The ESP errors in Figure are shown on two vdW surfaces, one which is further away from the nuclei (surface scaling factor 2.0) and one which is much closer (surface scaling factor 1.0). For the former, the errors in the reproduction of the ESP are comparable between PE, PDE, and CAM-B3LYP with root-mean-square deviations (RMSDs) of about 6.2, 5.4, and 7.7 kJ/mol, respectively. At this distance, the multipole expansion used in the PE potential is convergent, and the performance of the PE and PDE potentials is therefore similar. Some differences can be expected from the use of different methods, i.e., MP2 for the reference and CAM-B3LYP for the PE and PDE potentials. When moving closer to the nuclei (surface scaling factor of 1.0), the CAM-B3LYP method gives the best reproduction of the ESP (RMSD: 10 kJ/mol), followed by the PDE potential (RMSD: 18 kJ/mol). The Beyond a better reproduction of ESPs, the major advantage of the PDE model over classical embedding models is the inclusion of exchange repulsion. The host-guest complex of 2,3-diazabicyclo[2.2.2]oct-2-en (DBO) chromophore inside cucurbit [7]uril (CB [7]) has previously been shown to suffer from electron spill-out, with excitation energies being extremely redshifted when using the PE model to describe CB [7]. For this system, we calculated reference excitation energies based on supermolecular time-dependent Hartree-Fock (TDHF) and compared them to PE-TDHF and PDE-TDHF excitation energies of the DBO molecule in CB [7] (see table ). When using a non-augmented basis set (cc-pVDZ), both PE-and PDE-TDHF accurately reproduce the two lowest singlet excitation energies, which appear at around 3.5 and 6.5 eV for the supermolecular TDHF calculation. Both PE-and PDE-TDHF slightly overshoot the excitation energies, more so for the second state than the first (0.10 and 0.15 eV using PE, and 0.05 and 0.10 eV using PDE), but are in good quantitative agreement with the supermolecular reference. Upon augmentation of the basis set with diffuse functions (aug-cc-pVDZ 64 ), the supermolecular TDHF excitation energies change only very slightly (less than 0.01 eV). Meanwhile, using PE-TDHF results in two extremely low-lying states at 1.5 and 1.8 eV, which are clearly unphysical. The correct behavior is restored by including exchange repulsion through the PDE model, which gives excitation energies that still are in good agreement with the supermolecular TDHF reference (the errors are the same as for cc-pVDZ). In this case, the problem with the PE model arises only when using diffuse basis functions since compact basis sets simply do not extend far enough into the environment to make the problem apparent. With the introduction of the MFCC method, the PDE model is now applicable to large biomolecular systems. As an illustrative example, we consider the case of the Nile Red chromophore embedded in the binding pocket of the β-lactoglobulin (BLG) protein. This system has been studied previously due to the strong solvatochromism of the Nile Red dye. Figure shows simulated one-and two-photon absorption spectra of Nile Red embedded in the protein and in the gas-phase. For the condensed-phase spectra, configurational sampling is included by extracting 125 snapshots from a QM/MM molecular dynamics (MD) trajectory. In all cases, the singlet excitation energies and associated one-and two-photon transition strengths are computed using the CAM-B3LYP functional along with the 6-31+G* basis set. Local-field effects are taken into account through the effective external field (EEF) method. The embedding-potential parameters are computed at the same level of theory.