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1 Electronic Supplementary Material (ESI) for Journal of Materials Chemistry C. This journal is The Royal Society of Chemistry 2016 Electronic Supplementary Information Understanding the efficiency drooping of blue organometallic phosphors: a computational study of radiative and non-radiative decay rates for triplets Qian Peng, Qinghua Shi, Yingli Niu, Yuanping Yi,* Shaorui Sun, Wenqiang Li, Zhigang Shuai* 1

2 Contents I. Methodology II. Tests of basis sets (Tables S1-S3). III. Tests of the solvent effect on geometrical relaxations (Table S4). IV. The orbital energy and molecular orbital composition (%) of FMOs at the optimized ground-state geometries for 1-5 (Table S4). V. Spatial plots of the selected frontier molecular orbitals at the optimized ground-state geometries for 1-5. (Figure S1). VI. The comparison of the calculated and experimental spectra of 3 at 77 K. (Figure S2) VII.The displacement vectors and wavenumbers of the vibration normal modes involved in the emission spectra. (Figure S3) VIII. The calculated Huang-Rhys factors versus the normal mode wavenumber at the ground state for 1-5. (Figure S4). IX. The transition energies (E, ev), electric transition dipole moments (, Debye) and the Ir-d orbital components of the transition configurations with (, d%) for the lowest ten singlet states (S n, n=1-10) and the first triplet state (T 1 ) at the ground-state optimized geometries for 1-5. (Figure S5) X. The derivation of the intersystem crossing rate formula from the general form to Equation (2). XI. Reorganization energies versus the normal mode wavenumbers for 1-5 (Figure S6). XII.Selected reorganization energy and the vibrational normal mode frequencies for 1-5 (Table S6). XIII. The selected bond lengths, angles and dihedral angles of the S 0 and T 1 states and the corresponding modification between the two states for 1-5. Tables S7-S11. 2

3 I. Methodology i) Radiative Decay Rate Constant and Emission Spectrum. The radiative decay rate constant was calculated by integrating over the whole emission spectrum, ( ) (, ) r T em T d (S-1) (S-2) Here P i is the Boltzmann distribution function of the initial state at certain temperature; is the nuclear vibrational wave function. is the electric transition dipole moment between two electronic states. By applying the fourier transformation for the delta function, the Eq. (2) can be written as the form of thermal vibration correlation function, (S-3) em (t,t ) Tr e i f Ĥ f e i iĥi (S-4) Analytical solution to Eq. (4) can be obtained by virtue of Gaussian integration. ii) Non-radiative Decay Rate Constants Based on the time-dependent perturbation theory and Born-Oppenheimer adiabatic approximation, the thermal average rate constant from the initial electronic state i with the vibrational quantum numbers v to the final electronic state f with the vibrational quantum numbers u reads: 3

4 2π H f vf, nv H n nvn, ivi, (S-5) f i Pi v H i f vf,iv E i iv E i fvf h E E vi, vf n, vn ivi nvn 2 H denotes the interaction between two different Born-Oppenheimer states, consisting of two contributions: SO r; Q Q r; Q Q Hˆ Hˆ Hˆ BO ivi i ivi i ivi (S-6) where BO Ĥ is the non-adiabatic coupling and H SO is in Eq. (57), and r and Q are the electronic and normal mode coordinates, respectively. For the organometallic complex, the spin-orbit coupling elements (>100 cm -1 ) are much larger than those in pure organic fluorescent molecules (<1.0 cm -1 ). 20 Therefore, it is reasonable to calculate the non-radiative rate constant ( nr ) by using the first-order perturbation rate formula. The intersystem crossing rate constant between two electronic states with different spin state can be expressed as, (S-7) Here ISC (t,t ) is the same thermal vibration correlation function with eq. 4. All the emssion spectrum, radiative and nonradiative decay rates equation are solved in MOMAP program. iii) Reorganization energy The reorganization energy for phosphorescence from the T 1 state to the ground state can be obtained from the adiabatic potential energy surfaces of the ground states: λ = E g (T 1 geometry) E g (S 0 geometry) (S-8) where E g (T 1 /S 0 geometry) is the ground-state energy at the T 1 /S 0 equilibrium geometry. Under the harmonic oscillator approximation, the reorganization energy can be also expressed as a summation over all the normal modes: 4

