Zero-Magnetic-Field Splitting in the Excited Triplet States of

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Zero-Magnetic-Field Splitting in the Excited Triplet States of Octahedral Hexanuclear Molybdenum(II) Clusters: [{MoX}Y] (X, Y = Cl, Br, I) 6

8

6

2–

Soichiro Akagi, Sho Fujii, and Noboru Kitamura J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b09339 • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 29, 2018

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The Journal of Physical Chemistry

Zero-Magnetic-Field Splitting in the Excited Triplet States of Octahedral Hexanuclear Molybdenum(II) Clusters: [{Mo6X8}Y6]2– (X, Y = Cl, Br, I)

Soichiro Akagi,† Sho Fujii,†,‡ and Noboru Kitamura†,‡,*

†

Department of Chemical Sciences and Engineering, Graduate School of Chemical Sciences and Engineering and ‡Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo,060-0810, Japan

Corresponding Author Noboru Kitamura E-mail: [email protected] Phone: +81-(0)11-706-2697 Fax: +81-(0)11-706-4630

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Abstract The temperature (T) dependences of the emissions from the tetra-n-butylammonium salts of [{Mo6X8}Y6]2– (X, Y = Cl, Br, and I) in optically transparent polyethyleneglycol dimethacrylate matrices were studied in the T range of 3–300 K. [{Mo6Cl8}Y6]2–, [{Mo6Br8}Y6]2–, and [{Mo6I8}I6]2– showed the T-dependent emission characteristics similar to other hexanuclear Mo(II), Re(III), and W(II) clusters reported previously, while [{Mo6I8}Br6]2– and [{Mo6I8}Cl6]2– exhibited the emission properties different from other [{Mo6X8}Y6]2– clusters. The photophysical behavior of these clusters was explained by the excited triplet state spin-sublevel (Φn, n = 1–4) model irrespective of nature of X and Y. The zero-magnetic-field splitting energies between the lowest (Φ1) and the higher-energy spin sublevels (Φ4 or Φ3) caused by the first- or second-order spin-orbit coupling, ΔE14 or ΔE13, were evaluated to be 620–870 or 50–99 cm–1, respectively. We found the linear correlation between the ΔE14 or ΔE13 value and the forth power of the atomic number (Z) of the inner halide X: ΔE14 or ΔE13 vs. {Z(X)}4 (correlation coefficient: cc = ~ 0.999). Furthermore, we also found the correlation between ΔE14 or ΔE13 and the 95Mo NMR chemical shift of the cluster. These findings gave very important aspect into the spin-orbit coupling and zeromagnetic-field splitting in the excited triplet states of transition metal complexes.

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Introduction An octahedral hexamolybdenum(II) cluster with the general formula of [{Mo6(μ3Q)8}L6]z–, where Q and L are the capping and terminal ligands, respectively (for the structure, see Chart 1), is known to show long-lived red phosphorescence.1–17 Besides the interesting phosphorescence properties, the clusters are thermally stable and, therefore, have attracted broad interests in the research fields of a solar cell,18,19 bioimaging20,21 and organic light emitting diodes (OLEDs).22–25 We recently reported the photophysical properties of a series of the hexanuclear metal clusters ([{Mo6Cl8}Cl6]2–, [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br, or I), [{W6Cl8}Cl6]2–, and [{Re6S8}Cl6]4–) in the crystalline phases or polymer matrices were dependent largely on zero-magnetic-field splitting (zfs) in the excited triplet (T1) states of the clusters.26–29

Chart 1. Structure of an octahedral molybdenum(II) cluster and the abbreviations of the cluster samples. In these clusters, the lowest-energy excited singlet (S1) state produced upon photoexcitation undergoes intersystem crossing (ISC) to the T1 state by spin-orbit coupling 2 ACS Paragon Plus Environment


(SOC), by which the spin momentum change (i.e., spin quantum number (n) change) upon ISC is compensated by the angular momentum (i.e., azimuthal quantum number (l > 1) change. Since the heavier is the atom (i.e, large atomic number (Z)) composed of a complex, the larger is the strength of the magnetic-field generated by the excited electron motions in the relevant atomic orbital with l. Therefore, although the three spin-sublevels in the T1 state of an ordinary molecule is degenerated in energy, the T1 state of a transition metal complex having a heavy metal atom(s) experiences large SOC, resulting in the energy-splitting of the degenerated T1 state into spin-sublevels (Φn) due to the generated large zero-magnetic-field. Since each Φn possesses the inherent emission energy (ṽn), radiative rate constant (krn), emission lifetime (τn), and quantum yield (Φem), a transition metal complex with a large Z atom(s) sometimes show large temperature (T)-dependent ṽem, τem, and Φem, reflecting the thermal Boltzmann distributions between Φn. The first experimental demonstration for the zfs energies of a transition metal complex was reported by Crosby et. al on [Ru(bpy)3]2+ (bpy = 2,2’-bipyridine) and they reported that the zfs energy between the lowest-energy (Φ1) and higher-energy-lying Φ2 (ΔE12) or Φ3 (ΔE13) was 0.1 or 62.1 cm–1, respectively.30 Later, several research groups reported zfs in the T1 states of transition metal complexes. As an example, the ΔE13 values of [Rh(bpy)3]3+, [Pt(bpy)2]2+, [Ir(4-phenylpyridine)3]2+ and [Os(bpy)3]2+ have been reported to be ~0, 0.1, 151, and 210 cm–1, respectively.31–34 Although these studies cover d6 and d8 transition metal complexes, the factors governing zfs in the T1 state have not been cleared yet. Therefore, systematic studies on the evaluation of zfs energies and the effects of nature of the constituted atom(s) in a transition metal complex on zfs energies are absolutely necessary to understand


