An accurate theoretical framework for the optical and electronic properties of paracyclophanes

Abstract

Aromatic $π$-stacking interactions play an important role in both natural and artificial systems, influencing processes such as charge separation in photosynthesis and charge transport in organic semiconductors. Controlling the geometry and distance between aromatic units is therefore crucial for tuning intermolecular interactions and charge-transfer efficiency. Due to their well-defined stacking geometry, paracyclophanes (PCPs) composed of two or more aromatic units connected by rigid linkers, provide an ideal platform for a systematic study of such effects. Despite extensive experimental studies of PCPs, a comprehensive and quantitatively validated theoretical description linking the structure with the electronic and optical properties is still missing. Here, we present an extensive computational and experimental investigation of the electronic and optical properties of homo-PCPs containing naphthalene diimide (NDI) or pyrene chromophores linked by bridges of varying length and rigidity. We introduce a robust methodology for an accurate simulation of the absorption and fluorescence spectra of PCPs based on a combined TD-DFT and CC2 approach, achieving excellent quantitative agreement with experiment. We also present and validate a fragment-based description of PCPs using the Frenkel exciton model. Such approach is valuable not only for interpretation of the electronic and optical properties of PCPs, but it can also significantly reduce the cost of the calculation while maintaining the accuracy of the supermolecular approach. This work establishes a quantitatively reliable framework linking structure, excitonic coupling, and charge-transfer interactions in PCPs with optical properties, providing design principles for next-generation optoelectronic materials.

Figures (8)

• Figure 1: Chemical structure of the studied monomeric units. NDI units are represented in blue, and pyrene ones in red. The red capping groups of the linkers are present in the synthesized molecules used for the experimental measurements, however, for the theoretical calculations the groups highlighted in red are replaced by methyl groups. This does not influence optical or redox properties.
• Figure 2: Structures of the studied homo-paracyclophanes. Schematic representation of the paracyclophanes composed of two monomeric units and a linker (on the left) and the corresponding optimized structures at DFT level in implicit DCM solvent.
• Figure 3: Optical spectra and corresponding electronic excitations of the monomeric reference compounds.(a) Computed and experimental absorption and fluorescence spectra of NDI, pyrene and pyrene with tBuPh and Ada linkers. The computed spectra show excellent agreement with the experimental ones without inclusion of arbitrary shifts. The experimental spectrum for NDI-cyc-NDI was obtained from Ref. Wu2015, and for Pyrene-Et-Pyrene from Ref. Staab1979. (b) Transition densities and natural transition orbitals for the lowest excited states of the monomeric reference compounds. The experimental spectra $^{\ast}$ and $^{\#}$ for pyrene were taken from Ref. Gac2025 and Ref. Galisinova2013, respectively.
• Figure 4: Optical spectra and corresponding electronic excitations of the homoparacyclophanes.(a) Computed and experimental absorption and fluorescence spectra of NDI, pyrene and bis(aminomethyl)pyrene homo-paracyclophanes. (b) NDI and NDI-Ada-NDI PCP transition density for the corresponding lowest excited states. The green arrows represents the orientation of the transition dipole from the separate aromatic units. The lowest excited state of the H-type dimer is optically dark with unit transition dipoles oriented in opposite directions whereas the second excited state is bright with unit dipoles aligned. (c) Natural transition orbitals for the NDI and the second excited state for the NDI-Ada-NDI paracyclophane.
• Figure 5: Frenkel exciton model for the homo-paracyclophanes.(a) Representation of the Frenkel exciton Hamiltonian and decomposition into LE-LE and CT-LE blocks. (b) Representation of the paracyclophane as two separate units embedded in a dielectric environment. The blue area represents the solvent cavity. (c) Comparison of the exciton couplings between locally excited states computed from the Poisson-TrESP method and from diabatization of the supermolecule excited states with correlation coefficient 0.997. (d) Correlation between calculated LE-CT couplings and corresponding molecular orbital overlaps between the individual separate units with correlation coefficient of 0.983 and 0.964 for the NDI and Pyrene based PCPs, respectively.