3.1 Cyclometalated palladium and platinum complexes
3.1.2 Dimeric models
The solid-state behavior of the Pd and Pt complexes were studied computationally using dimeric models because experimentally it was shown that all complexes, except Pt-4, form dimeric structures with close metal-metal contacts in the solid state.III, IV Bond lengths for the (TD-)DFT optimized dimers in the ground state and lowest lying singlet and triplet excited states are given in Tables 4 and 5.
Table 4. Selected structural parameters for Pd-1-dim and Pd-2-dim.
Pd-1-dim Pd-2-dim S0 S1 T1 S0 S1 T1 bonds [Å]
M-M’ 3.353 2.907 2.862 3.511 2.919 3.523 M-Ncis 1.981 1.988 1.963 1.992 1.991 1.976 1.981 1.968 1.986 1.993 1.979 1.994 M-Ntrans 2.135 2.149 2.102 2.127 2.153 2.131 2.135 2.107 2.145 2.132 2.124 2.133 M-C 1.976 1.982 1.994 1.965 1.971 1.948 1.976 1.996 1.982 1.966 1.976 1.966 M-CCN 1.950 1.953 1.962 1.953 1.953 1.958 1.950 1.961 1.953 1.953 1.959 1.953
Table 5. Selected structural parameters for 1-dim, 2-dim, 3-dim and Pt-4-dim.
Pt-1-dim Pt-2-dim Pt-3-dim Pt-4-dim
S0 S1 T1 S0 S1 T1 S0 S1 T1 S0 S1 T1 bonds [Å]
M-M’ 3.458 2.925 2.861 3.508 2.905 2.858 3.423 2.875 2.816 - - - M-Ncis 1.984 1.983 1.981 1.992 1.993 1.988 2.012 2.002 2.001 1.994 1.994 1.994
1.984 1.992 1.982 1.993 1.992 1.988 2.011 2.013 2.002 1.999 1.974 1.978 M-Ntrans 2.110 2.104 2.110 2.102 2.126 2.121 2.132 2.137 2.139 2.118 2.120 2.118 2.110 2.130 2.111 2.104 2.117 2.112 2.120 2130 2.123 2.129 2.091 2.137 M-C 1.980 2.005 1.994 1.973 1.981 1.980 1.973 1.990 1.985 1.981 1.980 1.981 1.980 1.989 1.993 1.973 1.980 1.979 1.973 1.983 1.984 1.979 1.933 1.953 M-CCN 1.945 1.957 1.955 1.946 1.954 1.954 1.946 1.958 1.958 1.947 1.946 1.946 1.945 1.951 1.955 1.946 1.953 1.954 1.944 1.952 1.956 1.950 1.966 1.958 In the optimized ground state structures, metal-metal distances between 3.353 Å and 3.511 Å are predicted for M-1-dim, M-2-dim and Pt-3-dim. These predictions
35 are close to the experimental values, obtained with X-Ray diffraction measure-ments.III, IV All metal-ligand bond lengths are similar to the corresponding values obtained for the monomeric models and correlate well with the experimental data.
The M-Ncis bond length is again distinctly smaller than the M-Ntrans, due to the trans-influence induced by the cyclometalating carbanion. The M-CCN bond length is also slightly smaller than the M-C bond length, which can be attributed to π-backdonation from the metal ion to the cyanide moiety.
In the lowest lying singlet and triplet excited states, severe contractions in the met-al-metal distances are predicted by the TD-DFT optimizations for all dimers except the T1 structure for Pd-2-dim. Whereas the M-M bond length is virtually unaffected by the S0 → T1 excitation in Pd-2-dim, metal-metal distances ranging from 2.925 Å to 2.816 Å are predicted for the rest of the excited state structures in M-1-dim, M-2-dim and Pt-3-M-2-dim as an electron is excited from a metal centered d-d* orbital. For the metal-ligand bond lengths only very minor alterations are predicted upon exci-tation. To study the metal-metal interactions in the dimeric models, QTAIM anal-yses were performed for M-1-dim, M-2-dim and Pt-3-dim at the optimized S0, S1 and T1 state structures and the data is collected to Table 6.
