Msc in high performance computing computational chemistry module introduction to molecular dynamics
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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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Msc in high performance computing computational chemistry module introduction to molecular dynamics

MSc in High Performance ComputingComputational Chemistry ModuleIntroduction to Molecular Dynamics

Bill Smith

Computational Science and Engineering

STFC Daresbury Laboratory

Warrington WA4 4AD


What is molecular dynamics
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).


Example simulation of argon

rcut

Example: Simulation of Argon

Pair Potential:

Lagrangian:


Lennard jones potential
Lennard -Jones Potential

V(r)

s

r

e

rcut


Equations of motion
Equations of Motion

Lagrange

Newton

Lennard-

Jones



Minimum image convention
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


Integration algorithms essential idea

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


Integration algorithms i
Integration Algorithms (i)

Verlet algorithm


Integration algorithms ii
Integration Algorithms (ii)

Leapfrog Verlet Algorithm


Integration algorithms
Integration Algorithms

Velocity Verlet

Algorithm

As Applied



Key stages in md simulation

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


Md further comments
MD – Further Comments

  • 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.


System properties static 1

Thermodynamic Properties

Kinetic Energy:

Temperature:

System Properties: Static (1)


System properties static 2

Configuration Energy:

Pressure:

Specific Heat

System Properties: Static (2)


System properties static 3

Structural Properties

Pair correlation (Radial Distribution Function):

Structure factor:

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

System Properties: Static (3)



Typical rdf

g(r)

1.0

separation (r)

Typical RDF


Free energies

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
System Properties: Dynamic (1) simulation. But

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


System properties dynamic 2

Mean squared displacement (Einstein relation) simulation. But

Velocity Autocorrelation (Green-Kubo relation)

System Properties: Dynamic (2)


Typical msds

Liquid simulation. But

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

Solid

time (ps)

Typical MSDs


Typical vaf

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

0.0

t (ps)

Typical VAF

1.0


Recommended textbooks
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

The DL_POLY Package simulation. But

A General Purpose Molecular Dynamics Simulation Package


Dl poly background
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
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

    • Dynamic load balancing


Supported molecular entities

Rigid simulation. But

molecules

Point ions

and atoms

Flexibly

linked rigid

molecules

Polarisable

ions (core+

shell)

Rigid bond

linked rigid

molecules

Flexible

molecules

Rigid

bonds

Supported Molecular Entities


Dl poly is for distributed parallel machines

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


Dl poly target simulations

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
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 and ensembles

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
The DL_POLY Java GUI simulation. But


The dl poly website
The DL_POLY Website simulation. But

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


Bill smith computational science and engineering stfc daresbury laboratory warrington wa4 4ad

The End simulation. But