Conservation laws, radiative decay rates, and excited state localization in organometallic complexes with strong spin orbit coupling

Conservation laws, radiative decay rates, and excited state localization in organometallic complexes with strong spin orbit coupling 1Scientific RepoRts | 5 10815 | DOi 10 1038/srep10815 www nature co[.]

www.nature.com/scientificreports OPEN received: 10 February 2015 accepted: 28 April 2015 Published: 30 June 2015 Conservation laws, radiative decay rates, and excited state localization in organometallic complexes with strong spin-orbit coupling B. J. Powell There is longstanding fundamental interest in 6-fold coordinated d6 (t26g ) transition metal complexes such as [Ru(bpy)3]2+ and Ir(ppy)3, particularly their phosphorescence This interest has increased with the growing realisation that many of these complexes have potential uses in applications including photovoltaics, imaging, sensing, and light-emitting diodes In order to design new complexes with properties tailored for specific applications a detailed understanding of the low-energy excited states, particularly the lowest energy triplet state, T1, is required Here we describe a model of pseudooctahedral complexes based on a pseudo-angular momentum representation and show that the predictions of this model are in excellent agreement with experiment - even when the deviations from octahedral symmetry are large This model gives a natural explanation of zero-field splitting of T1 and of the relative radiative rates of the three sublevels in terms of the conservation of timereversal parity and total angular momentum modulo two We show that the broad parameter regime consistent with the experimental data implies significant localization of the excited state Six-fold coordinated d6 (t 26g ) transition metal complexes, such as those shown in Fig.  1a,b, share many common properties These include their marked similarities in their low-energy spectra1, cf Table 1, and the competition between localization and delocalizsation in their excited states2 Beyond their intrinsic scientific interest, understanding and controlling this phenomenology is further motivated by the potential for the use of such complexes in diverse applications including dye-sensitized solar cells, non-linear optics, photocatalysis, biological imaging, chemical and biological sensing, photodynamic therapy, light-emitting electro-chemical cells and organic light emitting diodes1,3–6 As many of these applications make use of the excited state properties of these complexes a deep understanding of the low-energy excited states, particularly the lowest energy triplet state, T1, is required to enable the rational design of new complexes Coordination complexes where there is strong spin-orbit coupling (SOC) present a particular challenge to theory because of the need to describe both the ligand field and the relativistic effects correctly7 There has been significant progress in applying relativistic time-dependent density functional theory (TDDFT) to such complexes; but significant challenges remain, for example correctly describing the zero-field splitting7–11 There has been less recent focus on the use of semi-empirical approaches, such as ligand field theory7,8,12–14 However, semi-empirical approaches have an important role to play7,15 Firstly, they provide a general framework to understand experimental and computational results across Centre for Organic Photonics and Electronics, School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland, 4072, Australia Correspondence and requests for materials should be addressed to B.J.P (email: bjpowell@gmail.com) Scientific Reports | 5:10815 | DOI: 10.1038/srep10815 www.nature.com/scientificreports/ Figure 1.  