MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Homework #1 (page 1 of 2)
Simple MD code with Velocity Verlet algorithm
Write the simplest possible onedimensional “molecular dynamics code” for two particles
connected by a spring (Force = k(x
2
x
1
x
0
)) where
Δ
x=x
2
x
1
is the distance between particles,
x
0
is the equilibrium length of the spring.
Your code can have the following structure:
• Define the parameters of the system (k, x
0
, m
1
, m
2
), initial coordinates and velocities of the
particles in the system (x
1
0
, x
2
0
, v
1
0
, v
2
0
), initial time = 0, time of the simulation, and timestep
of integration,
Δ
t.
• Calculate initial force F
init
= k(x
2
0
x
1
0
x
0
)
•F
old
= F
init
, x
1
old
= x
1
0
, x
2
old
= x
2
0
, v
1
old
= v
1
0
, v
2
old
= v
2
0
• Time loop:
1. Calculate position at the current time
x
1
new
= x
1
old
+
Δ
t v
1
old
+
Δ
t
2
F
old
/2m
1
x
2
new
= x
2
old
+
Δ
t v
2
old

Δ
t
2
F
old
/2m
2
2. Calculate new forces
F
new
= k(x
2
new
x
1
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 Fall '11
 Zhigilei
 Force, Kinetic Energy, Mass, Molecular dynamics, Time loop, Calculate new velocities

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