N n |n⟩ with k = 0, 1, 2, . . . , N -1 and |n⟩ being the states with excitation on molecule n and all other molecules staying in their ground states. The transition dipole moments from the aggregate ground state to the exciton states are ⃗ µ k=0 = √ N ⃗ µ mon and ⃗ µ k̸ =0 = 0, where ⃗ µ mon is the transition dipole moment of the monomer. Further, for the H-type arrangement (e.g. cofacially stacked molecules with parallel transition dipole moments), the |k = 0⟩ state is the upper state of the exciton band and, thus, the upper state is the only bright state in this model. The transition to the |k = 0⟩ state is expected to be blue-shifted with respect to the monomeric transition if the exciton coupling shift surpasses the van der Waals shift. Now, without periodic boundary conditions, the exciton states can be calculated by diagonalizing the Frenkel-exciton Hamiltonian Ĥ = n E mon |n⟩⟨n|+ m n̸ =m V mn |m⟩⟨n| (see, e.g., Refs. 79,80). E mon is the monomer excitation energy and V mn are the exciton couplings. Further, in PDM, for an H-aggregate, the exciton coupling between molecules m and n is given by V mn = µ 2 mon R 3 mn (R mn is the distance between point transition dipoles of molecules m and n, which build an angle of 90 • with R mn ). For the S 0 → S 2 transition of azobenzene, µ 2 mon = 8.13 (in atomic units) at the TD-ωB97X-D/def2-SV(P) level. In Fig. the spectra of the linear decamer (with d = 5.5 Å) calculated using PDM and TD-DFT (with the ωB97X-D functional) are shown. First of all, we find, that not only the upper state is bright, but also four other states have nonzero transition dipole moments, in contrast to the model with periodic boundary conditions. The bright states alternate with dark states. It is interesting to note that this alternation has been observed for other systems (brick-wall-type PTCDA aggregates) as well. Secondly, the exciton band width (or exciton splitting, which we define as the difference of the energies of the highest-and the lowest-energy exciton states) is much larger for PDM than for TD-DFT, 780 meV vs. 307 meV, respectively. This situation is also realized for shorter chains, see Tab. 1, where we list PDM, ωB97X-D, and CIS exciton band widths. Here and in what follows we select ωB97X-D and CIS methods since (i) they do not suffer from spurious, low energy CT problem, (ii) ωB97X-D performs well for the monomer (see Fig. ), and (iii) ab initio CIS is affordable wave function based method for excited states of large aggregates. Further, we note that it was also reported for other systems (acenes) that excition couplings calculated with PDM are larger than those calculated using the TD-DFT supramolecular approach. The red dashed line is a spectrum calculated taking into account lower and higher energy states obtained using TD-ωB97X-D/def2-SV(P) (these lower and higher energy states lie outside the shown energy window). The monomer S 0 → S 2 transition (shown in black) was calculated using the same, TD-ωB97X-D/def2-SV(P), level of theory, and the obtained excitation energy and transition dipole moment of this transition were used for PDM calculations. Further, we analyzed characteristics of the brightest exciton state for linear chains of varying length and different intermolecular separation. The state label, excitation energy, and oscillator strength of the brightest state calculated with TD-ωB97X-D/def2-SV(P) and CIS/def2-SV(P) are shown in Fig. . For relatively large separation distances (4-5.5 Å), the brightest state is excited state 2N , as expected in the molecular exciton model introduced above. For smaller distances, deviations from this expectation are observed. In particular, the brightest state carries a label larger than 2N (for longer chains) starting at 3.7 Å for TD-ωB97X-D calculations and 3.5 Å for CIS calculations. The reason for this deviation is that (i) exciton states arising from the monomer states higher than S 2 may appear below the brightest exciton (which, in turn, arises from monomeric S 2 ) and (ii) charge-resonance states (or states with admixture of charge transfer contributions) stemming from S 2 (or S 1 ) may also have lower energies than the brightest exciton. In turn, (i) is caused by large dispersive red shift and, moreover, the corresponding states may exhibit some appreciable CT character. As a simple example, the brighest exciton of the trimer 3.5 Å is S 8 at the TD-ωB97X-D level (instead of S 6 expected from Kasha's exciton model). Inspection of NTOs of the S 6 and S 7 states of the trimer reveals that these states correspond to the S 3/4 states of the monomer (see the NTOs in Fig. and). We also note that mixed transitions, involving n → π * and π → π * excitations, may also take place (see the NTOs of the S 0 → S 10 transition in Fig. ).