Martini purdue universityhigh level course outline

Short Course on Molecular Dynamics Simulation

Lecture 2:

1. 2. 3. 4. 5. 6. 7. 8. 9.

Move All Atoms
to New
Positions

Molecular Dynamics Simulation	A. Martini	Last Updated 8/2009

Interaction Models

	Coulomb	EAM	Inter- atomic		Angle	Torsion	Out of Plane
	Coulomb	EAM	Reaction	Bond	Angle	Torsion	Out of Plane

	A. Martini	Last Updated 8/2009

Pair Potentials

Attractive

Molecular Dynamics Simulation	A. Martini	Last Updated 8/2009

– Lennard-Jones (n=12, m=6)

FLJr ()

−

dU r ( )

2⎛

⎜

A. Martini

0	r

ε

� Truncation
– The Lennard-Jones force (and similar models) decays rapidly with distance

– Significant computation time can be saved by neglecting pair interactions beyond a cut-off

U	LJ	,	t	(	r	)	=		⎛ 4 ε⎜⎜⎝		r ⎠	−⎛⎝		6		r	≤	r c
U	LJ	,	t	(	r	)	=		⎛ 4 ε⎜⎜⎝		0	−⎛⎝		6		r	>	r c

0

r c

Pair Potentials

1.	ε = ij				σ = ij
2.					σ ij		=	σ i		+
2.					σ ij		=	σ i
3.	ε ij	=	2 σ σ i 33 j			σ ij	=		σ i 6		+
			2 σ σ i 33 j								2
			σ i 6	+	σ 6						2
			σ i 6	+

� Coulombic interactions
– Included if electrostatics between atoms are significant
– Atomic charges qi and qj

Molecular Dynamics Simulation	A. Martini	Last Updated 8/2009

Coulombic Interactions

� Coulombic force decays slower than r-3

Molecular Dynamics Simulation	A. Martini	Last Updated 8/2009

– Electrostatic potential due to i is exclusively due to the fraction of qi that is not screened by the cloud– This fraction rapidly decays to zero

– But we want to evaluate the contribution from point charges, not screened charges

– So we correct for the screening clouds by
introducing a smooth, compensating charge density

=	+


							(	r	)	=	−		q i	( α π )			3 2	exp	(−	α r
U	Coulomb	=	1	∑k≠0	4 π	2 ρ ( ) exp						(−		k	2	4 α )
U	Coulomb	=	2 V	∑k≠0	k	2 ρ ( ) exp						(−		k	2	4 α )

Embedded Atom Model

Pair Potential	A. Martini

		Last Updated 8/2009

Embedded Atom Model

Molecular Dynamics Simulation	A. Martini	Last Updated 8/2009