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the emission characteristics of a transition metal complex in the T1 state. Among various transition metal complexes, we have focused on the T1 states of [{Mo6X8}Y6]2– clusters (X, Y = Cl, Br, or I), since one can introduce arbitrary X and/or Y (atomic number, Z: Cl = 17, Br = 35 or I = 53) to the cluster. Furthermore, we have already reported the T-dependent emission characteristics and the ΔE1n values of [{Mo6Cl8}Cl6]2–, [{W6Cl8}Cl6]2–, [{Re6S8}X6]2–, and [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br, or I).26,27 It is worth noting that we have also found the linear correlations between ΔE1n (n = 3 or 4) values of [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br, or I) and {Z(X)}4,27 suggesting that the strength of SOC of the cluster is determined primarily by nature of the face-capping ligand. However, since the photophysical properties of the cluster are also affected largely by the terminal ligands,1–17 the factors governing zfs in the T1 state of the cluster is worth studying in more detail. In the present paper, we report the T-dependences (3–300 K) of the emission properties of nine [{Mo6X8}Y6]2– (X, Y = Cl, Br, or I) clusters dispersed homogeneously in polymer matrices and the zfs parameters in the T1 states of the clusters evaluated by the Φn model in Chart 2.26,27 As the important findings of the present research, both face-capping (X) and terminal ligands (Y) played important roles in determining zfs as revealed by a systematic study on the photophysical properties of a series of [{Mo6X8}Y6]2–. Furthermore, we report for the first time that the ΔE1n (n = 3 or 4) values of a series of the clusters correlate very well with both {Z(X)}4 (X = Cl, Br, or I) and the 95Mo NMR chemical shift of the cluster as a measure of the effective nuclear charge on the Mo atom in [{Mo6X8}Y6]2–.



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Chart 2. Excited triplet state spin-sublevel models for the emission from [{Mo6(μ3Q)8}L6]z–.26,27

Experimental The tetra-n-butylammonium (TBA) salts of [{Mo6Cl8}Y6]2– (Y = Cl (1), Br (2), I (3)), [{Mo6Br8}Y6]2– (Y = Cl (4), Br (5), I (6)), and [{Mo6I8}Y6]2– (Y = Cl (7), Br (8), I (9)) used in the present study were essentially the same with those reported previously.17 Polyethyleneglycol dimethacrylate 550 and ethanol were purchased from Sigma-Aldrich Co., Ltd. and Japan Alcohol Trading Co., Ltd., respectively, and were used as supplied. Other reagents were obtained from Wako Pure Chemical Co., Ltd. and used without further purification.

Polyethyleneglycol

dimethacrylate

(PEG-DMA)

block

samples

of

[{Mo6X8}Y6]2– (1–9) were prepared by the similar procedures to those reported in the previous paper,27 and the sample concentrations in PEG-DMA matrices were set at ~5×10–5 mol/dm3 to prevent intermolecular interactions between the clusters. Temperature-controlled (3 < T < 300 K) spectroscopic and photophysical measurements were conducted by using the


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same apparatuses with those reported earlier.26,27

Results and Discussion T-Dependent Emission Spectra. The T-dependences of the emission spectra of [{Mo6X8}Y6]2– (1–9) in PEG-DMA matrices are shown in Figure 1 and those of the emission maximum energy (ṽem) and full-width at half maximum of the spectrum (fwhm) of each cluster are summarized in Figure 2. The emission spectra of the {Mo6Cl8}4+- and {Mo6Br8}4+-core clusters (1–6) and [{Mo6I8}I6]2– (9) are shifted to the lower energy on going from 3 to 60 K and, subsequently, the clusters showed higher-energy emission shifts above 60 K. These seven clusters commonly showed the minima in the τem – T plots at around 60 K (left panels in Figure 2), while the behavior observed for 9 was marginal. These results indicate that the critical temperature, below and above which the clusters show lower- and higher-energy shifts upon T-elevation, respectively, is almost common for these clusters. Furthermore, such T-dependent emission shifts of the clusters accompanied the increases in fwhm of the spectra as seen in Figures 1 and 2. It is worth pointing that T-dependent emission characteristics analogous to those of 1–6 and 9 have been also confirmed for [{Re6S8}X6]4– (X = Cl, Br, or I) and [{W6Cl8}Cl6]2–.26,29 In contrast, [{Mo6I8}Cl6]2– (7) and [{Mo6I8}Br6]2– (8) exhibited T-dependent emission characteristics completely different from other clusters. First, these two clusters showed the sharp (small fwhm) and higher-energy emission spectra compared to 1–6 irrespective of T (3–300 K), indicating such emission characteristics of 7 and 8 were inherent to an {Mo6I8}4+-core cluster. Second, the ṽem values of 7 and 8 were almost constant in 3 < T < 100 K and, then, T-elevation above 100 K gave rise to gradual lower-energy shifts of the spectra. On the other hand, the T-dependent emission 6 ACS Paragon Plus Environment


characteristics of 9 ([{Mo6I8}I6]2–) were marginal between those of 7/8 and 1–6.

Figure 1. T-dependences of the emission spectra of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices in 3 K < T < 300 K. Temperature variations are shown by color gradation from black (3 K) to highlight (300 K).


