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

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

Bill Smith

Computational Science and Engineering

STFC Daresbury Laboratory

• 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

Example: Simulation of Argon

Pair Potential:

Lagrangian:

V(r)

s

r

e

rcut

Lagrange

Newton

Lennard-

Jones

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

Leapfrog Verlet Algorithm

Velocity Verlet

Algorithm

As Applied

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.

Kinetic Energy:

Temperature:

System Properties: Static (1)

Pressure:

Specific Heat

System Properties: Static (2)

Structure factor:

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

System Properties: Static (3)

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!

Free Energies?

System Properties: Dynamic (1) simulation. But

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

Mean squared displacement (Einstein relation) simulation. But

Velocity Autocorrelation (Green-Kubo relation)

System Properties: Dynamic (2)

Liquid simulation. But

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

Solid

time (ps)

Typical MSDs

<v simulation. But i(t).vi(0)>

0.0

t (ps)

Typical VAF

1.0

Recommended Textbooks simulation. But

• 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 simulation. But

A General Purpose Molecular Dynamics Simulation Package

DL_POLY Background simulation. But

• 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 simulation. But

• 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 simulation. But

molecules

Point ions

and atoms

Flexibly

molecules

Polarisable

ions (core+

shell)

Rigid bond

molecules

Flexible

molecules

Rigid

bonds

Supported Molecular Entities

M simulation. But 4

P4

M0

P0

M5

P5

M1

P1

M6

P6

M2

P2

M7

P7

M3

P3

DL_POLY is for Distributed Parallel Machines

Atomic systems simulation. But

Ionic systems

Polarisable ionics

Molecular liquids

Molecular ionics

Metals

Biopolymers and macromolecules

Membranes

Aqueous solutions

Synthetic polymers

Polymer electrolytes

DL_POLY: Target Simulations

DL_POLY Force Field simulation. But

• 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 simulation. But

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

Algorithms and Ensembles

The DL_POLY Java GUI simulation. But

The DL_POLY Website simulation. But

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

The End simulation. But