Molecular Dynamics Simulations - Johnson Grouppuccini.che.pitt.edu/~karlj/Classes/CHE3935/MD_simulations.pdf · Molecular Dynamics Simulations . Professor Albert C. ... • Extract

Professor Albert C. To, Department of Mechanical Engineering and Materials Science, University of Pittsburgh

Molecular Dynamics Simulations


Molecular Dynamics (MD) Simulations

Computer simulation of time evolution of

interacting atoms based on classical

Newtonian mechanics:

To solve numerically the N-body problem of classical mechanics

Deterministic method: state of the system at any future time can be predicted from its current state

Nanowires

Biomolecules

Nanotubes

http://lammps.sandia.gov

: Interatomic potentialU

: External forceextf

, : mass and position of atomthm r


http://nanohub.org

Multiscale Modeling and Simulations


MD Examples

Systems MD can simulate Atomic systems

Metals

All-atom or Bead-spring polymers

Organic molecules

Granular systems

Hybrid systems



Ionic Diffusion

Flow of water and ions thru a silica pore Work of Paul Crozier at Sandia National Laboratories to study how narrow

cylindrical pores in silica can regulate the passage of water and ions in the presence of a pressure gradient for purposes of desalination.

- Water molecules

- Ions

- Amorphous SiO2


Shear Flow

Shear flow on corrugated slip/stick surface Work of Nikolai Priezjev at Princeton to study how fluid flow is affected by

molecular-scale interactions at a solid-liquid interface. The solid surface is patterned with alternating stripes with no-shear and finite-slip attributes.


Carbon Nanotube Welding

CNT welding by high heat (3000 K) Work done by Xueming Yang and

Albert To


Nanowire Formation

Au nanowire formation and extension Work of Harold Park at Vanderbilt and Jon Zimmerman at Sandia to study how

nanowires form under tensile loading at differing strain rates.

Atoms are colored by their

potential energy for an EAM

potential.


Shock Impact

Shock induced by a piston velocity of 689 m/s. Yellow atoms note grain boundaries caused by the shock

Work by Kai Kadau at Los Alamos National Lab


Displacement Cascade

MD simulation of the development of a displacement cascade from a 200

keV recoil in iron at 100K (by R. E. Stoller, Oak Ridge National Lab)


Helium Bubble Formation

Metal response to helium bubble formation Work of Jon Zimmerman at Sandia to study of how helium bubble formation in a

metal induces defect formation. As nanobubbles grow, they force the surrounding metal to respond.

Atoms are colored by their local

centro-symmetry value.


Rhodopsin Solvation

Rhodopsin in solvated lipid bilayer Work of Paul Crozier and Mark Stevens at Sandia to study the conformational

properties of Rhodopsin protein in both dark- and light-adapted states.

The movie shows the loop and

helix dynamics of the

Rhodopsin protein in a lipid

bilayer surrounded by water

and counter-ions.


Protein Dynamics

RuBisCO protein simulations Work of Paul Crozier at Sandia to study the properties of the RuBisCO enzyme

which is a ubiquitous protein involved in converting CO2 to organic forms of carbon and in the photosynthetic process.

An all-atom model with the binding

pocket in color. Even though the pocket is

closed, a CO2 molecule escapes.


General Overview of LAMMPS

LAMMPS: Large-scale Atomic/Molecular Massively Parallel Simulator

Potential for

Soft materials; biomolecules, polymers

Solid-state materials; metals, semiconductors

Coarse-grain systems

Executes On single-processor machines

In parallel using message-passing techniques (MPI) with spatial-decomposition of the domain (distributed- or shared-memory machines or Beowulf-style clusters)

Distributed As an open source code under the terms of the GPL license

By Sandia National Laboratories a US Department of Energy (DOE) Laboratory

http://www.sandia.gov/


http://www.energy.gov/


Installing/Running LAMMPS

Windows-based machines

Laptop

Desktop

Linux-based machines



Go to http://lammps.sandia.gov/download.html

Download the first two files as shown below in red box

The first file lammps.tar.gz has sample LAMMPS input scripts

The second file lmp_win_no-mpi.exe is the executable file for

executing a LAMMPS input script



Extract all the directories and files in lammps.tar.gz to a local directory, say

your c: drive (suggest to use a freeware called winRAR)

Put the executable file lmp_win_no-mpi.exe into the lammps-27Aug11

directory (see below)