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Figure 2. T-dependences of the ṽem (left panel) and fwhm (right panel) values of a) [{Mo6Cl8}Y6]2–, b) [{Mo6Br8}Y6]2–, and c) [{Mo6I8}Y6]2– in polymer matrices. The fwhm values of the clusters with Y = I (3, 6, or 9) at a given T are the approximated values as estimated by extrapolation of each spectrum by a Gaussian function. T-Dependent Emission Lifetimes. The emission decay profiles of 1–9 at several temperatures are shown in Figure 3. As a typical example, the emission decay profiles of [{Mo6Br8}Br6]2– (5) shown in Figure 3 were fitted by single exponential functions irrespective of both T and the spectral shifts with T in Figure 1. The emission from the other



clusters (1–4 and 6–9) also showed single exponential decay in the T range of 3–300 K as the fitting results being reported in Supporting Information, Figure S1–S9. Costuas et al. reported recently that the emission from the cesium and TBA salts of [{Mo6Br8}Br6]2– (5) in the solid states at low temperatures exhibited double exponential decay, and demonstrated that such emission characteristics were ascribed to the emissions from the structurally different two excited states (dual-emission model).35 Under our experimental conditions with each cluster being dispersed homogeneously in a polymer matrix, however, we could not observe two components emission. Therefore, we suppose that the two components emissions reported by Costuas et al. would be due to the intermolecular interactions between adjacent cluster molecules in the crystalline phase as reported by our research group on 1 in the crystalline phase.26


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Figure 3. Emission decay profiles of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices at 10 (black), 30 (red), 100 (green), 200 (blue), and 300 K (cyan). The black broken curve in each figure represents the instrument response function.



Figure 4. T-dependences of τem of a) [{Mo6Cl8}Y6]2–, b) [{Mo6Br8}Y6]2–, and c) [{Mo6I8}Y6]2– in polymer matrices. The solid curves are the best fits of the observed data by eq. 2 with the fitting parameters, ΔE1n and τn, being shown in Figure 5. The T-dependences of τem evaluated for 1–9 are summarized in Figure 4 and Supporting Information, Tables S1–S3. The τem values of 1–6 decreased sharply upon Televation from 3 to 100 K, while those exhibited monotonous decreases above ~100 K. In contrast, the {Mo6I8}4+-core clusters (7–9) showed T-dependent τem different from 1–6 as


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seen in Figure 4. In practice, 7 showed a gradual decrease in τem from 3 to 300 K (from 433 to 196 μs) and 8 also exhibited moderate T-dependent τem (from 628 to 123 μs) compared to 1–6: from 203 (3 K) to 77 μs (300 K) for 5 as an example. Importantly, furthermore, the τem value of 9 was insensitive to T in the entire T-range studied: 110 (3 K)–48.9 μs (300 K). Since these clusters, 1–9, are isostructural and isoelectronic with one another, such T-dependent emission characteristics (ṽem, τem, and fwhm) of the nine clusters should be explained by a common model. Analysis of T-dependent Emission Lifetimes by Spin Sublevel Model. We reported that the Φn model in Chart 2 explained very well the T-dependent emission characteristics of [{Mo6Cl8}Cl6]2–, [{Re6S8}Cl6]4–, [{W6Cl8}Cl6]2–, and [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br, or I) as mentioned before.26,27 Therefore, we also analyzed the T-dependent τem data (τ(T)) of the clusters in Figure 4 based on the Φn (n = 1–4) model and eq 1. τ (T ) 

g g τ

n n

exp   ΔE1n k BT 

(1)

exp   ΔE1n k BT 

n

In eq 1, gn and τn are the multiplicity (g1 = g3 = 2, g2 = 1, and g4 = 3) and emission lifetime of Φn, respectively. The analysis of the τ(T) data in Figure 4 was conducted by τn (n = 1–4) and the zfs energy between Φ1 and Φn (n = 2–4) (ΔE1n) as fitting parameters,26,27 while the ΔE12 value was fixed at 4 cm–1 for the simulations since the splitting to Φ1 and Φ2 is due to Jahn-Teller distortion: discussed later again.36 As seen in Figure 4, the present simulations (solid curves) reproduced very well the observed τ(T) data on 1–9 with the correlation coefficients (R2) of the fittings being 0.982–0.999. The ΔE1n and τn values thus evaluated by the analysis of the τ(T) data in Figure 4 are summarized in Figure 5.



Figure 5. zfs parameters of [{Mo6X8}Y6]2–. The ΔE13 and ΔE14 values of the clusters, 1–9, were in the range of 50–99 and 620– 13 ACS Paragon Plus Environment

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870 cm–1, respectively, whose values were almost comparable to those observed for [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br, or I): ΔE13 = 47–114 cm–1 and ΔE14 = 650–1000 cm– 1.27

Furthermore, it is worth emphasizing that the ΔE14 values are comparable to those

evaluated by Ramirez-Tagle et al. based on relativistic TD-DFT calculations: 0.1–0.2 eV (ca. 800–1600 cm–1).37 Since ΔE14 and ΔE13 of the clusters are responsible for splitting of the degenerated T1 state by the first- and second-order SOC, respectively (see also Chart 2), the ΔE14 values should be proportional to the ΔE13 values.38 In practice, we found a linear relationship between ΔE14 and ΔE13 with R2 being 0.998 as shown in Figure 6. The linear relationship in Figure 6 demonstrates clearly that the analysis of the τ(T) data for the nine clusters by the Φn model has been done satisfactorily and provides the zfs parameters in the T1 states of the clusters.

Figure 6. Relationship between ΔE14 and ΔE13 of [{Mo6X8}Y6]2– (1–9). The solid line represents the linear regression line.



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Simulations of Emission Spectra by Spin Sublevel Model. On the basis of the ΔE1n values, we simulated the emission spectrum of the cluster at a given T as the sum of the Φn emission spectrum by the following equations.

