The supplementary materials for the article "Room-temperature quantum coherence of entangled multiexcitons in a metal-organic framework" by Akio Yamauchi et al. provide detailed mathematical models and computational methods used to study the dynamics of multiexcitons in a metal-organic framework (MOF). The key components include: 1. **Electron Spin Polarization Model**: A model considering molecular motions and exciton migrations in the TT and T+T states, where the quintet-triplet and singlet-triplet mixings are considered in the T+T states. The coupled stochastic-Liouville equations describe the dynamics of the system, including the effects of conformational changes between different states. 2. **Master Equation**: The master equation is derived to describe the time evolution of the density matrix, incorporating the effects of decoherence and relaxation processes. 3. **Transverse Magnetization in Pulsed EPR Measurements**: The computational methods for calculating the nutation profiles and echo-detected field-swept spectra of triplet pairs are detailed, including the treatment of off-resonance effects and the influence of molecular conformation on the EPR signals. 4. **Time-Dependent EPR Transition Energy**: The impact of fluctuating dipolar interactions due to changing dihedral angles on the EPR transition energy is discussed. 5. **Spectral Data and Model Comparisons**: Detailed comparisons of computed EPR spectra with experimental data, including the analysis of angle selectivity and the role of molecular conformation in quantum gates. 6. **THz Spectra and Conformational Motions**: THz spectra of the MOF are measured, and the influence of conformational motions on singlet-quintet population relaxation is discussed. 7. **Tables and Parameters**: Various tables provide parameters and matrix elements used in the computational models, including zero-field splitting parameters, conformational angles, and kinetic parameters. These supplementary materials provide a comprehensive foundation for understanding the experimental observations and theoretical models presented in the main article.The supplementary materials for the article "Room-temperature quantum coherence of entangled multiexcitons in a metal-organic framework" by Akio Yamauchi et al. provide detailed mathematical models and computational methods used to study the dynamics of multiexcitons in a metal-organic framework (MOF). The key components include: 1. **Electron Spin Polarization Model**: A model considering molecular motions and exciton migrations in the TT and T+T states, where the quintet-triplet and singlet-triplet mixings are considered in the T+T states. The coupled stochastic-Liouville equations describe the dynamics of the system, including the effects of conformational changes between different states. 2. **Master Equation**: The master equation is derived to describe the time evolution of the density matrix, incorporating the effects of decoherence and relaxation processes. 3. **Transverse Magnetization in Pulsed EPR Measurements**: The computational methods for calculating the nutation profiles and echo-detected field-swept spectra of triplet pairs are detailed, including the treatment of off-resonance effects and the influence of molecular conformation on the EPR signals. 4. **Time-Dependent EPR Transition Energy**: The impact of fluctuating dipolar interactions due to changing dihedral angles on the EPR transition energy is discussed. 5. **Spectral Data and Model Comparisons**: Detailed comparisons of computed EPR spectra with experimental data, including the analysis of angle selectivity and the role of molecular conformation in quantum gates. 6. **THz Spectra and Conformational Motions**: THz spectra of the MOF are measured, and the influence of conformational motions on singlet-quintet population relaxation is discussed. 7. **Tables and Parameters**: Various tables provide parameters and matrix elements used in the computational models, including zero-field splitting parameters, conformational angles, and kinetic parameters. These supplementary materials provide a comprehensive foundation for understanding the experimental observations and theoretical models presented in the main article.