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


Periodic boundary conditions

Periodic Boundary Conditions


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


Verlet algorithm derivation

Verlet Algorithm: Derivation


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)


Radial distribution function

Radial Distribution Function

R

R


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)

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


System properties dynamic 2

Mean squared displacement (Einstein relation)

Velocity Autocorrelation (Green-Kubo relation)

System Properties: Dynamic (2)


Typical msds

Liquid

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

Solid

time (ps)

Typical MSDs


Typical vaf

<vi(t).vi(0)>

0.0

t (ps)

Typical VAF

1.0


Recommended textbooks

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

The DL_POLY Package

A General Purpose Molecular Dynamics Simulation Package


Dl poly background

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 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

    • Dynamic load balancing


Supported molecular entities

Rigid

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

M4

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

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

  • 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

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


The dl poly website

The DL_POLY Website

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


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

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