ΔE13 ΔE12 )  kr3 F (ν% ν% ) 3 ) exp(  k BT k BT

2 % % I (ν%, T )  kr1 F (ν% ν% 1 )  k r F (ν  ν2 ) exp( 

 kr4 F (ν% ν% 4 ) exp( 

ΔE14 ) k BT

(2)

In eq 2, krn is the radiative rate constant of Φn relative to that of Φ1 (i.e., kr1 = 1.0). F(ṽ – ṽn) and ṽn are a spectral Gaussian function and the emission maximum energy of each Φn, respectively, and F(ṽ – ṽn) is given by eq 3.

  ν% ν% 2  n F (ν% ν% exp  2    n)  π   fwhm(Φn )   fwhm(Φn ) 2 1

(3)

In eq 3, fwhm(Φn) represents fwhm of the emission spectrum of each Φn and we assume here that fwhm(Φn) at a given T is the same for n = 1–4, but varies with T. Figure 7 shows the observed (shown by black curves) and simulated emission spectra (shown by given colors) of 1–9 at several T. The ṽn values simulated are included in Figure 5. Figure 7 demonstrates clearly that the observed spectrum is reproduced almost satisfactorily by　ΔE1n, ṽn (Figure 5), eqs 2 and 3 irrespective of X, Y, and T with R2 ~0.999. The T-dependent fwhm(Φn) values employed for the fittings of the spectra are reported in Supporting Information Table S4. In the case of 5, typically, the fwhm(Φn) value was necessary to vary from 2020 to 3220 cm–1 on going from 3 to 300 K, while that of 8 varied from 1020 at 3 K to 1580 cm–1 at 300 K. It is worth noting that, although the T-dependent emission shifts and fwhm of 1–6 and 9 are 15 ACS Paragon Plus Environment

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different largely from those of 7 and 8 as mentioned before, eqs 2 and 3 reproduce very well the I(ṽ, T) data on 1–9 based on the ΔE1n values evaluated by the analysis of the τ(T) data in Figure 4. Therefore, both τ(T) and I(ṽ, T) data on a given cluster are analyzed properly by the common parameters and a single context of the present Φn model.

Figure 7. Simulations of the T-dependent emission spectra of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices. The spectra shown by the black curves are the observed ones, while the simulated spectra are shown by the colors indicated in the figures. In order to show the validity of the present data analysis, we summarize the contribution percentage of each Φn (Φn%) in the emission spectra of 1–9 at 300 K in Figure 8 and Table 1. In the case of [{Mo6X8}Br6]2– (2, 5, and 8), as examples, the emission spectra of 2 and 5 16 ACS Paragon Plus Environment


at 300 K are explained almost satisfactorily by the contributions from the Φ3 and Φ4 emissions (Φ3 and Φ4: 68 and 32% for 2, 53 and 47% for 5) as seen in Figure 8b and 8e, while the Φ1 (10%) and Φ2 emissions (55%) also contribute to the spectrum of 8 in addition to the contributions of the Φ3 (25%) and Φ4 emissions (11%): Figure 8h. Such tendencies have been also found for Φn% in the emission spectra of [{Mo6X8}Cl6]2– (1, 4, and 7), [{Mo6X8}I6]2– (3, 6, and 9) at 300 K as seen in Figure 8. According to the zfs parameters in Figure 5, it is easily predicted that the relatively large ΔE14 value of 8 (780 cm–1) compared to that of 2 (630 cm–1) or 5 (655 cm–1) gives rise to the smaller contributions of the Φ3 and Φ4 emissions to the emission from 8 at 300 K. In the case of a [{Mo6I8}Y6]2– series (7–9), on the other hand, the emission spectrum of 7 at 300 K is characterized by relatively small Φ3 (9%) / Φ4 (2%) and large Φ1 (49%) / Φ2 (41%) contributions (Figure 8g), while that of 9 is explained by large contributions from the Φ3 (37%) and Φ4 (42%) emissions: Figure 8i. The Φn% values of the emission from 8 are marginal between those of 7 and 9 as seen in Table 1 and Figure 8h. It is worth noting that the Φ3 and Φ4% values increase in the sequence Y = Cl (7) < Br (8) < I (9), which agrees very well with the decreasing order of ΔE13 and ΔE14: Y = Cl (7, 99 and 870 cm–1) > Br (8, 80 and 780 cm–1) > I (9, 70 and 730 cm–1). The ΔE1n and Φn% values mentioned above thus determine the emission spectrum of a given cluster at 300 K. Furthermore, since Φn% of the cluster is a function of T, the T-dependent emission shifts of the clusters will be also explained by the variation of Φn% with T as described later in detail.


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Table 1. Contribution Percentages (Φn%) of the Φn Emissions to the Observed Spectra of 1–9 at 300 K. [{Mo6Cl8}Y6]2–

[{Mo6Br8}Y6]2–

[{Mo6I8}Y6]2–

1

2

3

4

5

6

7

8

9

Φ1 / %

0

0

0

0

0

0

0

0

0

Φ2 / %

3.2

0

0

0

0

0

40.6

54.6

21.4

Φ3 / %

64.9

67.7

46.5

54.5

52.9

42.7

8.5

25.1

36.6

Φ4 / %

31.9

32.3

53.5

45.5

47.1

57.3

1.7

10.8

42.0

Figure 8. Observed and simulated emission spectra of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices at 300 K. The observed and simulated emission spectra are shown by the black and red colors, respectively. The relative contributions of the Φn emission spectra to the observed spectrum of a given cluster are shown by green (n = 1), blue (n = 2), cyan (n = 3), and magenta (n = 4), respectively.



