Intersystem Crossing in Diplatinum Complexes - The Journal of

Sep 26, 2016 - Intersystem crossing (ISC) in solid [(C4H9)4N]4[Pt2(μ-P2O5(BF2)2)4], abbreviated Pt(pop-BF2), is remarkably slow for a third-row trans...
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Intersystem Crossing in Diplatinum Complexes Yan Choi Lam,† Harry B. Gray, and Jay R. Winkler* Beckman Institute, California Institute of Technology, Pasadena, California 91125, United States S Supporting Information *

ABSTRACT: Intersystem crossing (ISC) in solid [(C4H9)4N]4[Pt2(μP2O5(BF2)2)4], abbreviated Pt(pop-BF2), is remarkably slow for a third-row transition metal complex, ranging from τISC ≈ 0.9 ns at 310 K to τISC ≈ 29 ns below 100 K. A classical model based on Boltzmann population of one temperature-independent and two thermally activated pathways was previously employed to account for the ISC rate behavior. An alternative we prefer is to treat Pt(pop-BF2) ISC quantum mechanically, using expressions for multiphonon radiationless transitions. Here we show that a two-channel model with physically plausible parameters can account for the observed ISC temperature dependence. In channel 1, 1A2u intersystem crosses directly into 3A2u using a high energy B−F or P−O vibration as accepting mode, resulting in a temperature-independent ISC rate. In channel 2, ISC occurs via a deactivating state of triplet character (which then rapidly decays to 3A2u), using Pt−Pt stretching (160 cm−1) as a distorting mode to provide the energy needed. Fitting indicates that the deactivating state, 3X, is moderately displaced (S = 0.5− 3) and blue-shifted (ΔE = 1420−2550 cm−1) from 1A2u. Our model accounts for the experimental observation that ISC in both temperature independent and thermally activated channels is faster for Pt(pop) than for Pt(pop-BF2): in the temperature independent channel because O−H modes in the former more effectively accept than B−F modes in the latter, and in the thermally activated pathway because the energy gap to 3X is larger in the latter complex.

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INTRODUCTION Dimers of d8 metal centers are rare examples of transition metal complexes exhibiting luminescence from both singlet and triplet excited states.1−3 The luminescent states arise from promotion of an electron from a metal−metal antibonding dσ* orbital into a metal−metal bonding pσ orbital, producing 1A2u and 3A2u states in the idealized D4h symmetry that describes many of these complexes. Decay of the 1A2u state is dominated by intersystem crossing (ISC) to 3A2u, but these nonradiative transitions are remarkably slow for transition metal complexes. ISC in [(C4H9)4N]4[Pt2(μ-P2O5(BF2)2)4] (Pt(pop-BF2)) is notable for its long 1A2u lifetime (>1 ns at room temperature).4,5 Room temperature ISC in the parent complex, [Pt2(μ-P2O5H2)4]4− (Pt(pop)),3,4 is 2 orders of magnitude faster.4−6 The difference in 1A2u lifetimes likely is not attributable to variations in spin−orbit coupling, given that the 3A2u zero-field splitting is virtually identical (40 cm−1) in both complexes. The temperature dependence of the 1A2u lifetime in Pt(pop-BF2) provides important insights into the decay mechanism: the ISC time (τISC) increases from ∼29 ns below 100 K to ∼0.9 ns at 310 K.4 In a classical Arrhenius analysis of this process, one temperature-independent and two thermally activated pathways were required for an adequate fit of the data.4 Classical Arrhenius models provide useful ISC descriptors, but they ignore the quantum mechanical and vibronic aspects of nonradiative transitions that are particularly important at cryogenic temperatures. Moreover, they do not provide insight into fundamental parameters such as state-to-state electronic © XXXX American Chemical Society

couplings. We suggest that it is preferable, therefore, to treat ISC using the formalism of multiphonon radiationless transitions,7−9 which leads naturally to a finite rate constant in the low-temperature limit and classical behavior in the hightemperature limit.10−20 Within this formalism, the ISC rate constant for the transition from electronic state A to B is given by eq 1, where the vibrational levels of A are assumed to be populated according to a Boltzmann distribution.6,21 kISC =

