Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.7 Theoretical and computing modeling 477
the following integrals [8.110] and [8.111] between the limits r=r c and r=∞, and assuming
that g(r)=1 for r>r c:
E
N
βP
ρ
() ()
2
= 2πρ
∫vr
gr r dr
[8.110]
πβρ
= 1− ∫vr
() gr () r dr
2
3
3
[8.111]
As already mentioned above, the extent of “tail corrections” strongly depends on the
property under study. In the case of pressure, this correction can be very large; for example,
in the case of a Lennard-Jones potential truncated at r c=2.5σ, at conditions close to the triple
point, E/Nε=-6.12, to which the tail correction contributes -0.48, but βP/ρ=0.22, of which
-1.24 comes to the tail. The neglecting of the tail correction would lead to a strongly positive
value for pressure. 42
Usually, when a cut-off radius is exploited, for the calculation of the interaction between
a particle and the others, the “nearest-neighbor” convention is used. It means that, assuming
the particles of interest lie in a cell and that this basic unit is surrounded by
periodically repeated images of itself, a particle i lying on the central cell will interact only
with the nearest image of any other particle j. The interaction is then set to zero if the distance
between i and the nearest image is greater than r c. The usual assumption r c