5 λ = 3n 6 λ = = 1 3n 6 = 1 3n ω2 Q2 = ħω S = 1 (S-9) Here, represent the frequency of the th normal mode at the ground state, and S and Q are the Huang-Rhys factor and the displacement along the th normal mode coordinate between the equilibrium positions of the ground state and the T 1 state. II. Tests of Basis Sets fac-ir(ppy) 3 is a typical Iridium(III) complex applied for OLED. Its geometry is very similar with those of the compounds in this study. Especially there are rich crystal structure data about it. So we firstly optimized the structure of fac-ir(ppy) 3 at the ground state by using the Los Alamos ECP (Lanl2dz) / Stuttgart Dresden ECP (SDD) for Ir(III) and 6-31g*/ 6-31g** for other light atoms and presented the results in Table S1. It can be seen that the Ir-N bonds are always overestimated by all basis sets while SDD is a little better than Lanl2dz; comparatively, the calculated Ir-C bonds are close to the experimental values. Interesting, the Ir-C bonds got by SDD are closer to the experiments in ref.s1 while the Ir-C bonds got by Lanl2dz are in better agreement with the values in ref.s2. Of course, 6-31g** is better than 6-31g* due to considering more basis functions. Therefore, we chose the basis set SDD for Iridium and 6-31g** for other light atoms in all the geometrical and electronic structure calculations for the compounds under study. Then, the spin-orbit coupling matrix elements (SOCME) were evaluated by adopting different basis sets on light atoms (H, C and N) in Ir(ppz) 2 (ppy) (see Table S2). The results indicate that 6-31G** is the best choices when considering the balance between computational cost and accuracy. We further compared SOCME and the transition dipole moment elements computed with Lanl2dz and SDD for Iridium coupled with 6-31G** for other atoms in Table S3. From Table S3, it can be seen that both SOC and got by Lanl2dz are smaller than those of SDD. Furthermore, we compared the radiative rate constants based on the electronic structure information and the transition dipole moment got by Lanl2dz/6-31g** and SDD/6-31g** 5

6 respectively and found the latter is much closer to the experiments. Therefore, all the electronic structure and properties calculations were performed by using SDD for Ir atom and 6-31G** for other atoms in this paper. S1. J. Breu, P. Stossel, S. Schrader, A. Staruhin, W. J. Finenzeller, H. Yersin, Chem. Mater. 2005, 17, S2. F. Garces, K. Dedeian, N. Keder, R. Watts, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1993, 49,

7 Table S1. Calculated bond lengths (Å) in the optimized ground state (the numbers in parentheses denote the various ppy ligands). Lanl2dz SDD Lanl2dz SDD Expt a) Expt b) /6-31g* /6-31g* /6-31g** /6-31g** Ir-N(1) Ir-C(1) Ir-N(2) Ir-C(2) Ir-N(3) Ir-C(3) Notes: a) reference S1; x ray; b) reference S2, x ray. Table S2. Calculated Spin-orbit coupling elements (cm -1 ) for 1 with B3LYP LR method with different basis sets on light atoms and SDD on Ir atom. ˆ E /ev SO 0 1, S H T ˆ SO x 0 1, y ˆ SO S H T S0 H T1, 6-31G G* G** G* z Table S3. Calculated spin-orbit coupling (SOC) and transition dipole moments of 1 from T 1 to S 0 using Lanl2dz/SDD on Ir atoms and 6-31G** on other atoms (C, H, N and F) Lanl2dz SDD SOC x: cm -1 y: cm -1 z: cm -1 x: cm -1 y: cm -1 z: cm Debye Debye 7