2πHAB 2 1 ρ(ϵB) Q ℏ ⎛ ϵA, m ⎞ ∑ ∑ exp⎜⎝− ⎟⎠I[A, m],[B, n]2δ(ϵA,m − ϵB,n) kT m

n

(1)

Equation 1 is an expression for the thermally weighted probability per unit time of transitioning from vibrational level m of initial state A, with energy ϵA,m, to vibrational level n of final state B with energy ϵB,n. ρ(ϵB) is the density of final states, Q the vibrational partition function for A, ℏωi the accepting mode frequency, and I[A,m],[B,n] the overlap integral of vibrational wave functions. HAB is the electronic coupling matrix element for the A → B transition. The delta function arises from the energy conservation requirement. Several approximations lead to a simpler expression for kISC. In the harmonic oscillator model, only vibrational modes Received: August 4, 2016 Revised: September 13, 2016

A

DOI: 10.1021/acs.jpca.6b07891 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A associated with changes in nuclear configuration or force constant produce nonzero values of I[A,m],[B,n] (m ≠ n) and promote an A → B transition.19 If only one such harmonic oscillator accepting mode is considered and is assumed to have the same force constant in the initial and final states (i.e., ℏωA = ℏωB), the final density of states ρ(ϵB) =

1 , ℏω

kISC =

⎡ ⎛ ℏω ⎞⎤ π ⎟ exp⎢ − S coth⎜ ⎝ 2kT ⎠⎥⎦ ⎣ λkT +∞ ⎧ 2⎤ ⎡ ⎡ ⎤ ∑ ⎨exp⎢⎣ mℏω ⎥⎦ exp⎢− (−ΔE + mℏω + λ) ⎥ 2kT 4λkT + MLW ⎦ ⎣ m =−∞ ⎩ HAB 2 ℏ

⎪

⎪

⎡ ⎛ ℏω ⎞⎤⎫ ⎟ ⎬ I|m|⎢S csch⎜ ⎝ 2kT ⎠⎥⎦⎭ ⎣

the vibrational

⎪

⎪

partition function is Q =

1 2

( 2ℏkTω )

csch

and the Boltzmann

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population of the mth vibrational level of A is (2m + 1)ℏω ℏω PA, m = 2 sinh 2kT exp⎡⎣ − 2kT ⎤⎦. Equation 1 then simplifies to eq 2a.

RESULTS AND DISCUSSION Although 1A2u → 3A2u ISC kinetics of microcrystalline Pt(popBF2) (Table S1 in Supporting Information)4 are temperature independent from 30 to ∼90 K, a ∼27-fold increase is observed from 90 to 310 K. Here we show that a two-channel model with physically plausible parameters can account for this temperature dependence. In channel 1, 1A2u intersystem crosses directly by a multiphonon process into 3A2u, ΔE = −5750 cm−1, and S is small since the 1A2u and 3A2u potential energy surfaces are virtually nested.2 In channel 2, ISC occurs into a deactivating state of triplet character, which then rapidly decays to 3A2u.

( )

kISC =

2 2π HAB ℏ ℏω

∑ ∑ PA,mI[A, m],[B, n]2δ[ΔE + (n − m)ℏω] m

n

(2a)

Owing to the delta function, nonzero terms occur only for integer values of ΔE/(ℏω) = n0. In practice, low-frequency lattice modes are always present that allow transition at ΔE/ (ℏω) ≈ n0.21 Equation 2a can be expressed in terms of the Huang−Rhys displacement parameter S and a modified Bessel function (of the first kind) of order |n0| (absolute value of the integer closest to ΔE/(ℏω)) (eq 2b).6,21 kISC =

