Critical Assessment of Configurational Disorder Effects on Singlet–Triplet Gaps in a Metal–Organic Framework via QM/MM Calculations

Abstract

The singlet-triplet energy gap $(\Delta E_{\mathrm{ST}})$ is a key determinant of thermally activated delayed fluorescence (TADF) in organic and hybrid materials. Using hybrid quantum mechanics/molecular mechanics (QM/MM) calculations, we critically assess how configurational disorder of nitrogen atoms in a donor-acceptor metal-organic framework (MOF) influences $(\Delta E_{\mathrm{ST}})$ and related excitonic properties. Across nine disordered configurations, we find that the vertical gap at the experimental crystal geometry remains near-zero (< 0.6 meV) for all cases, reflecting the intrinsic charge-transfer character of the lowest excitations. However, upon full structural relaxation of the $(S_0), (S_1)$, and $(T_1)$ states, the adiabatic energy differences exhibit a wider distribution (ranging from −20 to +37 meV, depending on the functional), demonstrating that differential structural relaxation—driven by disorder—significantly modulates the excited-state landscape. The qualitative trends are robust across multiple density functionals, although the magnitude shows notable functional dependence—a finding that underscores the importance of method selection for charge-transfer-dominated systems. We identify three chemically intuitive structural descriptors—donor-acceptor separation, orbital overlap, and exciton localization—that correlate with $(\Delta E_{\mathrm{ST}})$, providing a practical framework for rational MOF design. This work provides a critical benchmark for QM/MM modeling of disorder in crystalline frameworks and establishes configurational disorder as a computationally accessible factor influencing singlet-triplet energetics.