Scientific Computing & Modelling NV, Vrije Universiteit, Theoretical Chemistry, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands c

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1 Electonic Supplementy Mteil (ESI) fo Physicl Chemisty Chemicl Physics. This jounl is The Royl Society of Chemisty 2014 Suppoting Infomtion fo: Pedicting phosphoescent lifetimes nd zeo-field splitting of ognometllic complexes with time-dependent density functionl theoy including spin-obit coupling K. Moi, T. P. M. Goumns, b E. vn Lenthe b nd F. Wng c Ryok Systems Inc., Science nd Technology Systems Division, Tokyo Skytee Est Towe 1-1-2, Oshige, Sumid-ku, Tokyo , Jpn, moi@si.co.jp b Scientific Computing & Modelling NV, Vije Univesiteit, Theoeticl Chemisty, De oeleln 1083, 1081 HV Amstedm, The Nethelnds c College of Chemisty, Sichun Univesity, 24, South Section 1, Yihun Rod, Chengdu, Sichun, P. R. Chin Contents p. 2 Tble S1. Clculted ZFS nd ditive lifetime τ t the 4 levels of theoy, petubtive o full SOC, gs phse o COSMO solvtion. p. 3 Tble S2. CPU timings fo I(ppy) 3 clcultions t the 4 levels of theoy, petubtive o full SOC, gs phse o COSMO solvtion. p. 4 Tble S3. Clculted ZFS nd ditive tes nd lifetimes fo I(ppy) 3 with (p) comped with pevious theoeticl studies nd expeimentl dt. p. 5 Figue S1. Clculted ZFS nd τ t the COSMO + level fo sevel I(N^C) 2 (cc) nd Pt(N^C)(cc) compounds, comped to expeimentl dt. p. 6 Figue S2. Clculted ZFS nd τ t the 4 levels of theoy (petubtive o full SOC, gs phse o COSMO solvtion), comped to expeimentl dt. p. 7 Refeences 1

2 Tble S1. Clculted ZFS (cm -1 ) nd ditive lifetime τ (s) t the 4 levels of theoy, petubtive o full SOC, gs phse o COSMO solvtion. No. Compound Symmety E(ZFS) (300K) Gs COSMO Gs COSMO 1 [Rh(bpy) 3 ] 3+ C E E E E+03 2 [I(bpy) 3 ] 3+ C Pd(thpy) 2 C Pt(s1-thpy)(cc) C Re(pbt)(CO) 4 C Pt(thpy)(cc) C Pt(4,6-dFpthiq)(dpm) C Pt(4,6-dFppy)(cc) C Pt(pbt)(cc) C Pt(thpy) 2 C I(s1-thpy) 2 (cc) C I(btp) 2 (cc) C I(thpy) 2 (cc) C I(4,6-dFppy) 2 (pic) C I(piq) 3 C [Ru(bpy) 3 ] 2+ C I(biq) 3 C I(piq) 2 (cc) C I(pbt) 2 (cc) C I(4,6-dFppy) 2 (cc) C I(dm-2-piq) 2 (cc) C C 1 n/ n/ n/ n/ I(ppy) 3 C [Os(bpy) 3 ] 2+ D C 2 n/ n/ n/ n/ bbevition fo lignds sme s in min ppe. 2

3 Tble S2. CPU timings (s) fo I(ppy) 3 clcultions t the 4 levels of theoy, petubtive o full SOC, gs phse o COSMO solvtion. Gs COSMO No. of excittions b 20 (10/10) 40 (20/20) 4 20 (10/10) 40 (20/20) 4 No. of itetions c 15 (6/9) 16 (7/9) (6/9) 20 (11/9) 11 Totl CPU time CPU time/ itetion Clcultions wee un on dul hex coe Intel(R) Xeon(R) CPU 2.00GHz. b The numbes of singlet nd tiplet excittion used in e epoted within pentheses s (singlet/tiplet). c The numbes of itetions which wee needed fo singlet nd tiplet excittions in e epoted within pentheses s (singlet/tiplet). While the computtionl effot of is bout ten times smlle thn tht of fo given numbe of excittions, 1 the psoc ppoch uses tuncted spce fo the petubtion expnsion, nd consequently moe excittions e needed fo bette desciption of the spin-mixed excittions obtined in. Fo the choice of 40 (20 singlet + 20 tiplet) excittions in, which wee used in min ppe, the gin in computtionl efficiency ove with 4 spin-mixed excittions is educed. 3

4 Tble S3. Clculted ZFS (cm -1 ) nd ditive tes (s -1 ) nd lifetimes (s) fo I(ppy) 3 with (p) comped with pevious theoeticl studies 2, 3 nd expeimentl dt. 4 Method ΔE 1,2 ΔE 1,3 k 1 k 2 k 3 k v (300K) τ v (300K) /Gs t T E E E E /Gs t T E E E E /COSMO t T E E E E /COSMO t T E E E E /Gs t S E E E E /Gs t S E E E E Othe psoc ppoch t T 1,b E E E E Othe psoc ppoch t T 1 b,c E E E E Othe psoc ppoch t S 0 b,c E E E E Exp. d,e E E E E Exp. f,g E+05 h 1.6 h Exp. g,i E PW91/LnL2DZ(I):D95(est) in condensed phse with n Onsge model; ef 2. b Repoted vlues e coected fo the efctive index of CH 2 Cl 2 (n=1.42) ccoding to the Stickle-eg eltionship. c 3LYP/SDD(I):6-311G*(est) in gs phse; ef 3. d In PMMA; ef 4. e The veged ditive te is clculted by use of the thee individul ditive decy times nd of the zeo-field splitting vlues ccoding to Eq. (1) fo tempetue of 300K. f In THF; ef 4. g The individul ditive tes of the tiplet substtes e not vilble. The veged ditive te is clculted fom the emission quntum yield nd the decy time mesued t mbient tempetue ccoding to Eq. (2). h In 2-MeTHF; ef 4. i In CH 2 Cl 2 ; ef e v kv k1 k2e k PL k n k k ( E 1, 2 ( E 1,2 e ( E k e 3 1,3 ( E 1,3 (1) (2) 4

5 Figue S1. Clculted ZFS (top, in cm -1 ) nd τ (bottom, in s) t the COSMO + level fo sevel I(N^C) 2 (cc) nd Pt(N^C)(cc) compounds, comped to expeimentl dt. 4 5

6 Figue S2. Clculted ZFS (top, in cm -1 ) nd τ (bottom, in s) t the 4 levels of theoy (petubtive o full SOC, gs phse o COSMO solvtion), comped to expeimentl dt

7 Refeences 1 F. Wng nd T. Ziegle, J. Chem. Phys., 2005, 123, K. Nozki, J. Chin. Chem. Soc., 2006, 53, E. Jnsson,. Minev, S. Schde, H. Ågen, Chem. Phys., 2007, 333, H. Yesin, A. F. Rusch, R. Czewieniec, T. Hofbeck nd T. Fische, Cood. Chem. Rev., 2011, 255,