⎡ ⎛ ℏω ⎞⎤ ⎛ ΔE ⎞ ⎟⎥ exp⎜ − ⎟ exp⎢ −S coth⎜ ⎝ ⎠ ⎝ 2kT ⎠ ⎣ ⎦ 2 kT ℏω ⎡ ⎛ ℏω ⎞⎤ ⎛ ΔE ⎞ ⎟⎥ δ ⎜ − n 0⎟ I|n0|⎢S csch⎜ ⎝ 2kT ⎠⎦ ⎝ ℏω ⎠ ⎣

kISC = k1(ΔE1 = −5750, S1 , ℏω1) + k 2(ΔE2 , S2 , ℏω2) (4)

Direct A2u → A2u Channel. Since A2u and A2u have identical orbital occupations and since the Pt−Pt stretching modes in the two electronic states are similar (160 and 168 cm−1, respectively),4 their potential energy surfaces are nearly nested and S1 is small. For the Pt−Pt mode, S1 may be approximated by eq 5 where SA and SB are the displacement parameters relative to the ground states of 1A2u and 3A2u, respectively (SA ≈ 6, SB ≈ 8). 1

2πHAB 2 2

⎡ ⎛ ℏω ⎞⎤ π ⎟ exp⎢ −S coth⎜ ⎝ 2kT ⎠⎥⎦ ⎣ λkT +∞ ⎧ 2⎤ ⎡ ⎡ ⎤ ∑ ⎨exp⎢⎣ mℏω ⎥⎦ exp⎢− (−ΔE + mℏω + λ) ⎥ 4λkT 2kT ⎦ ⎣ m =−∞ ⎩

k1 =

2πHAB 2 2

ℏω

SA )2 ≈ 0.14

3

(5)

⎛S m⎞ exp( −S1)⎜ 1 ⎟ ⎝ m! ⎠

(6)

The direct A2u → A2u channel in Pt(pop-BF2) gives a temperature-independent ISC rate of (2.65−3.00) × 107 s−1 (vide infra). For S1 = 0.14, ℏω1 = 1150 cm−1,22 HAB = 257−273 cm−1 from eq 6. This range of HAB values is an upper bound estimate, since the presence of other accepting modes would improve the Franck−Condon overlap and reduce the electronic coupling strength. For comparison, Pt(pop) has a temperatureindependent ISC rate of ∼1.5 × 109 s−1,6 more than 50 times faster. The presence of higher energy O−H modes in Pt(pop), computed at ∼2800 cm−1,23 reduces m (quantum number of the 3A2u vibrational level isoenergetic to the 1A2u ground state; see eq 5) and leads to faster temperature-independent ISC. 1

⎪

⎪

⎪

⎪

1

The combination of a small displacement and a large energy gap leads to very small Franck−Condon factors (FC ≈ I[A,m],[B,n]2) for all but the highest energy modes. For ℏω1 = 160 cm−1 (corresponding to the Pt−Pt mode in 1A2u) and S1 = 0.14, for example, the FC factor is 4.1 × 10−63 at 310 K. By contrast, for ℏω1 = 1150 cm−1 (B−F stretch), the highest energy mode in Pt(pop-BF2), and S1 = 0.14, FC is 4.0 × 10−7 at 310 K. The use of high energy accepting modes leads to temperatureindependent kinetics, since the average vibrational quantum number remains close to zero throughout the entire temperature range. In this limit, eq 2b can be simplified to give eq 6, where m is the integer closest to −ΔE1/(ℏω1).

H 2 = AB ℏ

⎡ ⎛ ℏω ⎞⎤⎫ ⎟ ⎬ I|m|⎢S csch⎜ ⎝ 2kT ⎠⎥⎦⎭ ⎣

3

S1 = ( SB −

(2b)

The aforementioned lattice modes (ℏω′) permit transitions at nonintegral values of ΔE/(ℏω) by providing the difference in energy between ΔE and (n − m)ℏω. For ℏω′ ≪ kT, these low-frequency modes can be treated classically, with the delta function in eq 2b replaced by a Gaussian function, ⎡ (−ΔE + mℏω + λ)2 ⎤ exp⎢⎣ − ⎥⎦, where λ = S′ℏω′ is the reorganization 4λkT energy for the lattice mode.21 The magnitude of this parameter can be estimated from the spectral line width in the lowtemperature luminescence spectrum (eq 3a). kISC

