Effect of choosing coordinate systems on computationally predicting nonradiative transition rates of flexible thermally activated delayed fluorescence molecules

Understanding nonradiative transition mechanisms is important in various situations. However, compared with radiative processes where temporal profiles of photon emission can be monitored in a straightforward manner, experimentally accessing the rate information may not be an easy task with nonradiative transitions. Hence, applying theoretical tools toward predicting the rates can be a useful tactic. Such predictions become very useful in designing optoelectronic materials as in the molecules adopted for constructing organic light-emitting diodes (OLEDs). The correlation function formalism is a method that can fulfill the purpose of designing OLED materials. The formalism requires information regarding the vibrational normal modes of the two electronic states before and after the transition. Because the method is also based on harmonic oscillator approximation, it can actually fail to provide high reliability when there is a large geometric distortion between the initial and the final states. In fact, the harmonic normal mode picture is more prone to lose reliability in the Cartesian coordinates than in the internal ones even at a small distortion, and hence adopting internal coordinates may be more preferable for practical calculations. This is because normal mode mixing becomes less severe when molecular coordinates are described with internal degrees of freedom such as bond stretching, bending, and torsion. In this regard, how much more reliable the nonradiative rate predictions in OLED materials become with the use of internal coordinate system deserves a close inspection. In this account, we review on the derivation of the correlation function formalism and provide how it can be adapted toward the use of the internal coordinates. As a demonstration, we evaluate the intersystem crossing and the internal conversion rates of a series of thermally activated delayed fluorescence (TADF) molecules with both Cartesian and internal coordinate systems. Overall, handling transitions involving substantial structural changes is improved indeed with the internal coordinates. However, limitations are still apparent for the TADF systems with a flexible donor–acceptor type construct especially when the inevitable inter-domain twisting takes place with the electronic transition. Future prospect for handling the issue is commented as a concluding remark.