Origin of T-dependent Emission Spectral Characteristics: ṽem and fwhm. The curious Tdependent emission shifts, showing lower- and higher-energy shifts upon T-elevation from 3 to ~60 K and above ~60 K, respectively, observed for 1–6 (Figures 1 and 2), have been also reported for the T-dependent emission from [{Mo6Cl8}Cl6]2–,26,28 [{Re6S8}Cl6]4–,26,29 [{W6Cl8}Cl6]2–,26 or [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br).27 The {Mo6I8}4+-core clusters, 7 and 8, showed the T-dependent emission shifts different considerably from 1–6 as mentioned before, while T-dependent emission similar to 7 or 8 has been also confirmed for that from [{Mo6I8}(n-C3F7COO)6]2–.27 Such T-dependent emission shifts of 1–9 can be explained in terms of the orders of the Φn and ṽn energies. Although the Φn energy increases in the sequence Φ1 < Φ2 < Φ3 < Φ4, the emission maximum energy of each Φn (ṽn) does not coincide with this sequence and, thereby, the Φn energy levels cannot explain the Tdependent emission shifts. In the case of 5 as an example, ṽn (× 103 cm–1) increases in the sequence ṽ2 (11.64) < ṽ1 (11.84) < ṽ3 (11.89) < ṽ4 (12.84). Such sequence of ṽn can be also confirmed for 1–4, 6, and 9: see Figure 5. This indicates that the Franck-Condon (FC) ground state responsible for each Φn emission transition is different. Knowing the energy difference between Φ1 and Φn (ΔE1n) and that between ṽ1 and ṽn (Δṽn), we evaluated the energy differences between the FC ground states for the Φn emissions (ΔE’) as the data were included in Figure 5. For 1–6 and 9, the ΔE’ value ranges in 40–2560 cm–1. We suppose that ΔE’ will be determined by the displacement of the potential surface between the Φn level and the relevant FC ground state along vibrational coordinates though we cannot discuss the absolute ΔE’ values in the present stage of the investigation. On the other hand, the ΔE’ values of 7 and 8 were as large as 4510–4870 cm–1 and such large ΔE’ values would not be


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explained by the difference in the vibrational modes between the T1 and S0 states. The participation of the ground states with different magnetic properties may explain such ΔE’ values. In the case of 5 at 3 K, since the main contribution to the observed emission (ṽem) is the Φ1 emission, ṽem is predicted to be ṽem ≈ ṽ1 = 11.84 × 103 cm–1, which agrees very well with the experimental observation: ṽem = 11.85 × 103 cm–1 at 3 K, see Figure 2. Upon T-elevation above 3 K, the Φ2 emission also participates in addition to the Φ1 emission. Assuming simple average between ṽ1 and ṽ2, ṽem becomes ~11.74 × 103 cm–1, leading to a higher-energy emission shift. Further T-elevation results in participation of the Φ3 and Φ4 emissions and, thus, the emission spectrum shifts gradually to the lower energy, reflecting the increase in the contribution percentages of Φ3 and Φ4 to the observed spectrum. In contrast, since ṽn of 7 or 8 increases in the sequence ṽ4 < ṽ3 < ṽ2 < ṽ1: see Figure 5, the cluster shows a gradual higher-energy shift upon T-elevation above 3 K. The Boltzmann population of Φn at a given T, the sequence of ṽn, and the ṽn value explain very well the T-dependent emission shifts of 1–9. Another factor characterizing the emission spectra of 1–9 is the fwhm value of each Φn: fwhm(Φn). As seen in Figure 2, the fwhm values of the observed spectra of 1–3 and 4–6 show the minima at around 60 K, corresponding to the critical temperatures for the emission shifts of the clusters as mentioned before. On going from 3 to 300 K, the fwhm values of 1–3 (X = Cl) and 4–6 (X = Br) vary from ~2600 to 3730–3950 cm–1 and from ~2500 to 3990–4240 cm–1, respectively, while those of 7–8 (X = I) increase almost monotonically with T from ~1400 to 2300–2860 cm–1 where that of 9 is an exceptional case: from 2180 to 4800 cm–1. In



contrast to the fwhm values, it is worth emphasizing the fwhm(Φn) values of 9 at a given T are similar to that of 7 and 8. For instance, at 300 K, the fwhm(Φn) value of 9 (1930 cm–1) is comparable to that of 7 or 8 (1370 or 1580 cm–1, respectively) and much smaller than those of the {Mo6Cl8}4+- and {Mo6Br8}4+-core clusters (1–6): 2940–3310 cm–1. Although the relatively small fwhm(Φn) values of 9 are inconsistent with the observed broad emission spectra of 9 above 200 K, the large difference in ṽn explains well the observed data. Namely, the ṽn values of 7–9 range in (10.5–14.7) × 103 cm–1 (Δṽn = 3290–4000 cm–1), while those of 1–6 lie in narrow ranges: Δṽn = 970–1590 and 980–1860 cm–1 for X = Cl (1–3) and Br (4– 6), respectively. As shown in Table 1 and Figure 8, the emission spectrum of 9 at 300 K is reproduced by almost equal contributions from the Φ2–Φ4 emissions owing to the marginal ΔE1n values between 1–6 and 7/8, resulting in the broad emission band shape of 9. Therefore, the narrow spectral band shapes observed for {Mo6I8}4+-core clusters4–17 are the inherent character to [{Mo6I8}Y6]2–. Factors Governing Zero-Magnetic-Field Splitting Energies of [{Mo6X8}Y6]2–. The characteristic T-dependent emission spectra and lifetimes of 1–9 have been adequately explained by the Φn model (n = 1–4) similar to the previous reports on those of other Mo(II), Re(III), and W(II) clusters.26,27 Analysis of the T-dependent emission data of the clusters by the Φn model has provided the zfs parameters: ΔE1n, τn, and ṽn. Among these zfs parameters, the ΔE1n values (n = 3 and 4) are related directly to the strength of SOC and are thus worth discussing in detail. A close inspection of the data in Figure 5 indicates that, for a given Y, the cluster having heavier (i.e., larger Z) X shows larger ΔE1n (n = 3, 4) values. In the case of a [{Mo6X8}Br6]2–


