Computational Characterization of Macrocyclic Compounds

Experimental details for the synthesis and purification of all compounds as well as characterization results confirming their identity and purity are provided in the ESI (see section 1.3 for compounds 1a–e, section 1.4 for precursors 2a–e, section 1.5 for precursors 3b–d, and section 1.6 for macrocycles BCyc-Et to PCyc-Hx†).
UV-vis absorption spectra were recorded on an Agilent Cary 60 UV-vis spectrophotometer at room temperature. The measurements were carried out with 5 μM solutions in CHCl₃ at a scan rate of 300 nm min⁻¹ and a data interval of 0.5 nm. Photoluminescence (PL) spectra were acquired on an Agilent Cary Eclipse fluorescence spectrophotometer with 5 μM solutions in CHCl₃ at a scan rate of 120 nm min⁻¹ and a data interval of 1 nm. The excitation and emission slits were set to 5 nm, the emission and excitation filters were set to ‘auto’ setting, and the detector voltage was set to ‘high’ (800 V). For PCyc-Et and PCyc-Hx additional spectra were recorded using ‘medium’ (600 V) detector voltage (ESI Fig. S44†), due to the peak of PCyc-Hx exceeding the maximum of 1000 counts with the ‘high’ setting.
Cyclic voltammetry measurements were performed in an argon atmosphere glovebox (LabStar, MBraun) using a PalmSens4 potentiostat controlled via Bluetooth connection in a standard three-electrode setup. Platinum disk electrodes of 2 mm diameter, a silver wire, and a platinum wire served as working, quasi-reference, and auxiliary electrodes, respectively. Small glass test tube vessels were used as open electrochemical cells. The electrolyte volume was below 0.4 mL. After the measurements, an arbitrary amount of ferrocene (internal reference) was added to the solution to evaluate the redox potentials of the studied compounds (ESI Fig. S45 and S48†). Cyclic voltammograms were fitted to simulated voltammograms using the DigiSim 3.03b software (Bioanalytical Systems). For steady-state voltammetry (ESI Fig. S47†), platinum disk ultramicroelectrodes of 25 μm diameter were used as the working electrode. Details for the EPR spectroelectrochemical measurements are provided in the ESI section 5.†Density functional theory computations considered singlet states of charge −6, −4, −2, −1, 0, +1, +2, +4, +6 as well as triplet states of charge −4, 0, +4. Geometries for these electronic states were optimized in vacuum using the PBE0 functional^{46,47 (link)} along with the def2-SV(P) basis set^{48 (link)} and the D3 dispersion correction^{49 (link)} in its optimized power parameterization.^{50 (link)} The nature of the stationary points as minima was verified using a finite difference Davidson procedure^{51 (link)} to avoid computation of the full ab initio Hessian.
Redox potentials were determined via single-point computations on the gas-phase optimized structures for the individual states using PBE0-D3 along with the def2-SVPD basis set (possessing additional diffuse basis functions) and including solvation effects using a conductor-like polarizable continuum model^{52 (link)} considering a dielectric constant ε of 10.125 to represent 1,2-dichloroethane. First, the ionization potential (IP) of a state of molecular charge (z) was computed according to
where G(z) corresponds to the total free energy in solution at the PBE0-D3/def2-SVPD level. No vibrational effects were included considering that a vibrational analysis was unfeasible for the largest systems considered and noting that vibrational effects are generally expected to play a minor role for redox potentials.^{53 (link)} Subsequently the redox potential for any given redox couple z₁/z₂ was computed aswhere e is the unit charge and E_ref is the absolute potential of the reference electrode (cf. ref. 53 (link)). A value of 4.70 V was used for E_ref. Redox potentials for the reductions were computed in complete analogy, only using the electron affinity instead of the IP. The values reported pertain to the redox couples (−6/−4), (−4/−2), (−2/−1), (−1/0), (0/+1), (+1/+2), (+2/+4), (+4/+6). These calculations were carried out in Q-Chem.^{54,55 (link)}Absorption wavelengths were computed using time-dependent DFT (TDDFT) with the ωPBEh functional^{46,56 (link)} (using 20% global Hartree–Fock exchange and ω = 0.1 a.u.) and the def2-SV(P) basis set and considering solvation in 1,2-dichloroethane (ε = 10.125, ε_∞ = 2.087). Approximate photoluminescence energies were computed at the triplet geometries, optimized via unrestricted Kohn–Sham (UKS) theory, considering that TDDFT geometry optimizations are not feasible for the largest systems considered here.
Nucleus independent chemical shifts (NICS)^{28 (link)} were computed at the PBE0/def2-SVP level using gauge including atomic orbitals^{57 (link)} as implemented in Gaussian 09.⁵⁸ NICS tensors were represented graphically using the VIST (visualization of chemical shielding tensors) method^{17 (link)} as implemented in TheoDORE 2.4^{59 (link)} and using VMD for rendering the figures.^{60 (link)} Additional current density computations were performed using the GIMIC 2.1.4 package^{25,35 (link)} in connection with PBE0/def2-SVP chemical shift computations in Turbomole 7.4.^61,62 These current densities were integrated along a plane bisecting the C<svg xmlns="http://www.w3.org/2000/svg" version="1.0" width="13.200000pt" height="16.000000pt" viewBox="0 0 13.200000 16.000000" preserveAspectRatio="xMidYMid meet"><metadata>
Created by potrace 1.16, written by Peter Selinger 2001-2019
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C double bond in a vinylene unit. Plots of the anisotropy of the induced current density (ACID) were computed using the AICD 3.0.3 program^{23 (link)} in connection with PBE0/def2-SVP computations in Gaussian 09.
The underlying computational research data is available via a separate repository (DOI: 10.17028/rd.lboro.14500482): geometries for the molecules studied in their different electronic states along with input/output files for characterization of stationary points, solvated calculations, vertical excitations, and NICS.