(3b)

(3a)

Since we treat this mode classically at all temperatures, a minimum line width factor (MLW) is added to the Gaussian function to account for a finite vibronic line width at low temperature (eq 3b). B

3

DOI: 10.1021/acs.jpca.6b07891 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Indirect Channel. Since direct 1A2u → 3A2u ISC cannot account for the observed thermal activation of Pt(pop-BF2) ISC, we propose that an indirect ISC channel (in which 1A2u crosses into a deactivating state of predominantly triplet character, which in turn undergoes rapid internal conversion to 3 A2u) accounts for the temperature dependence of ISC in Pt(pop-BF2). To test this proposal, the temperature-dependent ISC rates were fit to eq 7, equivalent to eq 3b plus a temperature independent term corresponding to decay through the direct channel. kISC(T ) = k1 +

HAB,2 2

The calculated parameters indicate that the deactivating state is moderately displaced from both 1A1g and 1A2u, with a 0−0 energy approximately 1400−2600 cm−1 higher than 1A2u, translating into vertical excitation energies of approximately 28100−28800 cm−1 from the ground state (Figure 3). Spectroscopic evidence for a triplet state in that energy region is provided by an xy-polarized feature in the Pt(pop) crystal absorption spectrum at ∼25 000 cm−1 (approximately 700−900 cm−1 below 1A2u) with a vibrational progression of ∼120 cm−1 peaking at a final vibrational quantum number of 1 or 2.3,24 This vibrational frequency is only slightly greater than that of the Pt(pop) ground state (Raman,25 116 cm−1; phosphorescence,26 112 cm−1), which, along with the small S value, indicates that the state is less distorted along the Pt−Pt coordinate than the 1,3A2u(dσ* → pσ) states. The shorter Pt− Pt bond in Pt(pop-BF2) (2.887 vs 2.925 Å for Pt(pop))27 indicates greater Pt−Pt overlap that could shift this state to higher energy in the fluorinated compound. The xy-polarized feature in the Pt(pop) spectrum was attributed to the 1A1g → 3 A1g (dσ → pσ) transition.3 Moreover, xy-polarized absorption features appear underneath the z-polarized 1A1g → 1A2u absorption band in crystal spectra of the potassium, barium, and (n-C4H9)4N+ salts of Pt(pop),3,28 as well as in d8−d8 dimers of Rh.24,29 Subsequent work suggested that the Pt(pop) absorption feature may be an artifact resulting from crystal misalignment and stray light leaking through the crystal.28 Our numerical simulations of an absorption profile indicate that stray light contamination will not produce the suggested absorption artifacts on the wings of the band.28 Neither DFT calculations on Pt(pop) nor TDDFT calculations on Pt(popBF2) identify an electronic state in the appropriate energy region (Pt(pop), 25 000 cm−1; Pt(pop-BF2), 28 100−28 800 cm−1).27,30 Both calculations find triplet charge transfer states (pπ → pσ) about 5000 cm−1 higher in energy than the states implicated in the experimental work. Neither calculation reported the energy of the 3A1g (dσ → pσ) state. Irrespective of the precise assignment of the transition, the crystal absorption spectra of Pt(pop) clearly indicate that additional excited states lie close in energy to the 1A2u state. Given the small oscillator strengths of the xy-polarized transitions from the ground state to these states, it is likely that they are spin triplets (or have triplet spin parentage) and may be responsible for the indirect deactivation pathway from 1A2u. We will refer to this deactivating state as 3X. Our proposal parallels earlier ones in which a ligand field state, specifically, 3B2u (dσ* → dx2−y2),6,31 or an LMCT (3Eu) state,5 facilitates excited-state decay. The ligand field and LMCT states inferred from polarized absorption spectroscopy of Pt(pop) are at least 2800 cm−1 above 1A2u,28 a value substantially larger than that obtained by Milder and Brunschwig,6 indicating a lower lying deactivating state. As discussed earlier, the deactivating state is likely displaced from 1 A2u along the Pt−Pt coordinate, since no triplet other than 3 A2u would have the 1A2u Pt−Pt distance. Consequently, the Pt−Pt stretching mode will be an effective distorting mode, contributing to temperature-dependent Franck−Condon overlap. Analogous reasoning has been applied to the excited state decay pathways in Rh(I) isocyanide dimers.31 Distortion along additional coordinates, e.g., Pt−P, could also contribute to Franck−Condon overlap. Given the limited information available, however, introduction of more parameters would not be wise. In any event, the proposed dσ → pσ deactivating

