1549380323-Statistical Mechanics Theory and Molecular Simulation

Problems 217

c. Express the average energy in terms of the radial distribution functiong(r)

and the new function ̃g(3)(r,s).

d. For isotropic systems, explain whyg(3)should only depend on the three dis-
tances|r 1 −r 2 |,|r 3 −r 2 |and|r 3 −r 1 |. Show, therefore, that in terms of
the variablesrands, the simplest distribution function can be expressed as
g ̄(3)(r,μ,ν), i.e., as a function of the three variablesr,μ, andν, wherer,μ
andνare given by

r=|r|

μ=|s+

1

2

r|+|s−

1

2

r|

ν=|s+

1

2

r|−|s−

1

2

r|.

(You do not need to obtain an explicit expression for ̄g(3).)