36
Table 6. Properties of the electron density at the M-M BCPs in the dimeric mod-els. The properties are: ρ = the electron density at the BCP; ∇²ρ = the Laplacian of the electron density; |V|/G = the ratio between potential and kinetic energy den-sities; Eint = the interaction energy between the two atoms186 and δ(A, B) = elec-tron delocalization index between atoms A and B.
Complex State ρ [eÅ-3] ∇²ρ [eÅ-5] |V|/G Eint [kJ/mol] δ(A, B)
Pd-1-dim
S₀ 0.093 0.814 1.02 -11.4 0.14
S₁ 0.212 1.238 1.28 -29.8 0.28
T₁ 0.233 1.330 1.30 -33.6 0.30
Pd-2-dim
S₀ 0.072 0.630 0.94 -7.7 0.10
S₁ 0.210 1.233 1.27 -29.5 0.27
T₁ 0.070 0.617 0.94 -7.4 0.10
Pt-1-dim
S₀ 0.106 0.852 1.04 -12.7 0.17
S₁ 0.278 1.533 1.28 -37.4 0.37
T₁ 0.316 1.672 1.32 -44.5 0.41
Pt-2-dim
S₀ 0.097 0.793 1.02 -11.3 0.16
S₁ 0.287 1.628 1.28 -39.8 0.38
T₁ 0.319 1.707 1.32 -45.4 0.41
Pt-3-dim
S₀ 0.112 0.897 1.06 -13.7 0.18
S₁ 0.304 1.704 1.30 -43.3 0.39
T₁ 0.346 1.814 1.35 -51.2 0.44
In the ground state structures the metal-metal interactions are almost pure closed-shell interactions, indicated by the small electron densities at the BCPs and |V|/G ratios close to unity, with interaction energies being comparable to weak hydrogen bonds.187,188 Upon excitation, distinct strengthening in the metal-metal interactions is predicted for nearly all dimers as the interactions gain partial covalent character as indicated by the 2-3-fold increases in the electron densities, interaction energies and delocalization indices. In the T1 structure of Pd-2-dim, however, no such strength-ening in the metal-metal interactions is observed, which is to be expected, given the structural similarity between the S0 and T1 states of Pd-2-dim. In the isostructural M-1-dim and M-2-dim, the metal-metal interactions are slightly stronger in case of the platinum containing congeners, both in the ground and excited states.
The metal-metal interactions also drastically alter the photophysical behavior of the complexes. As predicted by the TD-DFT calculations, virtually all low-lying vertical excitations can be characterized as MMLCT transitions for every dimeric model containing metal-metal contacts (Table 7, Figure 16). Compared to the monomeric
37 models, the low-lying excitations for M-1-dim, M-2-dim and Pt-3-dim are also sig-nificantly redshifted with the change in the S0 → S1 excitation wavelength between 53 nm and 95 nm. For Pt-4-dim, the lack of metal-metal interactions results in no changes in the nature of the low-lying vertical excitations, as the transitions can be characterized as metal-perturbed π-π* transitions, just like in the monomeric model (Figures 14 and 16). The estimated excitation wavelengths are in close agreement with the experimental solid-state excitation data.III, IV
Table 7. Two lowest lying singlet-singlet and the lowest lying singlet-triplet ver-tical excitation for the dimeric Pd and Pt models. (λ = excitation wavelength, f = oscillator strength).