8 III. Table S4. Calculated bond lengths (Å) of the optimized S 0 and T 1 of compound 1 in gas phase and toluene solvent (the numbers in parentheses denote the ligands). In gas phase In toluene S 0 -geom T 1 -geom S 0 -geom T 1 -geom Ir-N(1) Ir-C(1) Ir-N(2) Ir-C(2) Ir-N(3) Ir-C(3) From Table S4, it is obvious that the gometry slight varies when going from in gas phase to toluene solvent. Based on the have optimized the S 0 and T 1 molecular geometries in gas phase and toluene solvent adopted in the experiments, the molecular reorganization energies were calculated to be 2213 cm -1 in gas phase and 2233 cm -1 in toluene, which are very close to each other. This indicates that the T 1 is insensitive to the solvent environment because its dipole moment (4.30 Debye) is similar to that of S 0 (5.16 Debye). Therefore, we neglected the solvent effect on the photophysical properties of the compounds investigated in the wor. 8

9 IV. Table S5. The orbital energy and molecular orbital composition (%) of FMOs at the ground state optimized geometries for compounds 1-5. Orbitals E(eV) Ir-d ppz-i- ppz-ii- ppy- Bond nature L *(ppy) 9 1 H d(ir) +(ppy)+ (ppz) H d(ir) +(ppy)+ (ppz) H d(ir) +(ppy)+ (ppz) H (ppy)+(ppz) Orbitals E(eV) Ir-d F 2 ppz-i- F 2 ppz-ii- F 2 ppy- Bond nature L *(F 2 ppy) 2 H d(ir)+(f 2 ppz)+ (F 2 ppy) H d(ir)+(f 2 ppz)+ (F 2 ppy) H d(ir)+(f 2 ppz)+ (F 2 ppy) H (F 2 ppz) + (F 2 ppy) Orbitals E(eV) Ir-d F 2 ppz-i- F 2 ppz-ii- F 2 ppz-iii- Bond nature L *(F 2 ppz) L *(F 2 ppz) L *(F 2 ppz) 3 H d(ir)+(f 2 ppz) H d(ir)+(f 2 ppz) H d(ir)+(f 2 ppz) H (F 2 ppz) H (F 2 ppz) H (F 2 ppz) Orbitals E(eV) Ir-d F 2 ppz-i- F 2 ppz-ii- F 2 pypy- Bond nature L *(F 2 pypy) 4 H d(ir)+ (F 2 ppz) H d(ir)+ (F 2 ppz) H d(ir)+ (F 2 ppz)+ (F 2 pypy) H (F 2 ppz)

10 H (F 2 ppz) + (F 2 pypy) H (F 2 ppz)+ (F 2 pypy) Orbitals E(eV) Ir-d F 2 pmpz I- 5 F 2 pmpz II- F 2 pmpy- Bond nature L *(F 2 pmpy) H H H d(ir)+ (F 2 pmpz)+ ( F 2 pmpy) d(ir)+ (F 2 pmpz)+ ( F 2 pmpy) d(ir)+ (F 2 pmpz)+ ( F 2 pmpy) H (F 2 pmpz)+ ( F 2 pmpy) H Notes: H and L denote HOMO and LUMO, respectively. d(ir)+ (F 2 pmpz)+ ( F 2 pmpy) 10

11 V. 11

12 12

13 Figure S1. Profiles of the selected frontier molecular orbitals at the optimized ground-state geometries for

14 VI. Emission (arbitrary unit) Exp. This wor Wave Length (nm) Figure S2. The comparison of the calculated and experimental spectra of 3 at 77 K. 14

15 VII. 15

16 Figure S3. The displacement vectors of the vibration normal modes mainly involved in the emission spectra for 1-5: index number (wavenumber) 16

17 VIII. Huang-Rhy Factor (a) Huang-Rhy Factor 0.6 (b) Normal Mode Wavenumber (cm -1 ) Normal Mode Wavenumber (cm -1 ) 0.6 (c) 0.6 (d) Huang-Rhy Factor Huang-Rhy Factor Normal Mode Wavenumber (cm -1 ) Normal Mode Wavenumber (cm -1 ) 0.8 (e) Huang-Rhy Factor Normal Mode Wavenumber (cm -1 ) Figure S4. The calculated Huang-Rhys factors versus the normal mode wavenumber at the ground state for

