Reviews in Computational Chemistry Volume 18

where we have used q Cl ¼ qNa. The charge that minimizes this energy is
ðwNa qNa ¼
JNa þ JCl wClÞ 2JNaClðrNaClÞ At large distances, J NaClðr NaClÞ approaches zero, and, if the w and J parameters
are taken from Eqs. [33] and [34], then
qNa ¼ ðw Na w ClÞ
JNa þ J Cl
Electronegativity Equalization Models 111
¼
1
2 ðIPNa þ EANa IPCl EAClÞ IPNa EANa þ IPCl EACl which gives qNa ¼ 0:391 e. Thus the model predicts a significant amount of
charge transfer, even at large distances. Similar errors in the dissociation limit
are seen with certain electronic structure methods. 155,156 A significant amount
of charge separation, and a consequent overestimation of the dipole moment,
can be found for large polymers as well. Reducing this charge transfer along
the polymer can be accomplished with the AACT and BCI models. 146,149,150 In
addition, when comparing fluctuating charge models with ab initio results for
water trimers, agreement was found to be much better for the model without
charge transfer, even after the charge-transfer model was reparameterized by
fitting to the ab initio three-body energies. 145
These and associated problems with overestimated charge transfer are a
general characteristic of EE-based models. Unfortunately, such errors cannot
be eliminated through parameterization; the problem is a side effect of
attempting to treat quantum mechanical charge-transfer effects in a purely
classical way. As with all empirical potentials, the use of fractional charges
is necessary for an accurate description of the electrostatic potential. Yet by
allowing fractional charge transfer, the EE model has no means of enforcing
the transfer of only an integral number of electrons between distant species.
Indeed, the neutral dissociation products for NaCl are correctly predicted by
the EE model, if the infinitely separated ions are constrained to have integer
charge (see Figure 3). This constraint is difficult to apply in practice, however.
As discussed recently by Morales and Martinez, 157 the EE-based models can
be viewed as analytically differentiable approximations to a more rigorous statistical
interpretation of UðqÞ, which is discontinuous at integer values of
charge transfer and correctly predicts zero charge transfer at infinite distance.
In chemically bonded systems, the assumption of partial charge transfer is not
as unrealistic as in ionic compounds, as electrons are delocalized across covalent
bonds. However, in these covalent cases the EE model effectively assumes
that the coherence length of a delocalized electron is infinite and does not
depend on the surroundings. It is for this reason that the polarizability of polymers,
for example, increases too quickly with chain length under the EE
model. 149 Molecular charge constraints can avoid problems at the dissociation
½45Š
½46Š