The structures of two important pseudo-octahedral transition metal complexes: a) [Ru(bpy)3]2+ and b) Ir(ppy)3, where bpy is bipyridine and ppy is 2-phenylpyridyl Sketches of the π (c) and π* (d) orbitals of a bpy ligand with the reflection plane marked by the dashed line It is clear that these correspond to the bonding and antibonding combinations of singly occupied molecular orbitals of a pyridine radical whole classes of complexes Secondly, when properly parameterised they can provide accuracy that is competitive with first principles methods Thirdly, they can provide general design rules that allow one to effectively target new complexes for specific applications A long standing question in these complexes is whether the excited state is localized to a single ligand or delocalized2,7 The main semi-empricial approach to understanding organometallic complexes is ligand field theory Once all of the spatial symmetries are broken there is ligand field theory is limited to a perturbative regime near approximate symmetries, this makes an accurate description of localised excited states challenging In this paper we describe a semi-empirical approach, based on the pseudo-angular momentum approach that has found widespread use in, e.g., interpreting electron paramagnetic resonance experiments We derive conservation laws based on the total angular momentum (pseudo plus spin) that apply even when the pseudo-octahedral and trigonal symmetries are strongly broken These conservation laws imply selection rules for radiative emission We show that this model reproduces the experimentally measured trends in the radiative decay rates and excitation energies for all of the complexes for which we have data to compare with in the literature These trends are insensitive to the parameters of the model studied Finally, we show that for the wide parameter range compatible with experiment the pseudo-angular momentum model predicts significant localization of the excited state The pseudo-angular momentum model It has long been understood16 that the three-fold degenerate states can be represented by an l =  1 pseudo-angular momentum Perhaps the best known example of this are the t2g states of a transition metal in an octahedral ligand field In the d6 complexes considered here the t2g orbitals are filled, whereas the eg-orbitals are high lying virtual states Therefore we only include the t2g orbitals in the model described below Scientific Reports | 5:10815 | DOI: 10.1038/srep10815 www.nature.com/scientificreports/ EI,II [cm−1] Ir(biqa)3 Ir(ppy)3 (in PMMA) EII,III [cm−1] τI (1 / k IR ) [μs] τII (1 / k II R) [μs] τIII (1 / k III R) [µ s] 14 64 107 (114) 5.6 (5.7) 0.36 (0.38) 12.2 113 154 (175) 15 (17) 0.33 (0.34) Ir(ppy)3 (in CH2Cl2) 19 151 116 6.4 0.2 Ir(dm-2-piq)2(acac) 9.5–10 140–150 80–124 6.5–8.6 0.33–0.44 16 106 95 13 0.6 [Os(phen)]2(dppm)]2 + [Os(phen)2(dpae)] 21 92 100 10 0.7 Ir(piq)(ppy)2 16 91 64 10.5 0.3 Ir(4,6-dFppy)2(acac) 16 93 44 0.4 Ir(pbt)2(acac) 97 82 25 0.4 Ir(piq)2(acac) 87 47 0.3 [Os(dpphen)2(dpae)]2 + 19 75 92 0.7 [Os(phen)2(DPEphos)]2 + 16 68 104 14 0.9 [Os(phen)2(dppe)]2 + 19 55 107 12 0.9 2+ Ir(piq)2(ppy) 56 60 6.4 0.44 [Os(phen)2(dppene)]2 + 18 46 108 15 1.1 [Ru(bpy)3] 8.7 52 230 0.9 Ir(piq)3 11 53 57 5.3 0.42 Ir(4,6-dFppy)2(pic) 67 47 21 0.3 2+ 3.5 31 113 35 1.5 Ir(ppy)2(ppy-NPH2) Ir(thpy)2(acac) 21 188 19 1.8 Ir(ppy-NPH2)3 20 177 15 1.4 17 163 20 Ir(btp)2(acac) Ir(ppy)(ppy-NPH2)2 2.9 22 150 58 Ir(btp)2(acac) 2.9 11.9 62 19 Ir(s1-thpy)2(acac) 13 128 62 Ir(ppy)2(CO)(Cl)   0 (δ   0); whereas trigonal symmetry reduces the energy difference between the triplet and singlet basis states that contribute to state III (|Sy〉  and |Tx〉  for δ >  0) Thus the symmetry of the model dictates that kRI < kRII < kRIII , as is observed experimentally1,19,20, see Table 1 Finally, we turn to the question of localization in the excited state To measure this we define Ξψ = ∑ σ ψ a 0†σ a 0σ − † † (a1σ a1σ + a 2σ a 2σ) ψ , (12) where a m(†σ) annihilates (creates) a hole with spin σ in π orbital of the mth ligand Thus Ξ ψ measures the probability of the hole being found on ligand when the system is in state ψ—with Ξ ψ >  0 indicating localisation onto ligand and Ξ ψ   0 It is interesting to note that both Ξ II and Ξ III are non-zero for δ =  0 However, for δ =  0 states II and III are degenerate and Ξ II =  − Ξ III, consistent with trigonal symmetry Nevertheless, for δ >  0, one observes a rapid increase in Ξ II whereas Ξ III grows only rather slowly It is therefore clear that the pseudo-angular momentum model predicts significant localization of states I and II for values of δ compatible with the observed experimental results that kRI < kRII < kRIII and EI,II