Complex Transition λ [nm] f Major contributions* Assignment
Pd-1-dim
S₀ → S₁ 476 0.0331 97 % H → L MMLCT
S₀ → S₂ 460 0.0000 97 % H → L+1 MMLCT
S₀ → T₁ 497 - 95 % H → L MMLCT
Pd-2-dim
S₀ → S₁ 409 0.0428 94 % H → L MMLCT
S₀ → S₂ 395 0.0001 92 % H → L+1 MMLCT
S₀ → T₁ 428 - 89 % H → L MMLCT
Pt-1-dim
S₀ → S₁ 511 0.0358 97 % H → L MMLCT
S₀ → S₂ 499 0.0000 98 % H → L+1 MMLCT
S₀ → T₁ 542 - 96 % H → L MMLCT
Pt-2-dim
S₀ → S₁ 440 0.0514 95 % H → L MMLCT
S₀ → S₂ 424 0.0001 94 % H → L+1 MMLCT
S₀ → T₁ 468 - 92 % H → L MMLCT
Pt-3-dim
S₀ → S₁ 448 0.0586 97 % H → L MMLCT
S₀ → S₂ 425 0.0005 95 % H → L+1 MMLCT
S₀ → T₁ 482 - 95 % H → L MMLCT
Pt-4-dim
S₀ → S₁ 399 0.0012 79 % H-1 → L d, π → π*
S₀ → S₂ 398 0.0039 50 % H → L+1, 38 % H → L d, π → π*
S₀ → T₁ 443 - 70 % H-1 → L d, π → π*
[*] H = HOMO, L = LUMO
38
Figure 16. Natural transition orbital hole-particle pairs for the low-lying vertical excitations in the dimeric Pd and Pt models.
Because of the highly distorted structures of the 3MC states for 1-mono and Pd-2-mono, it is argued that the solid-state packing severely restricts the formation of the metal-centered states in the aggregated state and thus gives rise to potentially emissive species. To estimate the solid-state emission behavior of the studied di-meric species, the energy differences between the lowest lying singlet and triplet states were first compared (Table 8).
39 Table 8. Energy differences between the lowest lying singlet and triplet excited states for the studied dimeric models.
Complex ΔE(S₁-T₁) [eV]
Pd-1-dim 0.12 Pd-2-dim 0.29 Pt-1-dim 0.18 Pt-2-dim 0.25 Pt-3-dim 0.22 Pt-4-dim 0.56
Pd-1-dim and Pt-1-dim are characterized with a ΔE(S1-T1) values of 0.12 eV and 0.18 eV, respectively. Such low energy differences could mean the possibility of TADF emission. For M-2-dim, Pt-3-dim and Pt-4-dim, the energy differences are some-what higher with calculated estimates between 0.22 eV and 0.56 eV. The increased energy differences and the relatively large Stokes shifts observed in the experi-mental emission spectra hint that these complexes decay with phosphorescence emission. The calculated phosphorescence data for M-2-dim, Pt-3-dim and Pt-4-dim is collected to Table 9.
Table 9. Calculated radiative rates, lifetimes, emission wavelengths and emissive state characters for the phosphorescence emission in M-2-dim, 3-dim and Pt-4-dim.
Complex kr [s-1] τ [μs] λ [nm] Assignment Pd-2-dim 7.25 · 103 138 523 d, π → π*
Pt-2-dim 1.38 · 104 73 698 MMLCT Pt-3-dim 1.37 · 103 728 717 MMLCT Pt-4-dim 5.96 · 103 168 543 d, π → π*
For Pd-2-dim, the T1 state is characterized as a metal perturbed π-π* state (Table 9, Figure 17) even though the lowest lying singlet-triplet vertical excitation from the ground state was of MMLCT character. The estimated emission wavelength is 523 nm and the radiative lifetime 138 μs. The experimental emission spectrum shows vibronic progression in the region between 550 nm and 660 nm, agreeing closely with the TD-DFT results.III The low radiative rate also explains the poor quantum yield (< 0.01) observed experimentally. The phosphorescence in Pt-2-dim and Pt-3-dim is assigned to 3MMLCT state with estimated emission wavelengths of 698 nm and 717 nm, respectively. Experimentally, these complexes show broad unstruc-tured bands at 618 nm and 660 nm, although it should be noted that Pt-3 is sensitive to mechanical stimuli, showing a mechanochemical transitioning from vibronic fine
40
structure to unstructured emission band as the sample is ground.III The 3MMLCT assignments for Pt-2-dim and Pt-3-dim fits the broad unstructured bands observed experimentally, even though the calculated emission energies are somewhat under-estimated. For Pt-4-dim, TD-DFT calculations predict a metal perturbed π-π* state as the emissive state (Figure 17) with estimated emission wavelength of 543 nm and phosphorescent lifetime of 168 μs (Table 9). The calculated prediction contradicts the experimental emission spectra, which shows unstructured emission band, in-dicative of charge-transfer character.III The experimentally observed emission be-havior of Pt-4 is, however, sensitive to grinding, which could indicate intermolecu-lar π-π interactions affecting the solid-state emission. Such interactions are not cap-tured by the theoretical model, explaining the difference in the calculated and ex-perimentally observed phosphorescence behavior.
