Smoother Semiclassical Dispersion for Density Functional Theory via D3S: Understanding and Addressing Unphysical Minima in the D3 Dispersion Correction Model

One of the most widely used and computationally efficient
models
that accounts for London dispersion interactions within density functional
theory (DFT) is the D3 dispersion correction model. In this work,
we demonstrate that this model can induce the appearance of unphysical
minima on the potential energy surface (PES) when the coordination
number of atoms changes. Optimizing to these artifactual structures
can lead to significant errors in determining the interaction energy
between two molecules and in estimating the thermodynamic properties
of the system. In several specific examples, such as Kuratowski-type
H2–NiKur and H2–PdKur clusters,
these local minima exhibited extremely high PES curvature, resulting
in incorrect estimations of harmonic frequencies and significant overestimations
of zero-point energy and enthalpy values. Although such erroneous
behavior of the D3 model is relatively rare, it can occur across a
wide range of chemical species, including molecules like the [Li(C6H6)]+ complex and the dispiro(acridan)-substituted
pyracene (DSAP) molecule. Our analysis reveals that the root of the
problem lies in the definition of the AB atomic-pair dependent C6AB coefficients in the D3 model. To address this
issue, we propose a reparameterization of the D3 model by introducing
a modified C6AB functional form that now depends
on the specific pair of considered atoms. This new model, termed D3-Smooth
(or D3S for short), is designed to smooth out the PES associated with
the dispersion correction. By doing so, we demonstrate that D3S eliminates
unphysical local minima while maintaining the quite satisfactory accuracy
of the parent D3 method in interaction energy benchmark sets. For
example, the RMS difference between using the D3(BJ) correction to
B3LYP and the D3S(BJ) correction across the large MGCDB84 data set
of nearly 5000 data points is only 0.12 kJ/mol. Similar results are
obtained for every other D3-corrected functional tested. Consistent
with this result, no significant improvement could be obtained for
the B3LYP-D3S(0) correction by reoptimizing the damping function.