18 VIIII. Energy (ev) S 10 S 9 S 8 S 7 S 6 S 5 S 4 S 3 S 2 S 1 T 1 (0.52,47%) (0.54,46%) (0.10,51%) (0.28,42%) (0.20,50%) (0.13,49%) (0.93,50%) (1.78,40%) (0.48, 2%) (0.52,46%) (0.17,41%) (0.02,51%) (0.22,49%) (0.18,52%) (0.64,46%) (1.73,40%) (0.06,49%) (0.26,52%) T 1 (0.22,1%) (0.98,39%) (1.73,43%) (1.71,43%) (0.07,37%) (0.32,46%) (0.33,48%) (0.29,49%) (0.28,48%) (0.36,48%) (0.07,7%) (0.55,44%) (0.12,37%) (0.45,47%) (0.41,4%) (0.37,45%) (0.33,38%) (0.18,48%) (1.50,45%) (0.16,47%) (0.01,53%) (0.07,49%) (0.24,51%) T T (0.20,17%) 1 (0.21,16%) 1 T 1 (0.26,25%) (0.57,38%) (0.14,32%) (0.17,20%) (0.66,42%) (0.11,44%) (0.26,48%) (0.24, 5%) (1.27,30%) (0.24,44%) (0.28,47%) (0.13,12%) Figure S5. The transition energies (E, ev), electric transition dipole moments (, Debye) and the Ir-d orbital components of the transition configurations with (, d%) for the lowest ten singlet states (S n, n=1-10) and the first triplet state (T 1 ) at the ground-state optimized geometries for

19 X. Based on the first-order perturbation, the formula of intersystem crossing can be represented as 1 2 SO iif t 1 (0) isc H d e 2 t Zi f i ( t) h (S-10) where the correlation function (0) fi ( t) is a a K det 1 t F F D D det E 2 h f i (0) i ˆ ˆ f H i ih f i i T 1 T fi ( ) Tr e e exp K (S-11) where t f h (S-12) i t h i a b i/f, i/f, i/f i/f sin tan T A af S ais T B bf S bis E b a i i i/f, h i/f, i/f i/f, h i/f, i/f (S-13) (S-14) (S-15) (S-16) (S-17) (S-18) F T D D T T ES ES (S-19) F T S E T S E D D (S-20) B K A A B (S-21) In displaced oscillator model, S I (S-22) 19

20 i, f, (S-23) Then b b b f a f, f f, f tan h 2 f a f, f f, f cot h 2 i a i, i i, i tan h 2 (S-24) (S-25) (S-26) And i 1 T 1 T i t i t F K F D ED S (2n 1) ( n 1)e ne h 2 (S-27) And 1 Z i det a g det deta e K 1 (S-28) Here, n 1 h BT e 1 is the average number of the photons. So, 1 SO 2 is c H dtf t 2 h (S-29) where i t F t exp iif t S (2n 1) ( n 1) e n e i t (S-30) The real part of the function F t is even, and the imaginary part is odd. The integral is determined by the real part. The integral result in eq.(vii-21) is unchangeable when the variable t is replaced by -t. 1 isc H t i t S h SO 2 i t i t d exp 2 fi (2n 1) ( n 1)e ne (S-31) If S 1,and the short time approximation is adopted 20

21 e i t 1 1 it t (S-32) The analytic solution can be obtained 1 2π S SO 2 fi isc H exp h S n S n 2 (S-33) We can replace the frequency by the energy, 1 E n 2 h (S-34) The final form is obtained 1 π isc Eif H h E exp SO 2 if E 2 4 E (S-35) The broadening of Eq. (VII-27) is E. When E increases, the energy gap function, the rate of intersystem crossing, isc E if becomes broader. 21