Figure 17. Natural transition orbital hole-particle pairs for the phosphorescence emission in Pd-2-dim, Pt-2-dim, Pt-3-dim and Pt-4-dim.
Due to the small energy differences between the S1 and T1 states in Pd-1-dim and Pt-1-dim, a deeper look into the excited state dynamics was taken and so the ISC (and rISC) rates for these models were also calculated using the Marcus-Levich-Jortner method.189-191 For details of this approach, the reader is referred to the Sup-porting Information section of publication IV and references therein. In order to perform the normal mode analyses for the ISC rate calculations, the models were first reoptimized in the S1 and T1 states without the MM layers, but with restrictions imposed on the relative orientations of the two monomers based on the QM/MM optimizations. Following the subsequent optimization and frequency calculations, single point TD-DFT calculations were performed at the new geometries (Table 10).
41 Table 10. Calculated photophysical data (radiative rates, lifetimes and emission wavelengths) and excited state energy differences for Pd-1-dim and Pt-1-dim.
S1 → S0 T1 → S0
kr [s⁻¹] τ [ns] λ [nm] ΔE(S₁-T₁) [eV] kr [s⁻¹] τ [μs] λ [nm]
Pd-1-dim 4.45 · 106 225 647 0.11 7.47 · 102 1338 707 Pt-1-dim 3.50 · 106 286 764 0.18 3.98 · 103 251 882
The S1 state of Pd-1-dim, is characterized with a calculated prompt fluorescence rate of 4.45 · 106 s-1. However, with a ΔE(S1-T1) value of 0.11 eV and SOC matrix element of 12.3 cm-1, an ISC rate of 1.18 · 1010 s-1 is estimated, thus greatly exceeding the rate of prompt fluorescence, and resulting in an efficient population of the T1 state. For the T1 state, a radiative rate of 7.47 · 102 s-1 is calculated, but with the min-imized energy gap between the S1 and T1 states, a rISC rate of 3.03 · 108 s-1 is esti-mated, resulting in a TADF emission from a 1MMLCT state with estimated emission wavelength of 647 nm (Figure 18). For Pt-1-dim, TD-DFT calculations estimate a prompt fluorescence rate of 3.50 · 106 s-1, which is again greatly exceeded by the calculated ISC rate of 4.70 · 1010 s-1 with a ΔE(S1-T1) gap of 0.18 eV and <T1|HSO|S1> = 32.6 cm-1. The energy difference is, however, small enough to allow a nonzero rISC rate at 298 K, and indeed, a rISC rate of 7.22 · 104 is estimated for Pt-1-dim. Never-theless, the difference in the calculated ISC and rISC rates is almost six orders of magnitude, resulting in a phosphorescence emission from a 3MMLCT state with estimated lifetime of 251 μs and emission wavelength of 882 nm (Figure 18). The above considerations are in close agreement with the experimentally observed emission behavior for Pd-1 and Pt-1, even though the radiative rates and transition energies for the MMLCT transitions are clearly underestimated.IV
42
Figure 18. Natural transition orbital hole-particle pairs for the fluorescence emission in Pd-1-dim and phosphorescence emission in Pt-1-dim.