University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
The extended system method for constant pressure V.
Summary
Equations of motion:
i
i
i
3
/
1
i
i
d
V
m
V
3
2
F
V
d
m
&
&
&
&
−
=
−
ext
int
P
P
V
M
−
=
&
&
Two systems of variables are used:
1.
Real variables should be used to calculate forces, energy, structural
parameters of the system.
2.
Scaled variables to simulate evolution of the system (perform MD
simulation).
The equation of motion for the volume is defined so that deviation of the
internal pressure from its average works as a negative feedback and
keeps the pressure around a constant.
The simulation is performed in a constantenthalpy – constantpressure
ensemble.
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Relation between the equations of motion expressed in real
coordinates r
i
(Andersen paper in J. Chem. Phys. 72, 2384, 1980)
and scaled coordinates d
i
(this handout):
i
1/3
i
d
V
r
&
&
=
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 Fall '11
 Zhigilei
 Energy, Kinetic Energy, Atomistic Simulations, Leonid Zhigilei

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