.

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.

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.

### 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

- F(X) = -\nabla U(X)=M\dot(t)
- V(t) = \dot (t)

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).

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.

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 nkBT/2 where n is the number of degrees of freedom of the
system.

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 (10^ 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 variety of thermostat methods are available 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.

### 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.

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).

### 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 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

Main Article: Force fieldA 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.

The reduction from a fully quantum description to
a classical potential entails two main approximations. The first
one is the
Born-Oppenheimer approximation, which states that the dynamics
of electrons is so fast that they can be considered to react
instantaneously to the motion of their nuclei. As a consequence,
they may be treated separately. The second one treats the nuclei,
which are much heavier than electrons, as point particles that
follow classical Newtonian dynamics. In classical molecular
dynamics the effect of the electrons is approximated as a single
potential energy surface, usually representing the ground
state.

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.

### 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.

Because of the non-local nature of non-bonded
interactions, they involve at least weak interactions between all
particles in the system. Its calculation is normally the bottleneck
in the speed of MD simulations. To lower the computational cost,
force
fields employ numerical approximations such as shifted cutoff
radii, reaction field algorithms, particle
mesh Ewald summation, or the newer
Particle-Particle Particle Mesh (P3M).

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 for hydrocarbons and its further developments for the
C-Si-H and C-O-H systems. The ReaxFF potential can
be considered a fully reactive hybrid between bond order potentials
and chemistry force fields.

### Pair potentials vs. many-body potentials

The potential functions representing the
non-bonded energy are formulated as a sum over interactions between
the particles of the system. The simplest choice, employed in many
popular force
fields, is the "pair potential", in which the total potential
energy can be calculated from the sum of energy contributions
between pairs of atoms. An example of such a pair potential is the
non-bonded Lennard-Jones
potential (also known as the 6-12 potential), used for
calculating van der Waals forces.

U(r) = 4\varepsilon \left[ \left(\frac\right)^ -
\left(\frac\right)^ \right]

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.

- U_(r_) = \sum \frac \frac + \sum A_l \exp \frac + \sum C_l r_^ + \cdots

In many-body
potentials, the potential energy includes the effects of three
or more particles interacting with each other. In simulations with
pairwise potentials, global interactions in the system also exist,
but they occur only through pairwise terms. In many-body
potentials, the potential energy cannot be found by a sum over
pairs of atoms, as these interactions are calculated explicitly as
a combination of higher-order terms. In the statistical view, the
dependency between the variables cannot in general be expressed
using only pairwise products of the degrees of freedom. For
example, the Tersoff
potential, 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) and the Tight-Binding Second Moment Approximation
(TBSMA) potentials, 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.

### 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.

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

### Polarizable potentials

Main article: Force
field

Most classical force fields implicitly include
the effect of polarizability, e.g. by
scaling up the partial charges obtained from quantum chemical
calculations. These partial charges are stationary with respect to
the mass of the atom. But molecular dynamics simulations can
explicitly model polarizability with the introduction of induced
dipoles through different methods, such as Drude
particles or fluctuating charges. This allows for a dynamic
redistribution of charge between atoms which responds to the local
chemical environment.

For many years, polarizable MD simulations have
been touted as the next generation. For homogenous liquids such as
water, increased accuracy has been achieved through the inclusion
of polarizability. Some promising results have also been achieved
for proteins. However, it is still uncertain how to best
approximate polarizability in a simulation.

### Ab-initio methods

In classical molecular dynamics, a single
potential energy surface (usually the ground state) is represented
in the force field. This is a consequence of the
Born-Oppenheimer approximation. If excited states, chemical
reactions or a more accurate representation is needed, electronic
behavior can be obtained from first principles by using a quantum
chemical method, such as Density
Functional Theory. This is known as Ab Initio Molecular
Dynamics (AIMD). Due to the cost of treating the electronic degrees
of freedom, the computational cost of this simulations is much
higher than classical molecular dynamics. This implies that AIMD is
limited to smaller systems and shorter periods of time.

Ab-initio
quantum-mechanical
methods may be used to calculate the potential
energy of a system on the fly, as needed for conformations in a
trajectory. This calculation is usually made 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 calculations produce a vast amount of information that is
not available from empirical methods, such as density of electronic
states. A significant advantage of using ab-initio methods is the
ability to study reactions that involve breaking or formation of
covalent bonds, which correspond to multiple electronic
states.

A popular software for ab-initio molecular
dynamics is the Car-Parrinello
Molecular Dynamics (CPMD) package based on the density
functional theory.

### 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 most important advantage of hybrid QM/MM
methods is the speed. The cost of doing classical molecular
dynamics (MM) in the most straightforward 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
every other particle). 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(n2.7)). 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 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.

### 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) and Go-models.
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.

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.

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):

- 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.

- 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.

## Molecular dynamics algorithms

### Integrators

- Verlet integration
- Beeman's algorithm
- Gear predictor - corrector
- Constraint algorithms (for constrained systems)
- Symplectic integrator

### Short-range interaction algorithms

- Cell lists
- Verlet list
- Bonded interactions

### Long-range interaction algorithms

- Ewald summation
- generalized Born (GB)
- Particle Mesh Ewald (PME)
- Particle-Particle-Particle-Mesh (P3M)
- Reaction Field Method

### Parallelization strategies

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

## Major software for MD simulations

- ABINIT (DFT)
- AMBER (classical)
- Ascalaph (classical)
- CASTEP (DFT)
- CPMD (DFT)
- CHARMM (classical, the pioneer in MD simulation, extensive analysis tools)
- DL_POLY (classical)
- ESPResSo (classical, coarse-grained, parallel, extensible)
- Fireball (tight-binding DFT)
- GROMACS (classical)
- GROMOS (classical)
- GULP (classical)
- LAMMPS (classical, large-scale with spatial-decomposition of simulation domain for parallelism)
- MDynaMix (classical, parallel)
- MOLDY (classical, parallel)
- MOSCITO (classical)
- NAMD (classical, parallelization with up to thousands of CPU's)
- NEWTON-X (ab initio, surface-hopping dynamics)
- ProtoMol (classical, extensible, includes multigrid electrostatics)
- PWscf (DFT)
- SIESTA (DFT)
- VASP (DFT)
- TINKER (classical)
- YASARA (classical)
- ORAC (classical)
- XMD (classical)

## Related software

- VMD - MD simulation trajectories can be loaded and visualized
- PyMol - Molecular Modelling software written in python
- Packmol Package for building starting configurations for MD in an automated fashion
- 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).
- Molecular Workbench - Interactive molecular dynamics simulations on your desktop

## See also

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

## References

### 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.
- Understanding Molecular Simulation : from algorithms to applications
- 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.
- William Graham Hoover (1991) Computational Statistical Mechanics, Elsevier, ISBN 0-444-88192-1.

## External links

- The Blue Gene Project (IBM)
- 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

atomistics in German: Moleküldynamik

atomistics in Spanish: Dinámica molecular

atomistics in French: Dynamique
moléculaire

atomistics in Korean: 분자동역학

atomistics in Dutch: Moleculaire dynamica

atomistics in Japanese: 分子動力学法

atomistics in Polish: Dynamika molekularna

atomistics in Russian: Метод классической
молекулярной динамики

atomistics in Chinese: 分子动力学

atomistics in Serbian: Молекулска
динамика