## 2 Materials and Methods: Model Excitonic Hamiltonian
These surfaces were then fitted with simple analytical expressions, so that, when working with an ensemble, one can readily retrieve the coupling values for any given pair of QD radii or QD-to-QD distance. Examples of maps of coupling terms are given in Figure S8 (Section 3 of the SI) for local-local, local-CT and CT-CT exciton pairs. As we numerically computed the Coulomb integrals, we do not separate the local-local Coulomb matrix elements into short (Dexter) range and long (Foster) range interactions [80]. Solving the one particle Hamiltonian, \(\hat{H}_{e/h}(\mathbf{r})\), for the electron and hole confined to spherical wells as a function of the QD radius provides the zero order excitonic structure necessary to build the matrix of the Hamiltonian for the dimer, Equation (3). In terms of electronic configurations, the non-coupled zero order excitons correspond to singly excited configurations. These are coupled by Coulomb interactions. The diagonalization of the electronic excitonic Hamiltonian, Equation (3), corresponds to a configuration interaction single (CIS) in terms of electronic states and provides the eigen excitons. The size distribution (see Figure S10, Section 3 of the SI) leads to a dispersion in the one particle energies and wave functions, which in turn leads to a dispersion in the energies of the excitons and  
Figure 2: Schematic representation of the eight zero order exciton states taken into account in the model for a QD\({}_{\text{A}}\)–QD\({}_{\text{B}}\) dimer. in the Coulomb couplings. At the level of the ensemble, one obtains excitonic bands (see Figure 1B), which can be made to overlap by tuning the diameter of two QDs in the dimer. When bands of excitons overlap, accidental resonances play a role in increasing the effective strength of the Coulomb coupling. We focus on these aspects below and show that the coherent energy and charge dynamics of the dimer could be observed by transient absorption spectroscopy. The magnitude of the different kinds of intra and interdot couplings governs the time scales of the coherence dynamics. In Figure 3, we report the intra and interdot coupling strengths for a heterodimer, with QD diameters D\({}_{\text{A}}\) = 2.35 nm and D\({}_{\text{B}}\) = 3.85 nm with 3% size dispersion, for two values of surface to surface distance, L, of L = 0.2 nm, approximately corresponding to the S-CH\({}_{2}\)-S dithiol ligand (Figure 3A) and L = 0.55 nm, corresponding to S-(CH\({}_{2}\))\({}_{3}\)-S, Figure 3B. In Figure 3, Coulomb couplings (Equations (4) and (5)) are grouped according to the nature of the pair of zero order excitons involved and the intra or interdot character of the Coulomb coupling. The sizes of the two QDs are tuned to obtain a resonance in energy between the local exciton, h2e\({}_{\text{B}}\) (exciton 4 in Figure 2) on the large dot, QD\({}_{\text{B}}\), and the CT state h1\({}_{\text{B}}\)-e\({}_{\text{A}}\) (exciton 7), as shown in Figure 1B, which favors the otherwise weak interdot coupling through accidental resonances. Qualitatively, the efficiency of inter dot Coulomb coupling depends on the overlap between the hole and electron wave functions localized on each QD separately, see Figure S2 in Section 1. The overlap is controlled by the surface to surface distance, L, and the exponentially decaying leakage of the hole and the electron wave functions outside of the QD, which decreases with the QD diameter. Therefore, the interdot couplings decrease with both the QD diameter (Figure S8, Section 3 of the SI) and L, as shown in Figure 3 for two L values. For a given size, the wave function of the electron, \(\phi_{e}(\mathbf{r})\), is less confined than the hole wave functions and \(\phi_{h2}(\mathbf{r})\) is less confinedthan \(\phi_{h1}(\mathbf{r})\). The Coulomb couplings can be assigned to different groups based on the nature of the excitons involved and the range of energy they span.