Initiating Electron Transfer in Doubly Curved Nanographene Upon Supramolecular Complexation of C60

Abstract The formation of supramolecular complexes between C60 and a molecular nanographene endowed with both positive and negative curvatures is described. The presence of a corannulene moiety and the saddle shape of the molecular nanographene allows the formation of complexes with 1:1, 1:2, and 2:1 stoichiometries. The association constants for the three possible supramolecular complexes were determined by 1H NMR titration. Furthermore, the stability of the three complexes was calculated by theoretical methods that also predict the photoinduced electron transfer from the curved nanographene to the electron acceptor C60. Time‐resolved transient absorption measurements on the ns‐time scale showed that the addition of C60 to NG‐1 solutions and photo‐exciting them at 460 nm leads to the solvent‐dependent formation of new species, in particular the formation of the one‐electron reduced form of C60 in benzonitrile was observed.


General.
Unless otherwise noted, all materials including solvents were obtained from commercial suppliers and used without further purification. C 60 99.5 % was purchased from Solenne, toluene-d 8 99.6 % atom % D was purchased from Aldrich and NG-1 was prepared according to the procedure reported in the literature. 1 1 H NMR spectra of the titration were recorded at 300 (Bruker AVIII) MHz. 1 H NMR and 2D NMR spectra for the signals assignation were recorded at 500 (Bruker AV). Chemical shifts for 1 H NMR and 13 C NMR are expressed in parts per million (ppm) relative to the solvent. Data are reported as follows: chemical shift, multiplicity (s = singlet, bs = broad singlet, d = doublet), coupling constant (Hz), and integration.

Procedure
Complexation between curved NG-1 as host (Table S1, yellow) and C 60 as guest (Table S1, yellow) was performed by 1 H-NMR titration. In a NMR sample tube a 5x10 -4 M solution of NG-1 in toluene-d 8 was prepared. Sequential additions (4th column in Table S1) of a solution of C 60 (2x10 -3 M) and NG-1 (5x10 -4 M, added to maintain the concentration of NG-1 constant, table S1 3rd column) in toluene-d 8 were made. These additions led to the 1 H NMR spectra showed in figure S1 with chemical shifts values for protons H a , H b , H c and H d showed in green in table S1. Table S1. Experimental data of 1 H-NMR titration of supramolecular complexation between NG-1 and C 60 . Figure S1. 1 H-NMR spectra resulting for the sequential additions of C 60 .

Fitting models.
The calculation of association constants was made representing δ of each proton (Table S1 green columns) vs.
[G] 0 /[H] 0 (table S1 8th column) and fitting these points to the equations for changes of the 1 H NMR chemical shifts ∆δ of the corresponding stoichiometric model. 2 The fit was performed by using Pall Thordarson's Bindfit open source software with L-BFGS-B method. 3 2.2.1 1:1 Stoichiometry Figure S2. Association constants, mole fraction and fitting curves for 1:1 stoichiometry. Figure S3. Association constants, mole fraction and fitting curves for 1:2 stoichiometry. Figure S4. Association constants, mole fraction and fitting curves for 2:1 stoichiometry.

Analysis of excited states
The quantitative analysis of exciton delocalization and charge transfer in the donor-acceptor complexes is carried out in terms of transition density. [27][28][29] The analysis is convenient to perform in the Löwdin orthogonalized basis. The matrix λ C of orthogonalized MO coefficients is obtained from the coefficients C in the original basis λ C = S 1/2 C, where S is the atomic orbital overlap matrix. The transition density matrix T 0i for an excited state Φ * constructed as a superposition of singly excited configurations (where an occupied MO ψ i is replaced a virtual MO ψ a ) is computed where A i→a is the expansion coefficient and α and β are atomic orbitals.
A key quantity Ω (D,A) is determined by The weights of local excitations on D and A are Ω(D,D) and Ω(A,A). The weight of electron transfer configurations D→A and A→D is represented by Ω(D,A) and Ω(A,D), respectively. The index Δq, which describes charge separation and charge transfer between D and A, is

