Describing Excited States of Covalently Connected Crystals with Cluster and Embedded Cluster Approaches: Challenges and Solutions

Understanding excited-state processes is essential for designing new functional organic materials. Modeling excited states in organic crystals is challenging due to the need to balance localized and delocalized processes and the competition between intramolecular and intermolecular interactions. Cluster models have proven highly effective for describing weakly interacting organic crystals; however, nonperiodic calculations on periodic systems must account for mechanical and electrostatic coupling to the crystal lattice, particularly in cases of extended coordination where covalent bonds are severed, such as in organic polymers and metal-organic frameworks (MOFs). Point charge embedding is a low-cost method for incorporating long-range electrostatics, enabling the consideration of long-range interactions using Ewald embedding. Small clusters have been effective for modeling excited-state processes in MOFs, yet embedding has rarely been included in such studies. In this work, we examine some of the challenges in describing excited states in covalently connected organic crystals using ONIOM(QM:QM') embedding techniques across systems with increasing coordination: diC₄-BTBT (an organic molecular crystal), polythiophene (an organic polymer), and two MOFs (QMOF-d29cec2 and MOF-5). We analyze the effects of using different electronic structure methods, including TDHF, TDDFT, ADC(2), and CC(2). One of the main challenges is that embedded cluster models are susceptible to overpolarization near the QM:QM' boundary. To address this, we assess the impact of different charge redistribution schemes (Z-<i>N</i> (<i>N</i> = 0, 3), RC, and RCD) and implement them in fromage. Additionally, we compare cluster and periodic models. We find that localized models effectively reproduce excited states in both nonconnected systems (diC₄-BTBT) and fully connected MOFs, whereas polythiophene remains the most challenging due to band conduction. The accuracy of vertical excitations, oscillator strengths, and simulated spectra is strongly influenced by model size, boundary charges, redistribution schemes, and level of theory. We further analyze the effect of vibrational broadening using the nuclear ensemble approach to predict the absorption and emission spectra of MOF-5. Our results provide a heuristic guide for nonperiodic studies of crystalline excited states, highlighting the remarkable relationship between molecular crystals and MOFs, which will be explored in the future work.