Nitrogen-doped molecular bowls as electron donors in photoinduced electron transfer reactions

In recent years, the chemistry of curved π-conjugated molecules has experienced a sharp rise. The inclusion of a heteroatom in the carbon network significantly affects its semiconducting properties. In this work, we computationally study the photoinduced electron transfer in a series of C60 fullerene complexes with experimentally established nitrogen-doped molecular bowls. Our results demonstrate that introducing nitrogen into pentagonal rings of the bowl-shaped π-conjugated molecules and extending the π-conjugation can modulate their electron-transfer properties. Among the studied complexes, the hub-NCor⊃C60 complex exhibits the most desirable combination of ultrafast charge separation and slow charge recombination, suggesting its potential use in photovoltaics.

2. Table S1. HOMO/LUMO energies and HOMO-LUMO (HL) gap for studied bowls in equilibrium and complex geometries.
p. S8 3. Table S2. Charge separation between the fragments in electronic ground state for studied complexes.
p. S8-S9 4. Table S3. Parameters of selected bond critical points related to the non-covalent interactions of the fragments in studied complexes.
p. S9-S11 5. Table S4. Main contributions of the Kohn-Sham molecular orbitals to the corresponding occupied and vacant natural transition orbitals.
p. S11 6. Table S5. Excitation energies, main singly excited configuration (HOMO(H)-LUMO(L)) and its weight, oscillator strength, extent of charge transfer or localization of exciton computed for studied complexes in DCM.
p. S12 7. Table S6. Relative energies and solvation energies calculated for studied complexes in DCM.

Energy decomposition analysis
The interaction energy in the gas phase was examined in the framework of the Kohn-Sham MO model using a quantitative energy decomposition analysis (EDA) [22][23][24] 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: (1) The term ∆V elstat corresponds to the classical electrostatic interactions between the unperturbed charge distributions of the prepared (i.e. deformed) fragments 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 interactions, ∆E oi , account for electron-pair bonding, charge transfer (i.e., donoracceptor interactions between occupied orbitals on one moiety and unoccupied orbitals on the other, including 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. 25,26

Analysis of excited states
The quantitative analysis of exciton delocalization and charge transfer in the donor-acceptor complexes was carried out in terms of the transition density. [27][28][29] The analysis was done in the Löwdin orthogonalized basis, which is more convenient.. The matrix  C of orthogonalized MO coefficients is obtained from the coefficients C in the original basis  C = S 1/2 C, where S is the atomic orbital overlap matrix. The transition density matrix T 0i for an excited state  * constructed as a superposition of singly excited configurations (where an occupied MO  i is replaced a virtual MO  a ) is computed, where A ia . is the expansion coefficient.
A key quantity (D,A) is determined by:

Solvent Effects
The equilibrium solvation energy of a molecule (in the ground or excited state) in the medium with eq S E the dielectric constant  was estimated using a COSMO-like polarizable continuum model [30][31][32][33] in the monopole approximation: where the f() is the dielectric scaling factor, , Q -the vector of n atomic charges in the 1 ( )      f molecular system, 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. 30,34 The GEPOL93 scheme 35 was used to construct the molecular boundary surface.
The charge on atom X in the excited state  i , , was calculated as: where  is the reorganization energy and G 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.
The Marcus expression is derived for the high-temperature condition, , for all vibrational modes ℏ ≪ l. The semi-classical description of ET 40,41 includes the effect of the quantum vibrational modes in an effective way, the solvent (low frequency) modes are treated classically, while a single high-frequency intramolecular mode , is described quantum mechanically. Because ET occurs normally from , ℏ ≫ the lowest vibrational level of the initial state, the rate k can be expressed as a sum over all channels connecting the initial state with the vibrational quantum number n = 0 to manifold vibrational levels of the final state, , where An effective value of the Huang-Rhys factor S is estimated from the internal reorganization energy  i , As seen, an additional parameter (as compared to the Marcus equation) enters the semi-classical expression -the frequency ω i of a vibrational mode that effectively describes the nuclear intramolecular relaxation following the ET. Typically, in organic systems (including fullerene and nanotube derivatives) the main contribution to the internal reorganization energy is due to stretching of C=C bonds (the corresponding frequencies are found to be in the range 1400-1800 cm -1 ). Thus, the effective frequency was set to 1600 cm -1 . We have demonstrated that varying the parameter ω i within a reasonable range does not change significantly the computed ET rate (Table S4).

Reorganization energy
The reorganization energy is usually divided into two parts,  =  i +  s , including the internal and solvent terms. The solvent reorganization energy corresponds to the energy required to move solvent molecules from the position they occupy in the initial state to the location they have in the CT state, but without charge transfer having occurred. The  s for a particular CT states was computed as a difference between the equilibrium (E eq , see eq. 6) and non-equilibrium (E neq , see eq. 8) solvation energies for states of interest. The internal reorganization energy  i corresponds to the energy of structural changes when donor/acceptor fragments going from initial-state geometries to final-state geometries.

Activation energy
The activation energies or the electron transfer reaction were computed based on traditional Marcus theory and can be expressed as:

Interaction energies
The interaction energies were calculated directly from the electronic energy of complex and electronic energies of subsystems. For Host⊃C 60 , the interaction energy can be expressed as follows: (14) 60 60 int ( )

Quantum Theory of Atoms in Molecules (QTAIM)
Topological analysis of the electron distributions was conducted using the "Quantum Theory of Atoms in Molecules" (QTAIM) approach proposed by Bader. 42,43 Electron density properties measured at the bond critical point (BCP, saddle point on electron density curvature corresponding to a minimum in the direction of the atomic interaction line and a maximum in two perpendicular directions) give information about the character of different chemical bonds. [44][45][46] The AIMALL suite of programs 47

Non-covalent interactions (NCI)
The NCI method 48-50 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. The NCI analysis was carried out at the CAM-B3LYP/Def2-SVP level using Multiwfn program. 51 Table S1. HOMO/LUMO energies and HOMO-LUMO (HL) gap (in eV) for isolated bowls in equilibrium geometry and their complexes with fullerene computed at CAM-B3LYP-D3(BJ)/def2-SVP//B3LYP-D3(BJ)/def2-SVP level of theory.

Supramolecular host-guest systems Bowl⊃C 60
Cor