Solvent Effects
The equilibrium solvation energy eq S E of a molecule (in the ground or excited state) in the medium with the dielectric constant ε was estimated using a COSMO-like polarizable continuum model 30,31 in monopole approximation: , Q is the vector of n atomic charges in the molecular system, and D is the n x n symmetric matrix determined by the shape of the boundary surface between solute and solvent. D=B + A -1 B, where the m x m matrix A describes electrostatic interaction between m surface charges and the m x n B matrix describes the interaction of the surface charges with n atomic charges of the solute. [32][33][34] The GEPOL93 scheme 35 was used to construct the molecular boundary surface.
The charge on atom X in the excited state Φ i , i X q , was calculated as: where 0 X q is the atomic charge on X in the ground state and i X Δ is its change due to the redistribution of the electron density between the atoms X and Y which is caused by the excitation ψ 0 →ψ i .
The non-equilibrium solvation energy for excited state ψ i can be estimated as: 36 neq In Eq. (7), n 2 (the refraction index squared) is the optical dielectric constant of the medium and the vector Δ describes the change of atomic charges in the molecule by excitation in terms of atomic charges, see Eq. (6). By definition, the external (solvent) reorganization energy is the difference of the non-equilibrium (Eq. 7) and equilibrium solvation (Eq. 5) energies of the excited state.

Electron transfer rates
The rate of the nonadiabatic ET, k ET , can be expressed in terms of the electronic coupling squared, V 2 , and the Franck-Condon Weighted Density of states (FCWD): where λ is the reorganization energy and ΔG 0 is the standard Gibbs energy change of the process. The fragment charge difference (FCD) 38,39 method was employed to calculate the electronic couplings in this work.

Reorganization energy
The reorganization energy is usually divided into two parts, λ = λ i + λ s , including the internal and solvent terms. Solvent reorganization energy corresponds to the energy required to move solvent molecules from the position they occupy in the initial ground state (GS) to the location they have in the CT state, but without charge transfer having occurred. The λ s for particular CT states were computed as a difference between equilibrium and non-equilibrium solvation energies. The internal reorganization energy λ i corresponds to the energy of structural change when denoted fragments going from initial-state geometries to final-state geometries.

Energy decomposition analysis
The interaction energy in the gas phase is examined in the framework of the Kohn-Sham MO model using a quantitative energy decomposition analysis (EDA) [40][41][42] into electrostatic interactions, Pauli repulsive orbital interactions, and attractive orbital interactions, to which a term ∆E disp is added to account for the dispersion correction: The term ∆V elstat corresponds to the classical electrostatic interactions between the unperturbed charge distributions of the prepared (i.e. deformed) bases and is usually attractive. The Pauli repulsion, ∆E Pauli , comprises the destabilizing interactions between occupied orbitals and is responsible for any steric repulsion. The orbital interaction, ∆E oi , accounts for electron-pair bonding, charge transfer (i.e., donoracceptor interactions between occupied orbitals on one moiety and unoccupied orbitals on the other, including the HOMO-LUMO interactions) and polarization (empty-occupied orbital mixing on one fragment due to the presence of another fragment). The term ∆E disp accounts for the dispersion corrections. 43,44

Non-covalent interactions (NCI)
The NCI method 23,24 relies on two scalar fields to map local bonding properties: the electron density (ρ) and the reduced-density gradient (RDG, s), defined as: a quantity that is essential to the design of DFT functionals. The combination of s and ρ allows a rough partition of real space into bonding regions: high-s low-ρ corresponds to non-interacting density tails, lows high-ρ to covalent bonds, and low-s low-ρ to non-covalent interactions.      In order to estimate the effect of complexation on the excited state properties, we have compared the lowest-lying LE states of the studied complexes with the excited states of independent C 60 and NG-1 units. As seen from Table S7, the energetics of both LE types in the complexes is very similar to the lowest excited states energy in the corresponding monomers. The difference in energy has been found to be less than 0.1 eV. For all complexes, the excited state with maximum absorption is localized on the NG-1 fragment and lies at 3.8-3.9 eV. Despite the fact that in isolated NG-1 the highly absorptive state has a similar energy, it is characterized by a significantly stronger oscillator strength. The observed decrease in the oscillator strength can be explained by a change in the nature of such state. In all complexes, the excited state with high absorption is the mixed states with significant contributions of both LE and CT, while in isolated NG-1 no charge transfer processes are possible and these stats is purely LE. The greater contribution of CT, the weaker oscillator strength. Therefore, in isolated NG-1 the oscillator strength has the highest value.