The sample input scripts are contained in

the sub-directories in the examples

directory


Start a command prompt in Windows

Make current the crack directory (under the examples directory) by typing at

the prompt

cd c:\lammps-27Aug11\examples\crack

Press Enter and then type at the prompt

c:\lammps-27Aug11\lmp_win_no-mpi.exe


If youre lucky

If not

Running LAMMPS


If youre lucky

If not

read the supplied documentation carefully!

checkout the website http://lammps.sandia.gov

email me [email protected] or visit me in 508 BEH

Running LAMMPS


If youre really lucky, you should see this after a few minutes

If not

Running LAMMPS


If youre really lucky, you should see this after a few minutes

If not

You need to buy a new computer!

Running LAMMPS



in.crack



log.lammps



dump.crack

end of file



Input script parsing rules

LAMMPS does not read entire input script

Some commands are valid ONLY when they follow other commands

Sometimes command B will use values that can be set by command A

reduced LJ temperature



Input script parsing rules

each non-blank line is treated as a command

If the line ends with &, the command is assumed to continue on the next line

All characters following # are treated as a comment

$ followed by characters indicates a variable name

$temp or ${temp}

A line is broken into words separated by spaces OR tabs

letters, digits, underscores or punctuation characters

First word is a command, successive words are arguments

Text with spaces should be enclosed by double quotes

dump modify or fix print



Input script structure

LAMMPS script has 4 parts:

Initialization

Atom definition

Settings

Run a simulation

All most all commands need only be

used if a non-default value is desired.



Initialization

Set parameters before atoms are created or read-in from a file

Units

Dimension

Newton

Processors

Boundary

Atom style

Pair style



Atom definition

2 ways to define atoms

read from a data or restart file

Read data

Read restart

create atoms on a lattice

Lattice

Region

Create box

Create atoms



Settings

Force field coefficients

Bond coeff

Angle coeff

Special bonds

Simulation parameters

Group

Timestep

Run style

Impose boundary conditions, time integration

Fix

Compute

Output options



Run a simulation

MD simulation is executed via run

Energy minimization is performed via minimize

Parallel tempering can be done via temper

Monte Carlo simulations - simulation of multiple ensembles of a system on

multiple partitions of processors



default


Installing/Running LAMMPS Compiling xmovie

open Makefile inside the xmovie directory

$ make


Installing/Running LAMMPS Running xmovie

inside the xmovie directory type

$ mv ../../examples/crack/dump.crack dump.crack

next, startx

$ startx &

traverse to the xmovie directory

open dump.crack with xmovie by executing

$ run xmovie.exe scale dump.crack


LAMMPS - Visualization

Simple and fast visualizer xmovie Provided with the LAMMPS package




High-quality visualization packages

Raster3d

written mostly in FORTRAN

can download source code to compile

can download win32 binaries

http://www.bmsc.washington.edu/raster3d/raster3d.html





Raster3d

VMD

need to register

can download source code to compile

windows OpenGL available (2000/XP)

MacOS X (Intel x86 / PowerPC)

http://www.ks.uiuc.edu/Research/vmd





Raster3d

VMD

AtomEye

raw binaries available only

Windows with CYGWIN and X

MacOS X with Darwin

http://164.107.79.177/Archive/Graphics/A


Computer simulation of time evolution

of interacting atoms based on classical

Newtonian mechanics:

To solve numerically the N-body

problem of classical mechanics

Deterministic method: state of the

system at any future time can be

predicted from its current state

Nanowires

Biomolecules

Nanotubes


: Interatomic potentialU

: External forceextf

, : mass and position of atomthm r


54

Interatomic Potential

The most general form of the potential is given by the series

The one-body potential W1 describes external force fields (e.g.

gravitational filed), and external constraining fields (e.g. the wall

function for particles in a circular chamber)

The two-body potential describes dependence of the

potential energy on the distances between pairs of

atoms in the system:

The three-body and higher order potentials (important in

biomolecule) provide dependence on the geometry of atomic

arrangement/bonding. For instance, a dependence on the angle

between three mass points is given by

1 2 1 2 3

, , ,

( , ,..., ) ( ) ( , ) ( , , ) ...N i i j i j ki i j i i j i k j

U W W W

r r r r r r r r r

2 2( , ) ( ), | | | |i j ij i jW W r r r r r r rx

y

z

rj

rij

ri

i

j

3 3( , , ) (cos ), cos| | | |

ji jk

i j k ijk ijk

ji jk

W W

r r

r r rr r

x

y

z

rj rk

ijk

i

k

j

rji

rjk


55

Pair-Wise Potentials: Lennard-Jones

12 6

13 7

( ) 4

( )( ) 24 2

LJ

LJLJ

W rr r

W rF r

r r r

6( ) 0 2LJF

Here, is the depth of the potential energy well and is

the value of r where that potential energy becomes zero;

the equilibrium distance is given by

The first term represents repulsive interaction

At small distances atoms repel due to quantum

effects (to be discussed in a later lecture)

The second term represents attractive interaction

This term represents electrostatic attraction at

large distances


56

Pair-Wise Potentials: Morse

2 ( ) ( )

2 ( ) ( )

( ) 2

( ) 2

r r

M

r r

M

W r e e

F r e e

Another pair-wise potential model, effective for

modeling crystalline solids, is the Morse potential,

Here, is the depth of the potential energy well and

is a scaling factor; the equilibrium distance is given

by

Similarly to the earlier example,

The first term represents repulsive interaction

The second term represents attractive interaction

( ) 0MF


57

Truncated Potential

In system of N atoms

accumulates unique pair interactions

if all pair interactions are sampled, the number increases with the square of the

number of atoms

Saving computer time

Neglect pair interactions beyond some distance

Example: Lennard-Jones potential used in simulations

)1(2

1NN

12 6

4( )

0

c

LJ

c

r rW r r r

r r

cr


58

Potential for Biomolecules (DNAs and proteins)

# of bondsbond 2

0

1

( ) ( )bond n n nn

W r k b b

Bond length (vibrational)

spring constant

Current bond length

Equilibrium bond length

Bond angle

# of anglesangle 2

0

1

( ) ( )angle n n nn

W r k

spring constant

Current bond angle

Equilibrium bond angle


59


Dihedral angle

# of dihedrals

di

0

1

( ) 1 cos ( )dihedral n n nn

W r k m

spring constant

Current

dihedral angle

Equilibrium

dihedral angle

Period


60


# of atoms # of atoms

( )i j

Electrostatics

i j i ij

q qW r

r

12 6# of atoms # of atoms

( ) 4ij ij

LJ ij

i j i ij ij

W rr r

Non-bonded

interaction

Van Der Waals Force

(London Interaction)

Electrostatics

Charge

on atom i

Charge

on atom j - +


61


bond angle dihedral LJ Electrostatics

# of angles# of bonds # of dihedralsbond 2 angle 2 di

0 0 0

1 1 1

12 6

( ) ( ) 1 cos ( )

4

n n n n n n n n n

n n n

ij ij i j

ij

ij ij ij

W W W W W W

k b b k k m

q q

r r r

# of atoms # of atoms

i j i

Widely-used potentials having similar form to the above:

CHARMM potential (MacKarell, 1998)

AMBER potential (Duan et al, 2003)

GROMACS potential (Marrink et al, 2004)

Putting all the potentials together:


Other Lennard-Jones Potentials in LAMMPS

62


Embedded Atom Method (EAM) Potentials in LAMMPS

63

EAM potential (Daw and Baskes, 1984) many-body potential developed

primarily for the most common bcc and fcc metals (ie. Fe,Al,Cu), and their

metal alloys (ie. Ni-Al, Al-Cu, Co-Al, Cu-Zr)

Modified EAM (MEAN) potential (Baskes, 1992) more complex metal

alloys, also available for Si-C system


More Potentials in LAMMPS

64

(hydrocarbons, ie. CNT)

(oxides, ie. SiO2)

(colloids)

(electrostatic interaction)

(dipole-dipole interaction)

(add damping to the system)

(ellipsoids)

(granular materials)


More Potentials in LAMMPS

65

(ie. monodispersed microparticles)

(earliest potential for metals)

(continuum/brittle fracture)

(usually for intialization purposes)

(your name potential)

(well-known for Si-C, eg. CNT)

(models electrostatic screening)

(well-known for Si)

(good for chemical reactions)

(hydrocarbons)

Documents

Molecular Dynamics Simulations - Johnson Grouppuccini.che.pitt.edu/~karlj/Classes/CHE3935/MD_simulations.pdf · Molecular Dynamics Simulations . Professor Albert C. ... • Extract