22 XI. (cm -1 ) 1200 (a) Normal Mode Wavenumber (cm -1 ) (cm -1 ) 1200 (b) Normal Mode Wavenumber (cm -1 ) 1200 (c) 1200 (d) (cm -1 ) (cm -1 ) Normal Mode Wavenumber (cm -1 ) Normal Mode Wavenumber (cm -1 ) Normal Mode Wavenumber (cm -1 ) 1200 (e) (cm -1 ) Normal Mode Wavenumber (cm -1 ) Figure S6. Reorganization energies versus the normal mode wavenumbers for 1(a), 2(b), 3(c), 4(d), and 5(e). 22

23 XII. Table S6. Selected reorganization energy (cm -1 ) and the vibrational normal mode frequencies (cm -1 ) for

24 XIII. Table S7. the selected bond lengths (Å), angles ( ) and dihedral angles ( ) of the S 0 and T 1 states and the corresponding modification between the two states for 1. S 0 T 1 Δ(T 1 -S 0 ) S 0 T 1 Δ(T 1 -S 0 ) ppz-i L(Ir1-C2) A(C2-C5-C6) L(Ir1-N32) A(C6-C3-C7) L(C5-C2) A(Ir1-C2-C5) L(C7-C3) A(C6-C5-N36) L(N36-N32) A(C33-N32-N36) L(C5-N36) D(Ir1-C2-C5-N36) L(C34-C35) D(C4-C2-C5-N36) ppy L(Ir1-C12) A(C12-C15-C16) L(Ir1-N51) A(C16-C13-C17) L(C15-C12) A(Ir1-C12-C15) L(C17-C13) A(C16-C15-C52) L(C52-N51) A(C50-N51-C52) L(C52-C15) D(Ir1-C12-C15-C52) L(C49-C48) D(C14-C12-C15-C52) ppz-ii L(Ir1-C22) A(Ir1-C22-C24) L(Ir1-N37) A(C22-C24-C27) L(C24-C22) A(C27-C23-C26) L(C23-C26) A(C27-C24-N41) L(N41-N37) A(C38-N37-N41) L(N41-C24) D(Ir1-C22-C24-N41) L(C40-C39) D(C25-C22-C24-N41)

25 Table S8. the selected bond lengths (Å), angles ( ) and dihedral angles ( ) of the S 0 and T 1 states and the corresponding modification between the two states for 2. S 0 T 1 Δ(T 1 -S 0 ) S 0 T 1 Δ(T 1 -S 0 ) F 2 ppz-i L(Ir1-C2) A(C2-C5-C6) L(Ir1-N32) A(C6-C3-C7) L(C5-C2) A(Ir1-N32-C33) L(C6-C5) A(C6-C5-N36) L(N36-N32) A(C33-N32-N36) L(C5-N36) D(Ir1-C2-C5-N36) L(C34-C35) D(C4-C2-C5-N36) F 2 ppy L(Ir1-C12) A(C12-C15-C16) L(Ir1-N51) A(C16-C13-C17) L(C15-C12) A(Ir1-N51-C50) L(C16-C15) A(C16-C15-C52) L(C52-N51) A(C50-N51-C52) L(C52-C15) D(Ir1-C12-C15-C52) L(C49-C48) D(C14-C12-C15-C52) F 2 ppz-ii L(Ir1-C22) A(Ir1-N37-C38) L(Ir1-N37) A(C22-C24-C27) L(C24-C22) A(C27-C23-C26) L(C24-C27) A(C27-C24-N41) L(N41-N37) A(C38-N37-N41) L(N41-C24) D(Ir1-C22-C24-N41) L(C40-C39) D(C25-C22-C24-N41)

