Fundamentals of statistical mechanics
1
CHEM 6670
Computational Chemistry & Biophysics
Fundamentals of Statistical Mechanics
Feb 12, 2008
Course instructor: Dr. Jana Khandogin
[email protected]
Course web site:
http://ccb.ou.edu/teaching.aspx
Experiment, theory and simulation
Make
models
Real liquids
Model liquids
Wet
‐
lab
experiments
Computer
simulations
Approximate
theories
Experimental
results
Exact results
for models
Theoretical
predictions
2
compare
compare
Test of
models
Test of
theories
Allen & Tildesley
What is statistical mechanics
•
Relationship between microscopic dynamics of individual
particles and observed macroscopic properties
•
Mechanical properties:
Internal energy; conformation
Heat capacity; pressure etc
(depends on coordinates only)
Statistical
mechanics
6N variables!
A handful of variables!
3
•
Thermal properties:
Free energy;
Chemical potential, etc
(depends on volume and
evokes temperature)
Known:
Laws (Schrödinger or Newton’s equation)
describing particles and particle
‐
particle
interactions
Phase space
•
A classical system of N particles can be defined by 6 N variables
(3N position and 3N momenta).
•
Each combination of 3N positions and3N momenta can be
considered as a point (
microscopic state
Γ
) in the phase space.
•
The hamiltonian contains the momenta dependent kinetic
energy and the coordinate dependent potential energy
)
,...
,
;
,...
,
(
)
,
(
2
1
2
1
N
N
N
N
p
p
p
r
r
r
p
r
r
r
r
r
r
r
r
r
=
energy and the coordinate dependent potential energy.
4
∑
=
+
=
N
i
i
i
N
N
N
N
N
m
p
p
K
r
V
p
K
r
p
H
2
/
)
(
)
(
)
(
)
,
(
2
r
r
r
r
r

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