⎡ ⎛ ℏω ⎞⎤ π exp⎢ −S2 coth⎜ 2 ⎟⎥ × ⎝ 2kT ⎠⎦ ⎣ λkT

ℏ ⎧ ⎡ mℏω ⎤ ⎡ ( −ΔE + mℏω + λ)2 ⎤ 2 2 ⎥ ∑ ⎨exp⎢⎣ ⎥⎦ exp⎢ − kT kT 2 4 MLW λ + ⎦ ⎣ ⎩ m =−∞ +∞

⎪

⎪

⎡ ⎛ ℏω ⎞⎤⎫ I|m|⎢S csch⎜ 2 ⎟⎥⎬ ⎝ 2kT ⎠⎦⎭ ⎣

⎪

⎪

(7)

Since the Pt−Pt distance in the deactivating triplet state would be expected to be intermediate between those of 1A2u, a dσ* → pσ state with a formal Pt−Pt bond order of 1, and the 1A1g ground state, with a formal Pt−Pt bond order of zero, the deactivating state would likely be substantially displaced along the Pt−Pt stretching mode vis-à-vis 1A2u. For this reason, Pt−Pt stretching (160 cm−1) was chosen as the distorting mode (ℏω2), with S2 between 0.5 and 6, the displacement between 1 A1g and 1A2u (vide supra). Since vibrational progressions in the Pt(pop-BF2) fluorescence spectrum were associated with phonon satellites of ∼35 cm−1,4 λ can be estimated to be 25 cm−1 assuming a Huang−Rhys parameter of 0.7 for the phonon modes. Franck−Condon analysis of the Pt(pop-BF2) fluorescence spectrum recorded at 10 K (Supporting Information) showed that MLW is ∼2000 cm−2 (Figure S2). By use of these fitting parameters and eq 7, S2 values from 0.5 to 3, with corresponding values of ΔE2, HAB2, and k1 computed to minimize unweighted χ2 (sum of the squared deviations between calculated and observed ISC rate constants), were found to provide reasonable fits to the temperature-dependent ISC rate constants (Figures 1 and 2, Table 1).

Figure 1. Contour plot of χ2 as a function of S2 and ΔE2, obtained by fitting temperature-dependent ISC rates of Pt(pop-BF2) to eq 7. C

DOI: 10.1021/acs.jpca.6b07891 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 2. Temperature dependence of kISC of the 1A2u excited state of Pt(pop-BF2): (orange circles) experimental data from ref 4; (lines) fit to eq 7, with parameters in Table 1 (see text for details).

Table 1. Parameters Obtained from Best Fits (Lowest Unweighted χ2) of Temperature-Dependent ISC Rates of Pt(pop-BF2) (Supporting Information Table S1) to Equation 7, ℏω2 = 160 cm−1, λ = 25 cm−1, MLW = 2000 cm−2 a S2

S1A1g

ΔE2, cm−1

HAB,2, cm−1

k1, ×107 s−1

χ2, ×1015 s−2

0.5 1.1 1.5 2.1 3.0

3.0 2.0 1.5 1.0 0.5

+1400 +1730 +1910 +2190 +2530

199 93 70 61 46

2.82 2.94 2.93 3.03 3.12

1.91 2.21 2.58 2.79 3.24

a Ranges of S2 considered were 0.5−1, 1−1.5, 1.5−2, 2−3, and 3−6. Displacement parameters with respect to the ground state (S1A1g) were calculated using eq 5.

state is expected to have a Pt−P distance similar to dσ* → pσ 1 A2u, implying that distortion along this coordinate is small.32

