# Bill Smith Computational Science and Engineering STFC Daresbury Laboratory Warrington WA4 4AD - PowerPoint PPT Presentation

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MSc in High Performance Computing Computational Chemistry Module Introduction to Molecular Dynamics. Bill Smith Computational Science and Engineering STFC Daresbury Laboratory Warrington WA4 4AD. What is Molecular Dynamics?.

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Bill Smith Computational Science and Engineering STFC Daresbury Laboratory Warrington WA4 4AD

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## MSc in High Performance ComputingComputational Chemistry ModuleIntroduction to Molecular Dynamics

Bill Smith

Computational Science and Engineering

STFC Daresbury Laboratory

### What is Molecular Dynamics?

• MD is the solution of the classical equations of motion for atoms and molecules to obtain the time evolution of the system.

• Applied to many-particle systems - a general analytical solution not possible. Must resort to numerical methods and computers

• Classical mechanics only - fully fledged many-particle time-dependent quantum method not yet available

• Maxwell-Boltzmann averaging process for thermodynamic properties (time averaging).

rcut

Pair Potential:

Lagrangian:

V(r)

s

r

e

rcut

Lagrange

Newton

Lennard-

Jones

### Minimum Image Convention

Use rij’ not rij

L

xij = xij - L* Nint(xij/L)

rcut

j’

j

i

Nint(a)=nearest integer to a

rcut < L/2

r’ (t+Dt)

r (t+Dt)

v (t)Dt

Net displacement

r (t)

f(t)Dt2/m

[r (t+Dt), v(t+Dt), f(t+Dt)]

[r (t), v(t), f(t)]

### Integration Algorithms: Essential Idea

Time step Dt chosento balance efficiency

and accuracy of energy conservation

Verlet algorithm

### Integration Algorithms (ii)

Leapfrog Verlet Algorithm

Velocity Verlet

Algorithm

As Applied

Initialise

Forces

Motion

Properties

Summarise

### Key Stages in MD Simulation

• Set up initial system

• Calculate atomic forces

• Calculate atomic motion

• Calculate physical properties

• Repeat !

• Produce final summary

• Constraints and Shake

• If certain motions are considered unimportant, constrained MD can be more efficient e.g. SHAKE algorithm - bond length constraints

• Rigid bodies can be used e.g. Eulers methods and quaternion algorithms

• Statistical Mechanics

• The prime purpose of MD is to sample the phase space of the statistical mechanics ensemble.

• Most physical properties are obtained as averages of some sort.

• Structural properties obtained from spatial correlation functions e.g. radial distribution function.

• Time dependent properties (transport coefficients) obtained via temporal correlation functions e.g. velocity autocorrelation function.

Thermodynamic Properties

Kinetic Energy:

Temperature:

### System Properties: Static (1)

Configuration Energy:

Pressure:

Specific Heat

### System Properties: Static (2)

Structural Properties

Structure factor:

Note: S(k) available from x-ray diffraction

R

R

g(r)

1.0

separation (r)

### Typical RDF

All above calculable by molecular dynamics or Monte Carlo simulation. But NOT Free Energy:

where

is the Partition Function.

But can calculate a free energy difference!

### System Properties: Dynamic (1)

• The bulk of these are in the form of Correlation Functions :

Mean squared displacement (Einstein relation)

Velocity Autocorrelation (Green-Kubo relation)

### System Properties: Dynamic (2)

Liquid

<|ri(t)-ri(0)|2> (A2)

Solid

time (ps)

<vi(t).vi(0)>

0.0

t (ps)

1.0

### Recommended Textbooks

• The Art of Molecular Dynamics Simulation, D.C. Rapaport, Camb. Univ. Press (2004)

• Understanding Molecular Simulation, D. Frenkel and B. Smit, Academic Press (2002).

• Computer Simulation of Liquids, M.P. Allen and D.J. Tildesley, Oxford (1989).

• Theory of Simple Liquids, J.-P. Hansen and I.R. McDonald, Academic Press (1986).

• Classical Mechanics, H. Goldstein, Addison Wesley (1980)

## The DL_POLY Package

A General Purpose Molecular Dynamics Simulation Package

### DL_POLY Background

• General purpose parallel MD code to meet needs of CCP5 (academic collaboration)

• Authors W. Smith, T.R. Forester & I. Todorov

• Over 3000 licences taken out since 1995

• Available free of charge (under licence) to University researchers.

### DL_POLY Versions

• DL_POLY_2

• Replicated Data, up to 30,000 atoms

• Full force field and molecular description

• DL_POLY_3

• Domain Decomposition, up to 10,000,000 atoms

• Full force field but no rigid body description.

• I/O files cross-compatible (mostly)

• DL_POLY_4

• New code under development

Rigid

molecules

Point ions

and atoms

Flexibly

molecules

Polarisable

ions (core+

shell)

Rigid bond

molecules

Flexible

molecules

Rigid

bonds

M4

P4

M0

P0

M5

P5

M1

P1

M6

P6

M2

P2

M7

P7

M3

P3

### DL_POLY is for Distributed Parallel Machines

Atomic systems

Ionic systems

Polarisable ionics

Molecular liquids

Molecular ionics

Metals

Biopolymers and macromolecules

Membranes

Aqueous solutions

Synthetic polymers

Polymer electrolytes

### DL_POLY Force Field

• Intermolecular forces

• All common van der Waals potentials

• Finnis_Sinclair and EAM metal (many-body) potential (Cu3Au)

• Tersoff potential (2&3-body, local density sensitive, SiC)

• 3-body angle forces (SiO2)

• 4-body inversion forces (BO3)

• Intramolecular forces

• bonds, angle, dihedrals, improper dihedrals, inversions

• tethers, frozen particles

• Coulombic forces

• Ewald* & SPME (3D), HK Ewald* (2D), Adiabatic shell model, Neutral groups*, Bare Coulombic, Shifted Coulombic, Reaction field

• Externally applied field

• Electric, magnetic and gravitational fields, continuous and oscillating shear fields, containing sphere field, repulsive wall field

* Not in DL_POLY_3

Algorithms

Verlet leapfrog

Velocity Verlet

RD-SHAKE

Euler-Quaternion*

No_Squish*

QSHAKE*

[Plus combinations]

*Not in DL_POLY_3

Ensembles

NVE

Berendsen NVT

Hoover NVT

Evans NVT

Berendsen NPT

Hoover NPT

Berendsen NT

Hoover NT

PMF

### The DL_POLY Website

http://www.ccp5.ac.uk/DL_POLY/

The End