Before moving on, we note that this is not the first use of MFCC in the context of embedding. Apart from the PE model and the work by Söderhjelm et al., as mentioned above, the MFCC procedure has also been applied to frozen density embedding (FDE) by Jacob and Visscher 53 who presented a three-partition FDE (3-FDE) model. In this model, the density is mapped on a real-space grid, and the MFCC procedure can, therefore, be straightforwardly applied. However, the density can become negative in the cappinggroup regions, which is problematic for a model that employs density-functional exchangecorrelation kernels. To avoid this issue, special constraints are required to ensure positive densities. Benchmarks of the 3-FDE scheme showed good performance in terms of the quality of electronic densities and electrostatic potentials of peptides and proteins. It has also been used to investigate environmental effects in protein systems. One of the most important aspects of a classical embedding model is the ability to reproduce the electrostatic potential (ESP) created by the environment. For purely classical embedding, the ESP is the main factor determining the quality of the environment description. Figure shows the errors in the ESP of an insulin monomer relative to a DEC-MP2 59,60 /cc-pVDZ reference for two density-functional approximations and the PE and PDE potentials. The ESP errors are mapped onto a van der Waals (vdW) surface of the protein, with larger errors leading to saturated colors (blue or red). For this example, and in the following, an MFCC order of 2 was adopted (see figure ), since initial tests revealed that using larger orders did not provide substantial improvement (see the Supporting Information). The PDE-and PE-based ESPs are derived from fragment calculations using CAM-B3LYP 62 /cc-pVDZ, i.e., using the same basis set as was used in the reference MP2 calculation. As reported by Jakobsen et al., it is immediately apparent that large errors in the ESP are found when using the B3LYP functional. The poor reproduction of the ESP occurs due to severe self-interaction errors leading to incorrect delocalization of electrons, which may be exacerbated by the fact that there is not a stabilizing environment surrounding the protein. This highlights the need for using range-separated exchange-correlation functionals when treating large molecular systems. Accordingly, the range-separated CAM-B3LYP functional yields an ESP that is almost identical to the reference MP2-based ESP.