Next: Virial Expansion Up: Imperfect Gases and Liquids. Previous: Quiz Answers

Subsections

# Interaction Energy

## Methods For Configuration Integral Calculation

We need to calculate configuration integral

1.
Analytic methods:
(a)
Exactly solvable problems (ideal gas, ideal crystal, 2D-lattice and others)
(b)
Expansions around solvable models: virial expansion, high- and low-temperature expansions, imperfect solids...
(c)
Mean-field theories: neglecting fluctuations
(d)
Symmetry tricks--renormalization group etc.
2.
Computer simulation (Monte Carlo)

In all cases we need U.

## Pair Interactions

Assumption:
The total energy is the sum of pair interactions:

A good assumption for the majority of cases.
Symmetry:
For unstructured isotropic particles,

## Intermolecular Potential: Simple Case

Let us discuss non-polar neutral monoatomic molecules. Let r be the distance between them.

1.
Molecules cannot come too close:

2.
At large distances molecules do not interact

3.
Molecules repeal each other at small distances and attract at large distances.
4.
Exact result: at the energy is (dispersive forces)

Real Potential'':

Hard Core Potential:
The simplest one

Hard Core Plus Attraction:
Slightly more complex
 (2)

Lennard-Jones Potential:
The favorite among simulators

At potential behaves as -1/r6--correct. At potential diverges --correct.

Why 12? Because computers calculate x2 very fast!

## Intermolecular Potential: Other Cases

If you want to be realistic, you could add

• Complex interaction--Coulomb potential (very difficult!), dipole-dipole interactions, multipole terms...
• Bonds: chemical, hydrogen,...
• Realistic'' potentials--QM Computations (Computer only!)

Next: Virial Expansion Up: Imperfect Gases and Liquids. Previous: Quiz Answers

© 1997 Boris Veytsman and Michael Kotelyanskii
Thu Sep 18 22:50:29 EDT 1997