Abstract
The photophysical properties of four representative Cu(i) complex crystals have been investigated using the combination of an optimally tuned one- and two-dimensional range-separated hybrid functional with the polarizable continuum model, and the thermal vibration correlation function (TVCF) approach. The calculated excited singlet–triplet energy gap, radiative rates and lifetimes match the experimentally available data perfectly. At 300 K, the reverse intersystem crossing (RISC) proceeds at a rate of kdir.RISC ≈ 106–8 s−1, which is 4–5 orders of magnitude larger than the mean phosphorescence rate, kP ≈ 102–3 s−1. At the same time, the ISC rate kdir.ISC ≈ 109 s−1 is again 2 orders of magnitude larger than the fluorescence rate kF ≈ 107 s−1. In the case of kdir.RISC ≫ kF and kdir.RISC ≫ kP, thermally activated delayed fluorescence should occur. Vibronic spin–orbit coupling can remarkably enhance the ISC rates by the vital “promoting” modes, which can provide crucial pathways to decay. This can be helpful for designing novel excellent TADF Cu(i) complex materials.
Highlights
Under the environment of the larger dielectric constants, the optimal u values were greatly reduced to the range of 0.0491– 0.0559 bohrÀ1 for the solid phase system, which is compared with the default u 1⁄4 0.47 bohrÀ1 for longrange corrected (LC)-BLYP
From the perspective of the equation of range-separated exchange (RS) functionals as shown in eqn (1), a smaller u value corresponds to a larger interelectronic distance, R12, where the description of exchange switches from the short-range DFT-type to the long-range exact-exchange (HF-type) or, in other words, an effective electron delocalization length; the previously optimal u values were found to decrease with increasing system size and conjugation length
We found that LC-BLYP*a*1⁄40:2;b1⁄40:8 signi cantly improves the accuracy of these
Summary
The thermally activated delayed uorescence (TADF) materials displayed by organo-transition metal complexes and organic molecules have attracted great attention because of the remarkable variability in their emission properties for organic light-emitting diodes (OLED).[1,2,3,4] Under electrical excitation, the singlet–triplet counter pairs of electrons and holes are weighted to recombine and yield excitons, resulting in 25% singlet excitons and 75% triplet excitons in the electroluminescence device according to spin statistics.[5,6,7] the energies of all triplet excitons (75%) are dissipated as heat in the conventional uorescent materials, which leads to a theoretical upper limit of 25% for the internal quantum efficiency (Fig. 1).[6,7] To obtain high-efficiency OLED materials, recent studies have found that TADF emitters can rely on efficient thermal upconversion from the triplet state T1 into an emissive singlet state S1 through reverse intersystem crossing (RISC), which in principle, causes the efficiency of exciton utilization to reach 100%.8–10. The timedependent density functional theory (TD-DFT) is a useful and reliable tool to compute the excited states of relatively larger systems and is considerably more computationally efficient.[14] the conventional (semi)local exchange–correlation (XC) functionals may fail completely in predicting the electronic structure in donor–acceptor CT systems.[15] In addition, for molecular crystals, the surrounding environment is substantially different from that of single molecules, ascribed to polarization effects, which is essentially a phenomenon related to nonlocal correlation These systematic errors are mainly attributed to the inappropriate XC introduction and the potential and density can be incorrect at asymptotically large distances.[16,17,18] Recently, the range-separated exchange (RS) density functional comprising a suitable xed amount of exactexchange (eX) has overcome the incorrect asymptotic behavior in the long-range limit, and provides an improved description of the excited-state properties.[16,17,18,19,20,21] Abramson et al.[22] reported the dielectric constant (3) in a “screened” RS functional by replacing the 1/R asymptotic behavior with the more general asymptotic 1/(3 Â R), which is required when the calculations are performed on the periodic crystals. The kr radiative decay rates are determined via the Einstein relationship and the kISC decay rates are quantitatively calculated using the thermal vibration correlation function (TVCF) rate theory in combination with the PCMtuned LC-BLYP method in the solid-state.[24,25,26,27,28,29] In addition, vibronic spin–orbit coupling (SOC) has been taken into account from the promoted vibration modes
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