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CONCLUDING REMARKS We conclude that ISC in Pt(pop-BF2) occurs through direct 1 A2u → 3A2u and indirect 1A2u → 3X → 3A2u channels. Both channels can be treated within the multiphonon radiationless transition formalism. Owing to the small displacement between 1 A2u and 3A2u and the large energy gap between them, the direct channel has significant Franck−Condon overlap only for highenergy distorting modes (e.g., B−F, 1150 cm−1), resulting in a temperature-independent ISC rate. By contrast, our fitting indicates that the indirect channel involves ISC from 1A2u to a state that is moderately distorted (S = 0.5−3) along Pt−Pt (ℏω = 160 cm−1) and lies 1400−2600 cm−1 above 1A2u. This 3X state then undergoes rapid internal conversion to 3A2u. Electronic coupling matrix elements (HAB) appear reasonable, at less than ∼270 cm−1 for the direct channel and ∼50−210 cm−1 for the indirect channel. ISC via both the temperature independent and thermally activated pathways is slower for Pt(pop-BF2) than for Pt(pop). The former pathway is slower, owing to the presence of higher

Figure 3. Approximate energy curves for the ground (black) and dσ* → pσ excited states (triplet, cyan, blue; singlet, red) of Pt(pop-BF2). The green curves correspond to the estimated positions of the triplet state responsible for the thermally activated ISC process.

energy modes (O−H stretching) in Pt(pop) than in Pt(popBF2). The slower kinetics of indirect ISC are attributable to greater Pt−Pt overlap and therefore larger dσ−dσ* splitting in Pt(pop-BF2), which leads to a larger energy gap and unfavorable energetics.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b07891. D

