Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?

The development of
approximate exchange-correlation functionals
is critical for modern density functional theory. A recent analysis
of atomic systems suggested that some modern functionals are straying
from the path toward the exact functional because electron densities
are becoming less accurate while energies are becoming more accurate
since the year 2000. To investigate this trend for more chemically
relevant systems, the electron densities in the bonding regions and
the atomization energies are analyzed for a series of diatomic molecules
with 90 different functionals. For hybrid generalized gradient approximation
functionals developed since the year 2000, the errors in densities
and atomization energies are decoupled; the accuracy of the energies
remains relatively consistent while the accuracy of the densities
varies significantly. Such decoupling is not observed for generalized
gradient and meta-generalized gradient approximation functionals.
Analysis of electron densities in bonding regions is found to be important
for the evaluation of functionals for chemical systems.