Handbook of Solvents - George Wypych - ChemTech - Ventech!

490 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
Thermodynamical properties
Paying attention again to calculations for acetone and chloroform, we would like to mention
two papers by the Regensburg group 113,114 exploiting molecular Ornstein-Zernike (MOZ)
theory and site-site Ornstein-Zernike (SSOZ) theory for the calculation of excess internal
energies. In the MOZ framework, the internal excess energy per molecule is computed by a
configurational average of the pair potential V acting between molecules:
ex ρ
E = ∫ ∫ ∫V(
R ) g( R ) dR d d
2 2 12, Ω1, Ω2 12, Ω1, Ω2 12 Ω1 Ω2
[8.134]
Ω
with ρ the density of molecules.
Using instead SSOZ, E ex can be directly calculated from the site-site distribution function,
g αβ, as:
∞ k k
πρ∫ ∑ ∑ αβ
0 α=
1 β=
1
() ()
ex
2
E = 2 g r V r r dr
αβ
[8.135]
where k is the number of sites per molecule.
In both cases the calculated values are in good agreement with experimental data and
with calculations done exploiting the Monte Carlo computer simulation. In this case, E ex can
be obtained as:
E
ex
N N k k
1 ε zzer
rf −1
0
= ∑ ∑∑∑Vαβ(
rαβ,
ij ) +
3
N
2ε + 1 4πε
r
i = 1 j > 1 α = 1 β=
1
rf
2 2
α β αβ,
ij
0 cutoff
[8.136]
where k is the number of sites per molecule, rαβ,ij is the distance between site α of molecule i
and site βof molecule j. Only pairs i,j of molecules for which rij