Theories of phosphorescence in organo-transition metal complexes - from relativistic effects to simple models and design principles for organic light-emitting diodes

摘要

We review theories of phosphorescence in cyclometalated complexes. We focusprimarily on pseudooctahedrally coordinated $t_{2g}^6$ metals (e.g.,[Os(II)(bpy)$_3$]$^{2+}$, Ir(III)(ppy)$_3$ and Ir(III)(ptz)$_3$) as, forreasons that are explored in detail, these show particularly strongphosphorescence. We discuss both first principles approaches and semi-empiricalmodels, e.g., ligand field theory. We show that together these provide a clearunderstanding of the photophysics and in particular the lowest energy tripletexcitation, T$_1$. In order to build a good model relativistic effects need tobe included. The role of spin-orbit coupling is well-known, but scalarrelativistic effects are also large - and are therefore also introduced anddiscussed. No expertise in special relativity or relativistic quantum mechanicsis assumed and a pedagogical introduction to these subjects is given. It isshown that, once both scalar relativistic effects and spin-orbit coupling areincluded, time dependent density functional theory (TDDFT) providesquantitatively accurate predictions of the radiative decay rates of thesubstates of T$_1$ in phosphorescent organotranstion-metal complexes. Wedescribe the pseudo-angular momentum model, and show that it reproduces the keyexperimental findings. For example, this model provides a simple explanation ofthe relative radiative rates of the substates of T$_1$, which differ by ordersof magnitude. Special emphasis is placed on materials with potentialapplications as active materials in organic light-emitting diodes (OLEDs) andprinciples for the design of new complexes are identified on the basis of theinsights provided by the theories reviewed. We discuss the remainingtheoretical challenges, which include deepening our understanding of solventeffects and, vitally, understanding and predicting non-radiative decay rates.