Molecular Dynamics

1. Material modeling and
simulation Techniques

2. Introduction
• The main purpose of computational materials science is to discover
new materials, determining material behavior and mechanisms,
explaining experiments, and exploring materials theories.
Modeling & Simulation
• The term modeling refers to the development of a mathematical
representation of a physical situation.
• On the other hand, simulation refers to the procedure of solving the
equations that resulted from model development.

3. Materials simulation methods
• Quantum Mechanical Models
• Density Functional Theory
• Atomistic Methods
• Molecular Dynamics
• Kinetic Monte Carlo
• Continuum Simulation
• Finite element Method
• Finite Difference method
• Mesoscale Models
• Dislocation dynamics
• Phase field
• Crystal Plasticity

4. Atomistic Models: Molecular Dynamics
• Molecular Dynamics is a meshfree computer simulation technique, where
the time evolution of a set of interacting particles is followed, by
integrating their equations of motion.
• Molecular dynamics (MD) simulations represent the computer approach to
statistical mechanics. As a counterpart to experiment, MD simulations are
used to estimate equilibrium and dynamic properties of complex systems
that cannot be calculated analytically.
• In MD we follow the laws of classical mechanics, most notably Newton’s
second law, an ordinary DEQ of second order, for each particle i in a system
consisting of a total of N particles.:
• These are 5 most commonly used softwares for MD calculations:
GROMACS, CHARMM, AMBER, NAMD, and LAMMPS.

5. Applications of Molecular Dynamics
• MD is used in a multitude of research areas, comprising all three basic
states of matter (liquid, gaseous and solid).
Figure. Typical applications of MD in fluid, solid state and kinetic
gas theory. Depicted are fluctuations of atoms about their lattice
positions in a crystal, diffusive behavior of a particle in a fluid and
the ballistic motion of a particle in a gas in between collisions.

6. 1. Liquids and Fluid Dynamics.
• Particle simulations can serve as a new approach to the study of
hydrodynamical instabilities on the microscopic scale, e.g. the
Rayleigh-Taylor or Rayleigh-Bénard instability.
• Furthermore, molecular dynamics simulations allow investigation of
complex fluids, such as polymers in solution and fluid mixtures, e.g.,
emulsions of oil and water, but also of crystallization and of phase
transitions on the microscopic level.
• Through nonequilibrium techniques, transport phenomena such as
viscosity and heat flow have been investigated.

7. 2. Solid State Physics.
• The simulation (and virtual design) of materials on an atomic scale is
primarily used in the analysis of known materials and in the
development of new materials with specific desired properties, e.g. in
terms of stiffness.
• Examples of phenomena studied in solid state physics are the
structure conversion in metals induced by temperature or shock, the
formation of cracks initiated by pressure or shear stresses, fracture
and failure simulations, the propagation of sound waves in materials,
the impact of defects in the structure of materials on their load-
bearing capacity, and the analysis of plastic and elastic deformations.

8. 3. Soft Matter Physics and Biomacromolecules
• The dynamics of macromolecules on the atomic level is one of the
most prominent applications of MD.
• With such methods it is possible to simulate molecular fluids, crystals,
amorphous polymers, liquid crystals, zeolites, nuclear acids, proteins,
membranes and many more biochemical materials.

9. 4. Astrophysics
• In this area, simulations are primarily done to test theoretical models.
• In a simulation of the formation of the large-scale structure of the
universe, particles correspond to entire galaxies. In a simulation of
galaxies, particles represent several hundred up to thousand stars.
The force acting between these particles results from the
gravitational potential.

10. Limitations of MD
• While MD is a very powerful technique it also has its limitations.
• Artificial boundary conditions: The system size that can be simulated with
MD is very small compared to real molecular systems. Hence, a system of
particles will have many unwanted artificial boundaries (surfaces). In order
to avoid real boundaries, one introduces periodic boundary conditions
which can introduce artificial spatial correlations in too small systems.
• Cut off of long-range interactions: Usually, all non-bonded interactions are
cut off at a certain distance, in order to keep the cost of the computation of
forces as small as possible. These problems are to be expected with
systems containing charged particles. Here, simulations can go badly wrong
and, e.g. lead to an accumulation of the charged particles in one corner of
the box. Here, one has to use special algorithms.

11. • The simulations are classical: Hence, all those material properties
connected to the fast electronic degrees of freedom are not correctly
described. For example, atomic oscillations (e.g. covalent C-C-bond
oscillations in polyethylene molecules, or hydrogen-bonded motion in
biopolymers such as DNA, proteins, or biomembranes) are typically of
the order 1014 Hz.
• In MD simulations, particles (often interpreted as atoms) interact with
each other. These interactions give rise to forces which act upon
atoms and atoms move under the action of these instantaneous
forces. As the atoms move, their relative positions change and the
forces change as well.
• The forces are usually obtained as the gradient of a potential energy
function 𝜑(𝑟𝑖), depending on the positions of the particles. Thus, one
needs a realistic energy description of the system, otherwise one
does not know whether the simulation will produce something
useful.

12. • The electrons are in the ground state: Using conservative force fields
in MD implies that the potential is a function of the atomic positions
only. No electronic motions are considered. Thus, the electrons
remain in their ground state and are considered to instantaneously
follow the movement of the core. This means that electronically
excited states, electronic transfer processes, and chemical reactions
cannot be treated.