DOI: 10.1021/acs.jpca.6b07891 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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without Back Intersystem Crossing. Inorg. Chem. 1988, 27, 2203− 2214. (12) Zinato, E.; Adamson, A. W.; Riccieri, P. Photophysics of Chromium(III) Cyanoammines - Solvent Medium Effects. J. Phys. Chem. 1985, 89, 839−845. (13) Milder, S. J.; Kliger, D. S. Photophysics of Dinuclear Rhodium(I) Isocyanides - Intersystem Crossing from an Upper Excited-State of Rh2b42+. J. Phys. Chem. 1985, 89, 4170−4171. (14) Milder, S. J. Effects of Envrionment on the Activated Nonradiative Decay of the 3A2 State of Rh2(TMB)42+. Inorg. Chem. 1985, 24, 3376−3378. (15) Allen, G. H.; White, R. P.; Rillema, D. P.; Meyer, T. J. Synthetic Control of Excited-State Properties - tris-Chelate Complexes Containing the Ligands 2,2′-Bipyrazine, 2,2′-Bipyridine, and 2,2′Bipyrimidine. J. Am. Chem. Soc. 1984, 106, 2613−2620. (16) Caspar, J. V.; Meyer, T. J. Photochemistry of MLCT ExcitedStates - Effect of Nonchromphoric Ligand Variations on Photophysical Properties in the Series cis-Ru(bpy)2L22+. Inorg. Chem. 1983, 22, 2444−2453. (17) Allsopp, S. R.; Cox, A.; Kemp, T. J.; Reed, W. J.; Sostero, S.; Traverso, O. Inorganic Photophysics in Solution 4. Deactivation Mechanisms of the 2Eg State of CrIII Complexes from Lifetime Studies. J. Chem. Soc., Faraday Trans. 1 1980, 76, 162−173. (18) Van Houten, J.; Watts, R. J. Temperature Dependence of the Photophysical and Photochemical Properties of the Tris(2,2′bipyridyl)ruthenium(II) Ion in Aqueous Solution. J. Am. Chem. Soc. 1976, 98, 4853−4858. (19) Targos, W.; Forster, L. S. Thermal Quenching of Cr(III) Luminescence. J. Chem. Phys. 1966, 44, 4342−4346. (20) Caspar, J. V.; Meyer, T. J. Photochemistry of Ru(bpy)32+. Solvent Effects. J. Am. Chem. Soc. 1983, 105, 5583−5590. (21) Brunschwig, B. S.; Sutin, N. Rate-Constant Expressions for Nonadiabatic Electron-Transfer Reactions. Comments Inorg. Chem. 1987, 6, 209−235. (22) S1 is not known for the B−F stretching mode, but 0.14 may be taken as an upper limit. (23) Gellene, G. I.; Roundhill, D. M. Computational Studies on the Isomeric Structures in the Pyrophosphito Bridged Diplatinum(II) Complex, Platinum Pop. J. Phys. Chem. A 2002, 106, 7617−7620. (24) Rice, S. F. Optical Spectroscopic Studies of Square Planar d8 Dimers. Ph.D. Thesis, California Institute of Technology, 1982. (25) Stein, P.; Dickson, M. K.; Roundhill, D. M. Raman and Infrared Spectra of Binuclear Platinum(II) and Platinum(III) Octaphosphite Complexes - A Characterization of the Intermetallic Bonding. J. Am. Chem. Soc. 1983, 105, 3489−3494. (26) Baer, L.; Englmeier, H.; Gliemann, G.; Klement, U.; Range, K. J. Luminescence at High Pressures and Magnetic Fields and the Structure of Single-Crystal Platinum(II) Binuclear Complexes Mx[Pt2(POP)4]·nH2O (Mx = Ba2, [NH4]4; POP = P2O5H22‑). Inorg. Chem. 1990, 29, 1162−1168. (27) Záliš, S.; Lam, Y.-C.; Gray, H. B.; Vlček, A. Spin−Orbit TDDFT Electronic Structure of Diplatinum(II,II) Complexes. Inorg. Chem. 2015, 54, 3491−3500. (28) Stiegman, A. E.; Rice, S. F.; Gray, H. B.; Miskowski, V. M. Electronic Spectroscopy of d8-d8 Diplatinum Complexes. 1A2u (dσ* → pσ), 3Eu (dxz,dyz → pσ), and 3,1B2u (dσ* → dx2‑y2) Excited States of Tetrakis(diphosphonato)diplatinate(4-), Pt2(P2O5H2)44‑. Inorg. Chem. 1987, 26, 1112−1116. (29) Rice, S. F.; Gray, H. B. Metal-Metal Interactions in Binuclear Rhodium Isocyanide Complexes. Polarized Single-Crystal Spectroscopic Studies of the Lowest Triplet→Singlet System in Tetrakis(1,3diisocyanopropane)dirhodium(2+). J. Am. Chem. Soc. 1981, 103, 1593−1595. (30) Novozhilova, I. V.; Volkov, A. V.; Coppens, P. Theoretical Analysis of the Triplet Excited State of the [Pt2(H2P2O5)4]4‑ Ion and Comparison with Time-Resolved X-ray and Spectroscopic Results. J. Am. Chem. Soc. 2003, 125, 1079−1087.

Table S1, temperature dependence of the Pt(pop-BF2) fluorescence lifetimes, fluorescence quantum yields, and ISC rate constants (from ref 4.); Figure S1, a fit of the ISC kinetics to an alternative multiphonon radiationless decay expression; Figure S2, Franck−Condon simulation of the 10 K Pt(pop-BF2) fluorescence spectrum (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: 626-395-2834. Present Address †

(YCL) Department of Chemistry, University of Illinois at Urbana−Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We have enjoyed several stimulating discussions with Tony Vlček and Hartmut Yersin about the nature of excited-state decay pathways in diplatinum complexes. We thank them for their contributions to the field. Our work was supported by NSF CCI Solar Fuels (Grant CHE-1305124).

