文档介绍：3. Semiempirical Potentials
Form of the Potential
In Chap. 2 we discussed the various attractive and repulsive contributions
to the overall intermolecular interaction. The long-range asymptotic behav-
ior of the attractive interactions can be represented as R−n (n ≥ 3), which
decreases rather pared with the repulsive contribution, which de-
creases rapidly, as exp(−bR). For large R values, the potential will therefore
follow an R−n dependence; for example, the interaction between two non-
polar molecules follows the well-known R−6 dependence. For small R values
(R → 0) there will be a strong repulsion. We now consider a functional form
for the intermolecular potential, which is relatively simple and contains only
a few, physically meaningful, adjustable parameters. In addition, we require
that it gives an appropriate description for the two limiting cases R →∞and
R → 0. The asymptotic behavior for R →∞was discussed for the various
different contributions in the previous chapter. If we summarize the various
contributions obtained from second-order perturbation theory, we obtain the
following equation:
V = Vexov + Vpol + Vind + Vdisp
∞∞∞
C ,n C ,n C ,n ()
A −bR − pol − ind − disp ,
= exp( ) Rn Rn Rn
n=3 n=6 n=6
where Cpol,n in the electrostatic term depends on the multipole moments of
the monomer. For a noble-gas–molecule interaction this term will be zero.
Equation () represents a convenient form for the intermolecular potential,
with several angularly dependent parameters (A, b ), which can be
associated with physical quantities such as the multipole moment Qlm and
the polarizability of a monomer αr,r . However, the asymptotic behavior for
R → 0 is not correct, since the ration of charges has not yet been taken
into account. An obvious problem is that, in the present form, Vpol,Vind and
Vdisp will e infinitely negative for R = 0. The problem arises because
all power series were derived for the condition R>(|rA + rB|)