Part and whole in wavefunction/DFT embedding

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Density functional theory (DFT)-based subsystem and embedding methods have found a widespread use in Quantum Chemistry. The combination of correlated wavefunction (WF) methods and density-based embedding methods is particularly promising for accurate descriptions of complex systems. Here, we address some conceptual issues in such WF/DFT methods concerning (1) the interpretation of wavefunctions and densities in these frameworks, (2) the interpretation of subsystem and supersystem density changes as a polarization of the electronic system, and (3) non-orthogonality effects between wavefunctions of ground and excited states in WF/DFT embedding making use of state-specific embedding potentials. Illustrative examples are provided to analyze the significance of these issues in practical calculations. We find that physically reasonable subsystem densities and subsystem dipole moments can often be obtained from subsystem calculations making use of typical setups in practice, in spite of formal issues that are in principle in conflict with such interpretations. For excited-state WF/DFT calculations, we demonstrate that orthogonality violations due to state-specific embedding potentials are usually small.