Balancing the description of subsystems in wavefunction-in-DFT and DFT-in-lower embedding

Embedding methods rely on a careful balance between the description high- and low-level regions. I will discuss this issue in the context of wavefunction-in-DFT and DFT-in-lower embedding. First, for the case of projection-based wavefunction-in-DFT, the nature of the localized orbitals used to partition the wavefunction and DFT regions can change dramatically across a reaction coordinate. This can lead to qual. different embedded orbitals between geometries, resulting in unphys. cusps and even discontinuities in the potential energy surface. I present an even-handed framework for localized orbital partitioning that ensures that the span of the embedded orbitals is invariant throughout a geometry coordinate. Second, for the case of embedded mean field theory, I discuss cases where large errors manifest due to basis set superposition error or collapse of the SCF procedure. A d. matrix constraint formalism is introduced to correct these errors in a black-box manner.