The Role of Double Excitations in Exciton Dynamics of Multiazobenzenes: Trisazobenzenophane as a Test Case

Molecular exciton dynamics underlie energy and charge transfer processes in organic multichromophoric systems. A particularly interesting class of the latter is multiphotochromic systems made of molecules capable of photochemical transformations. Exciton dynamics in assemblies of photoswitches have been recently investigated using either the molecular exciton model or supermolecular configuration interaction (CI) singles, both approaches being based on a semiempirical Hamiltonian and combined with surface hopping molecular dynamics. Here, we study how inclusion of double excitations in nonadiabatic dynamics simulations affects exciton dynamics of multiazobenzenes, using trisazobenzenophane as an example. We find that both CI singles and CI singles and doubles yield virtually the same time scale of dynamical exciton localization, ∼50 fs for the studied multiazobenzene. However, inclusion of double excitations considerably affects the excited state lifetimes and isomerization quantum yields.

Here, I is absorbance, E is excitation energy, N sn = 100 is the number of selected snapshots, N st is the number of excited singlet states (N st = 2; 5; 18; and 20 for monomer, CIS; monomer, CISD; ring, CIS ; and ring, CISD, respectively), E i,α and f i,α are the excitation energy and oscillator strength, respectively, for the S 0 → S i transition, for snapshot α, and γ = 0.18598 eV (1500 cm −1 ) is a broadening parameter

S5 Contributions of single and double excitations
The current state wave function can be written as a sum of the singles (S) contribution (in which we also include the contribution of the reference, unexcited determinant) and the doubles (D) contribution: The overall contribution of singles can then be quantified as i C (S) i

2
. This quantity averaged over a swarm of trajectories (for the ring at the CISD level) is plotted in Fig. S9, top.

FRQWULERIVLQJOHV FRQWULERIVLQJOHV FRQWULERIVLQJOHV
Figure S9: Ensemble-averaged contribution of singles (top panel) and fractions of trajectories with the contribution of singles in certain intervals (as defined in the legend) (bottom panel) for the ring at the CISD level.
It is seen that the contribution of singles is on average > 0.9.In addition, in Fig. S9, bottom, we plot fractions of trajectories with a certain contribution of singles, namely (i) smaller than 0.25, (ii) between 0.25 and 0.75, and (iii) larger than 0.75.Fraction (iii) is larger than 0.9 at all times, fraction (ii) reaches a maximal value of 0.03 at short times, and fraction (i) is 0.05 at the end of the simulation.Thus, single excitations clearly dominate the dynamics.Interestingly, fraction (i) at long times stems from trajectories with CNNC dihedrals oscillating near 90-100 • (see Fig. S8).The corresponding doubly excited states are expected to be the singlet correlated triplet pair (TT) states.S1 Further, one can perform more detailed analysis rewriting the wave function as: Here, we distinguish between the reference contribution (C 0 Φ 0 ), "singles 1" (S1) contribu- provide a minor contribution.Interestingly, for the ring, we see that singles 1 contribution is on average larger than singles 2 contribution at longer times (particularly, for CIS).In this regard, we note that orbital character changes with geometry, e.g., HOMO may acquire a substantial π character.This should be kept in mind when comparing to Fig. 2 of the main text (e.g., there a ππ * population of 0.2 is observed for the ring at the CIS level at 10 ps).Table S2: Fractions of trajectories (in % with respect to the total number of trajectories which reached the ground state) corresponding to three decay pathways: (i) cis -reactive pathway leading to the cis isomer, (ii) "reactive" trans -unreactive pathway through the "reactive region" (CNNC dihedral < 121 • ) leading to the trans isomer, and (iii) "unreactive" trans -unreactive pathway through the "unreactive region" (CNNC dihedral > 121

Figure S1 :Figure S2 :
Figure S1: Molecular orbitals of the monomer (left) and the ring (right) used in the active space.The calculations are done at the CISD ground-state optimized geometries.

FigFigure S4 :
Figure S4: Contributions of individual states to the ππ * band, calculated as I i (E) = 1 Nsn

Figure S5 :Figure S6 :Figure S7 :Figure S8 :
Figure S5: Example of a reactive CISD trajectory showing isomerization of one azobenzene unit.Top panel shows three CNNC dihedrals and the bottom panel the current state.

Figure S11 :Figure
Figure S10: Ensemble-averaged contributions of the reference, singles 1, singles 2, doubles 1, and doubles 2 groups.See text for the details.

Figure S13 :
Figure S13: Ensemble-averaged CNNC dihedral angles as a function of time for the reactive (left) and unreactive (right) trajectories.For the ring, in the case of unreactive trajectories, the minimal of the three CNNC dihedrals was used.

Table S1 :
Initial populations (at t = 0) according to the sampling method of the brightest state.