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series (2, 5, and 8) as an example, ΔE13 and ΔE14 increase in the sequence X = Cl (2, ΔE13 = 51 and ΔE14 = 630 cm–1) < Br (5, 56 and 655 cm–1) < I (8, 80 and 780 cm–1). Since our previous study on [{Mo6X8}(n-C3F7COO)6]2– (X = Cl, Br, or I) has demonstrated that the ΔE13 and ΔE14 values of the clusters increase in the sequence X = Cl (ΔE13 = 47 and ΔE14 = 650 cm–1) < Br (59 and 720 cm–1) < I (114 and 1000 cm–1),27 we conclude such a tendency is commonly observed for a {Mo6X8}4+-core cluster for a given Y. Thus, the ΔE13 and ΔE14 values of the clusters, whose values are determined by the second- and first-order SOC, respectively, depend primarily on the nature of {Mo6X8}4+-core. The results will be very reasonable, since it has been reported theoretically that the T1 state of [{Mo6X8}X6]2– (X = Cl, Br, or I) is localized on the {Mo6X8}4+-core and the photophysical characteristics of the cluster is determined primarily by the electronic structures of the cluster-core.1–17,37,39,40 An SOC parameter, ξ, is known to be related to the atomic number (Z) of a constituted atom in a molecule through eq 4,41,42    e 2 h2  Z4 ζ nl   2 2 3  2m c a0  n3 (l  1)(l  1 )l  2  

(4)

where e, ℏ, m, a0, n, and l are the elementary electron charge, the reduced Planck constant, the mass of an electron, the Bohr radius, the principal and azimuthal quantum numbers of a molecule, respectively. Eq 4 demonstrates that the ξ value is proportional to the fourth power of Z. In the case of [{Mo6X8}(n-C3F7COO)6]2–, we have found linear relationships between ΔE1n and {Z(X)}4.27 In the present study, we have also confirmed the linear relationships between {Z(X)}4 and ΔE13/ΔE14 for a given Y as shown in Figure 9a, demonstrating that SOC of the cluster is determined primarily by nature of the face-capping ligands (X) and, thus, 22 ACS Paragon Plus Environment


{Z(X)}4.

Figure 9. Relationships between the splitting energy in the excited triplet states (ΔE13 and ΔE14) of [{Mo6X8}Y6]2– (1–9) and a) the forth power of the atomic number of face-capping ligand ({Z(X)}4), and b) the 95Mo NMR chemical shift of [{Mo6X8}Y6]2– whose data are taken from ref. 43–45. The solid lines in a) or curves in b) represent regression between the two parameters. The squares and circles represent the ΔE13 and ΔE14 data, respectively. Figure 9a demonstrates furthermore that the ΔE13 and ΔE14 values for a given {Mo6X8}4+-core cluster depends on nature of the terminal ligands: Y. In the case of the {Mo6Br8}4+-core clusters (4–6), as an example, the ΔE13 and ΔE14 values increase in the sequence Y = I (6, 53 and 635 cm–1) < Br (5, 56 and 655 cm–1) < Cl (4, 63 and 695 cm–1). Similar terminal ligand effects on ΔE13/ΔE14 to those of the {Mo6Br8}4+-core series can be also found for the {Mo6Cl8}4+- (1–3) and {Mo6I8}4+-core series (7–9), whose ΔE14 (ΔE13)


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values range in 620–650 (50–55) and 730–870 (70–99) cm–1 for the X = Cl and I series, respectively. As a result, [{Mo6I8}Cl6]2– (7) shows the largest ΔE13 and ΔE14 values (99 and 870 cm–1, respectively) among those of the nine clusters. It is worth pointing out that eq 4 indicates that the ΔE13/ΔE14 values should increase in the increase in the sequence Y = Cl < Br < I for a given {Mo6X8}4+-core cluster, while these values increase in the opposite trend as mentioned before: Y = Cl > Br > I. This indicates that the strength of the zero-magneticfield experienced by the {Mo6X8}4+-core increases in the sequence Y = I < Br < Cl, suggesting that the effective nuclear charge of the Mo atom(s) (Zeff) in [{Mo6X8}Y6]2– should be considered to explain the data in Figure 9a. In the case of a non-hydrogen like atom, Zeff is expressed by Zeff = Z – σ, where σ is a screening constant to the electron in an atomic orbital interested. Unfortunately, since we are not aware of the actual Zeff values of the Mo atoms in 1–9, we focus on the

95Mo

NMR

chemical shifts of 1–9 reported by Preetz and co-workers,43–45 as a measure of Zeff of the Mo atom in the cluster. Then, we plotted the ΔE14/ΔE13 values of 1–9 against the

95Mo

NMR

chemical shifts of the clusters. As the results are shown in Figure 9b, the ΔE14 and ΔE13 values increase with an increase in the 95Mo NMR chemical shift and, thus, a decrease in the d-electron density on the Mo atom in the cluster. In the present case, since SOC is the main factor determining zfs as described before,46,47 the low d-electron density on the Mo atom therefore would give rise to an increase in Zeff, leading to that of the zfs energy as predicted by eq 4. The results in Figure 9b demonstrate that the zfs energy of a transition metal complex can be controlled by the d-electron density on the metal atom and predicted qualitatively based on the NMR chemical shift of the metal atom. To the best of our knowledge, this is the



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first demonstration for the quantitative and systematic investigations on the factors governing zfs and SOC in the T1 state of a transition metal complex.