26 Table S9. the selected bond lengths (Å), angles ( ) and dihedral angles ( ) of the S 0 and T 1 states and the corresponding modification between the two states for 3. S 0 T 1 Δ(T 1 -S 0 ) S 0 T 1 Δ(T 1 -S 0 ) F 2 ppz-i L(Ir1-C2) A(Ir1-C2-C4) L(Ir1-N36) A(C37-C38-C39) L(C5-C2) A(C2-C5-C6) L(C6-C5) A(C7-C3-C6) L(N36-N40) A(C39-N40-N36) L(C5-N40) D(Ir1-C2-C5-N40) L(C7-C3) D(C4-C2-C5-N40) F 2 ppz-ii L(Ir1-C12) A(Ir1-C12-C14) L(Ir1-N32) A(C53-C33-C34) L(C15-C12) A(C12-C15-C16) L(C16-C15) A(C17-C13-C16) L(N32-N35) A(C34-N35-N32) L(N35-C15) D(Ir1-C12-C15-N35) L(C17-C13) D(C14-C12-C15-N35) F 2 ppz-iii L(Ir1-C22) A(Ir1-C22-C25) L(Ir1-N41) A(C42-C43-C44) L(C24-C22) A(C22-C24-C27) L(C24-C27) A(C26-C23-C27) L(N45-N41) A(C44-N45-N41) L(N45-C24) D(Ir1-C22-C24-N45) L(C26-C23) D(C25-C22-C24-N45)

27 Table S10. the selected bond lengths (Å), angles ( ) and dihedral angles ( ) of the S 0 and T 1 states and the corresponding modification between the two states for 4. S 0 T 1 Δ(T 1 -S 0 ) S 0 T 1 Δ(T 1 -S 0 ) F 2 ppz-i L(Ir1-C2) A(Ir1-C2-C4) L(Ir1-N30) A(C31-C32-C33) L(C5-C2) A(C2-C5-C6) L(C6-C5) A(C7-C3-C6) L(N30-N34) A(C33-N34-N30) L(C5-N34) D(Ir1-C2-C5-N34) L(C7-C3) D(C4-C2-C5-N34) F 2 pypy L(Ir1-C12) A(Ir1-C12-C14) L(Ir1-N49) A(C48-C47-C46) L(C14-C12) A(C12-C14-C15) L(C14-C15) A(C15-C56-C16) L(C15-N56) A(C49-N50-N51) L(C46-C51) D(Ir1-C12-C14-N50) L(C14-C50) D(C13-C12-C14-C50) F 2 ppz-ii L(Ir1-C20) A(Ir1-C20-C22) L(Ir1-N35) A(C36-C37-C38) L(C25-C22) A(C20-C22-C25) L(C20-C22) A(C24-C21-C25) L(N35-N39) A(N35-N39-C38) L(N39-C38) D(Ir1-C20-C22-N39) L(C21-C25) D(C23-C20-C22-N39)

28 Table S11. the selected bond lengths (Å), angles ( ) and dihedral angles ( ) of the S 0 and T 1 states and the corresponding modification between the two states for 5. S 0 T 1 Δ(T 1 -S 0 ) S 0 T 1 Δ(T 1 -S 0 ) F 2 pmpz-i L(Ir1-C2) A(Ir1-C2-N48) L(Ir1-N20) A(N48-C5-N49) L(C3-C2) A(C2-C3-C4) L(C3-C4) A(C3-C4-N49) L(N20-N24) A(C23-N24-N20) L(C3-N24) D(Ir1-C2-C3-N24) L(C4-N49) D(N48-C2-C3-N24) F 2 pmpy L(Ir1-C8) A(Ir1-C8-N47) L(Ir1-N39) A(C8-C9-C40) L(C8-C9) A(C8-C9-C10) L(C9-C40) A(C10-N46-C11) L(C40-N39) A(N39-N40-C41) L(C8-N47) D(Ir1-C8-C9-C40) L(C10-N46) D(N47-C8-C9-C40) F 2 pmz-ii L(Ir1-C14) A(Ir1-C14-C15) L(Ir1-N25) A(C14-C15-N29) L(C14-C15) A(C14-C15-C17) L(C15-N29) A(N51-C16-N50) L(N29-N25) A(N25-N29-C15) L(N51-C14) D(Ir1-C14-C15-N29) L(C17-N50) D(N25-N29-C15-C17)