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REFERENCES

(1) Rice, S. F.; Milder, S. J.; Gray, H. B.; Goldbeck, R. A.; Kliger, D. S. Photophysical Properties of the Lowest Electronic Excited States of Binuclear Rhodium(I) Isocyanide Ccomplexes. Coord. Chem. Rev. 1982, 43, 349−354. (2) Winkler, J. R.; Marshall, J. L.; Netzel, T. L.; Gray, H. B. Picosecond Spectroscopic Studies of (d8-d8) Binuclear Rhodium and Iridium Complexes: a Comparison of 1B2 and 3B2 Reactivity in Bis(1,5cyclooctadiene)bis(μ-pyrazolyl)diiridium(I). J. Am. Chem. Soc. 1986, 108, 2263−2266. (3) Rice, S. F.; Gray, H. B. Electronic Absorption and Emission Spectra of Binuclear Platinum(II) Complexes. Characterization of the Lowest Singlet and Triplet Excited States of Pt2(H2P2O5)44‑. J. Am. Chem. Soc. 1983, 105, 4571−4575. (4) Hofbeck, T.; Lam, Y. C.; Kalbác,̌ M.; Záliš, S.; Vlček, A.; Yersin, H. Thermally Tunable Dual Emission of the d8−d8 Dimer [Pt2(μP2O5(BF2)2)4]4−. Inorg. Chem. 2016, 55, 2441−2449. (5) Durrell, A. C.; Keller, G. E.; Lam, Y. C.; Sykora, J.; Vlcek, A.; Gray, H. B. Structural Control of 1A2u-to-3A2u Intersystem Crossing in Diplatinum(II,II) Complexes. J. Am. Chem. Soc. 2012, 134, 14201− 14207. (6) Milder, S. J.; Brunschwig, B. S. Factors Affecting Nonradiative Decay: Temperature Dependence of the Picosecond Fluorescence Lifetime of Tetrakis(dihydrogen diphosphate)diplatinum(4-). J. Phys. Chem. 1992, 96, 2189−2196. (7) Bixon, M.; Jortner, J. Intramolecular Radiationless Transitions. J. Chem. Phys. 1968, 48, 715−726. (8) Englman, R.; Jortner, J. Energy Gap Law for Radiationaless Transitions in Large Molecules. Mol. Phys. 1970, 18, 145−164. (9) Freed, K. F.; Jortner, J. Multiphonon Processes in the Nonradiative Decay of Large Molecules. J. Chem. Phys. 1970, 52, 6272−6291. (10) Lumpkin, R. S.; Kober, E. M.; Worl, L. A.; Murtaza, Z.; Meyer, T. J. Metal-to-Ligand Charge-Transfer (MLCT) Photochemistry Experimental Evidence for the Participation of a Higher Lying MLCT State in Polypyridyl Complexes of Ruthenium(II) and Osmium(II). J. Phys. Chem. 1990, 94, 239−243. (11) Ryu, C. K.; Endicott, J. F. Synthesis, Spectroscopy, and Photophysical Behavior of Mixed-Ligand mono(Polypyridyl)Chromium(III) and bis(Polypyridyl)Chromium(III) Complexes Examples of Efficient, Thermally Activated Excited-State Relaxation E

DOI: 10.1021/acs.jpca.6b07891 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A (31) Miskowski, V. M.; Rice, S. F.; Gray, H. B.; Milder, S. J. ExcitedState Decay Processes of Binuclear Rhodium(I) Isocyanide Complexes. J. Phys. Chem. 1993, 97, 4277−4283. (32) A qualitatively different proposed mechanism for thermally activated ISC involves populating higher vibrational levels of specific promoting modes, levels with better electronic coupling to 3A2u than the ground vibrational level (refs 5 and 27). ISC from excited vibrational levels is possible, but HAB at the ground vibrational level is already quite large (HAB,1 > 250 cm−1) owing to the large 1A2u−3A2u energy gap. An even larger HAB at excited vibrational levels would be required to account for the observed temperature dependence, which is unlikely. A more plausible mechanism would combine a promoting mode and a deactivating state; i.e., ISC would occur from excited vibrational levels into a low-lying triplet state. The advantage of such a model is that a smaller energy gap results in larger Franck−Condon overlap and does not require an implausibly large HAB. However, as with the model involving distortion along multiple modes discussed above, modeling a mechanism requiring so many parameters would not provide deeper insight.

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DOI: 10.1021/acs.jpca.6b07891 J. Phys. Chem. A XXXX, XXX, XXX−XXX