Conclusions We studied the applicability of our excited triplet state spin-sublevel (Φn, n = 1–4) model to explain the large T-dependent emission characteristics of [{Mo6X8}Y6]2– (1–9) in polymer matrices in the T range of 3–300 K. [{Mo6I8}Cl6]2– (7) and [{Mo6I8}Br6]2– (8) showed curious T-dependent emission properties different largely from the {Mo6Cl8}4+-, {Mo6Br8}4+-core (1–6), and [{Mo6I8}I6]2– (9) clusters. Although 1–9 showed different Tdependent emission characteristics with one another, the Φn model explained almost satisfactorily the emission characteristics of the nine clusters. In the present study, we found that the ΔE13 and ΔE14 values (in cm–1) increased in the sequence, 3 (ΔE13 = 50 and ΔE14 = 620) < 2 (ΔE13 = 51 and ΔE14 = 630) < 6 (53 and 635) < 1 (55 and 650) < 5 (56 and 655) < 4 (63 and 695) < 9 (70 and 730) < 8 (80 and 780) < 7 (99 and 870). The larger is the ΔE14 value for a given X (1–3, 4–6, or 7–9) or Y series ((1, 4, 7), (2, 5, 8), and (3, 6, 9)), the smaller is the contribution of the emission from the highest-energy spin sublevels (Φ4) to the observed emission spectrum at 300 K with the sequence of the Φ4% being Y = I > Br > Cl or X = Cl > Br > I for given X or Y, respectively, and thus the larger is the contributions of the emissions from the lower-energy spin sublevels (Φ3, Φ2, or Φ1). The variation of Φn% at 300 K with that of X and Y in [{Mo6X8}Y6]2– mentioned above explained very well the ṽem value of the cluster as the sum of the emission from Φn. As the very important result, furthermore, the ΔE13 and ΔE14 values were shown to correlate well with {Z(X)}4 and the

95Mo

NMR

chemical shift of the cluster as demonstrated in Figure 9. Through the present studies on the 25 ACS Paragon Plus Environment

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T-dependent emissions from 1–9, we succeeded in the detailed discussions on the factors governing SOC and zfs in the T1 states of the nine clusters.

Supporting Information Description T (3–300 K)-dependences of the emission decay profiles, emission lifetimes (τ(T)), and fwhm of the emission spectrum of each Φn (fwhm(Φn)) of [{Mo6X8}Y6]2– (1–9) in polymer matrices. Least-means-square fitting results of the emission decay profiles of 1–9 at several temperatures.

Acknowledgement NK acknowledges a grant-in-aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the Japanese Government for the support of the research No. 26248022 (Grant-in-Aid for Scientific Research (A)).

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0-3): Evidence for Electronic Delocalization. J. Phys. Chem. 1993, 97, 12705–12709. Costuas, K.; Garreau, G.; Bulou, A.; Fontaine, B.; Cuny, J.; Gautier, R.; Mortier, M.; Molard, Y.; Duvail, J.-L.; Fauques, E.; et al. Combined Theoretical and Timeresolved Photoluminescence Investigations of [{Mo6Bri8}Xa6]2– Metal Cluster Unit: Evidence of Dual Emission. Phys. Chem. Chem. Phys. 2015, 17, 28574–28585. Although the ΔE12 value fixed at 4 cm–1 for the simulations of the τ(T) data is much smaller than ΔE13 and ΔE14, the ΔE12 value responsible for the participation of the Jahn-Teller distortion in the T1 state of the cluster is essential to reproduce the experimentally observed τ(T) data. In the case of (TBA)2[{Mo6Cl8}Cl6] in poly(methyl methacrylate) matrices, the analysis of the τ(T) data by the three state φn model in Chart 2 (without assuming the Jahn-Teller effects in the T1 state) failed to reproduce the experimental results as reported in detail in ref 25. Ramirez-Tagle, R.; Arratia-Pérez, R. Electronic Structure and Molecular Properties of the [Mo6X8L6]2–; X = Cl, Br, I; L = F, Cl, Br, I Clusters. Chem. Phys. Lett. 2008, 460, 438–441. Azumi, T.; Saito, Y. Electronic Structures of the Lower Triplet Sublevels of Hexanuclear Molybdenum(II) Chloride Cluster J. Phys. Chem. 1988, 92, 1715–1721. Ramirez-Tagle, R.; Arratia-Pérez, R. The Luminescent [Mo6X8(NCS)6]2– (X = Cl, Br, I) Clusters?: A Computational Study Based on Time-dependent Density Functional Theory Including Spin-orbit and Solvent-polarity Effects. Chem. Phys. Lett. 2008, 455, 38–41. Ramirez-Tagle, R.; Arratia-Pérez, R. Pyridine as Axial Ligand on the [Mo6Cl8]4+ Core Switches off Luminescence. Chem. Phys. Lett. 2009, 475, 232–234. Condon, E. U.; Shortley, G. H. The Theory of Atomic Spectra; Cambridge University Press: London, 1953. Montalti, M.; Credi, A.; Prodi, L.; Gandolfi, M. T. Handbook of Photochemistry, 3rd ed.; Taylor & Francis: Boca Raton, 2006. Preetz, W.; Harder, K. Synthesis, Structure and Properties of the Cluster Anions [{Mo6Cli8}Xa6]2– with Xa ≡ F, Cl, Br, I*. J. Alloys Compds. 1992, 183, 413–429. Preetz, W.; Bublitz, D. Darstellung, Kristallstruktur und spektroskopische Eigenschaften der Clusteranionen [{Mo6Bri8}Xa6]2– mit Xa = F, Cl, Br, I. Z. Anorg. Allg. Chem. 1994, 620, 234–246. Brückner, P.; Preetz, W.; Pünjer, M. Darstellung, Kristallstruktur, NMR30 ACS Paragon Plus Environment


