Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

148 Perturbation Theories for Fluids and Solids

6.4.2 WEEKS–CHANDLER–ANDERSEN PERTURBATION THEORY

In the Weeks–Chandler–Andersen (WCA) theory (Chandler and Weeks 1970,

Andersen et al. 1971, Weeks et al. 1971), the reference and perturbation parts of

the potential are

u

0

(r) =



u(r) − u(r

m

), r ≤ r

m

0, r ≥ r

m

u

1

(r) =



u(r

m

), r ≤ r

m

u(r), r ≥ r

m

, (6.69)

where r

m

is the position of the minimum of the potential. In this way, the reference

includes all the contribution to the repulsive forces. Then, introducing the cavity

distribution function y

0

(r) for the reference fluid

y

0

(

r

)

= g

0

(

r

)

e

βu

0

(

r

)

, (6.70)

for strongly repulsive reference potentials it is reasonable to ...