  Projection-based embedding offers a simple framework for embedding correlated
wavefunction methods in density functional theory. Partitioning between the
correlated wavefunction and density functional subsystems is performed in the
space of localized molecular orbitals. However, during a large geometry
change--such as a chemical reaction--the nature of these localized molecular
orbitals, as well as their partitioning into the two subsystems, can change
dramatically. This can lead to unphysical cusps and even discontinuities in the
potential energy surface. In this work, we present an even-handed framework for
localized orbital partitioning that ensures consistent subsystems across a set
of molecular geometries. We illustrate this problem and the even-handed
solution with a simple example of an SN2 reaction. Applications to a nitrogen
umbrella flip in a cobalt-based CO2 reduction catalyst and to the binding of CO
to Cu clusters are presented. In both cases, we find that even-handed
partitioning enables chemically accurate embedding with modestly-sized embedded
regions for systems in which previous partitioning strategies are problematic.