Schwingungsspektren und Normalkoordinatenanalyse der Clusteranionen [{Mo6Ii8}Xa6]2–, Xa = F, Cl, Br, I. Z. Anorg. Allg. Chem. 1997, 623 8–17. (46) (47)

Griffith, J. S. The Theory of Transition Metal Ions; Cambridge University Press: Cambridge, 1964. Vrjamasu, V. V.; Bominaar, E. L.; Meyer, J.; Münck, E. Mössbauer Study of Reduced Rubredoxin As Purified and in Whole Cells. Structural Correlation Analysis of Spin Hamiltonian Parameters. Inorg. Chem. 2002, 41, 6358–6371.


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Table of Contents and Synopsys

The temperature (T)-dependent emission spectra and lifetimes of [{Mo6X8}Y6]2– (X, Y = Cl, Br, or I) in 3 < T < 300 K were analyzed by an excited triplet state spin sublevel (Φn, n = 1– 4) model and the Φn model parameters explained successfully the emission characteristics of the clusters at given T. The splitting energy between the lowest- (Φ1) and third- (Φ3) or fourth-spin sublevels (Φ4) (ΔE13 or ΔE14, respectively) correlates well with the fourth-power of the atomic number (Z) of X in [{Mo6X8}Y6]2– (ΔE1n (n = 3 or 4) vs. {Z(X)}4 as well as with the 95Mo NMR chemical shift of the cluster.



Chart 1. Structure of an octahedral molybdenum(II) cluster and the abbreviations of the cluster samples. 130x63mm (150 x 150 DPI)


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Chart 2. Excited triplet state spin-sublevel models for the emission from [{Mo6(μ3-Q)8}L6]z–.26,27 175x84mm (150 x 150 DPI)



Figure 1. T-dependences of the emission spectra of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices in 3 K < T < 300 K. Temperature variations are shown by color gradation from black (3 K) to highlight (300 K). 412x293mm (150 x 150 DPI)


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Figure 2. T-dependences of the ṽem (left panel) and fwhm (right panel) values of a) [{Mo6Cl8}Y6]2–, b) [{Mo6Br8}Y6], and c) [{Mo6I8}Y6] in polymer matrices. The fwhm values of the clusters with Y = I (7–9) at a given T are the approximated values as estimated by extrapolation of each spectrum by a Gaussian function. 322x290mm (150 x 150 DPI)



Figure 3. Emission decay profiles of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and

[{Mo6I8}Y6]2– (lower panel) in polymer matrices at 10 (black), 30 (red), 100 (green), 200 (blue), and 300 K (cyan). The black broken curve in each figure represents the instrument response function. 662x471mm (150 x 150 DPI)


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Figure 4. T-dependences of τem of a) [{Mo6Cl8}Y6]2–, b) [{Mo6Br8}Y6]2–, and c) [{Mo6I8}Y6]2– in polymer matrices. The solid curves are the best fits of the observed data by eq. 2 with the fitting parameters, ΔE1n and τn, being shown in Figure 5. 172x289mm (150 x 150 DPI)



Figure 5. zfs parameters of [{Mo6X8}Y6]2–. 171x225mm (150 x 150 DPI)


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Figure 6. Relationship between ΔE14 and ΔE13 of [{Mo6X8}Y6]2– (1–9). The solid line represents the linear regression line. 240x167mm (150 x 150 DPI)



Figure 7. Simulations of the T-dependent emission spectra of [{Mo6Cl8}Y6]2– (upper panel), [{Mo6Br8}Y6]2– (middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices. The spectra shown by the black curves are the observed ones, while the simulated spectra are shown by the colors indicated in the figures. 432x303mm (150 x 150 DPI)


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Figure 8. Observed and simulated emission spectra of [{Mo6Cl8}Y6]2– (upper panel),[{Mo6Br8}Y6]2–

(middle panel), and [{Mo6I8}Y6]2– (lower panel) in polymer matrices at 300 K. The observed and simulated emission spectra are shown by the black and red colors, respectively. The relative contributions of the Φn emission spectra to the observed spectrum of a given cluster are shown by green (n = 1), blue (n = 2), cyan (n = 3), and magenta (n = 4), respectively. 432x303mm (150 x 150 DPI)



Figure 9. Relationships between the splitting energy in the excited triplet states (ΔE13 and ΔE14) of

[{Mo6X8}Y6]2– (1–9) and a) the forth power of the atomic number of face-capping ligand ({Z(X)}4), and b) the 95Mo NMR chemical shift of [{Mo6X8}Y6]2– whose data are taken from ref. 11. The solid lines in a) or curves in b) represent regression between the two parameters. The squares and circles represent the ΔE13 and ΔE14 data, respectively. 347x214mm (150 x 150 DPI)


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83x47mm (150 x 150 DPI)


Zero-Magnetic-Field Splitting in the Excited Triplet States of

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