Accurate Internal Conversion Rates from Mixed-Reference Spin-Flip Time-Dependent Density Functional Calculations

Understanding organic luminescent molecules necessitates accurate evaluation of electronic transition rates between molecular states. Among all relevant electronic transition processes, the kinetic rate of internal conversion (IC) is the most difficult one to predict reliably. IC rates are commonly evaluated using Fermi’s golden rule (FGR), with the ground and excited states typically described by density functional theory (DFT) and time-dependent DFT (TDDFT), respectively. However, this conventional DFT-TDDFT protocol often leads to pronounced underestimations of IC rates. To address this limitation, we examined various factors that affect the IC accuracy and proposed a hybrid computational strategy: using mixed-reference spin-flip TDDFT (MRSF) for geometry optimizations and frequency analyses, and using TDDFT to calculate nonadiabatic coupling matrix elements. Tests on 13 representative systems demonstrate that this strategy generally yields IC rates in much closer agreement with benchmark values. This improvement is achieved without sacrificing computational efficiency or requiring additional corrective treatments. The origin of this enhancement was further investigated in subsequent detailed decomposition analyses of the calculated IC rates, through which it was attributed mainly to the more reliable description of vibrational contributions within the MRSF framework. Finally, we demonstrated another advantage of this MRSF-based strategy: accurate IC rate calculations do not rely on the choice of coordinate systems, which may break down in the DFT-TDDFT protocol for some systems. Overall, this work provides a practical and broadly applicable approach for accurate FGR-based IC rate calculations.