Monica C.
Carey
,
Sara L.
Adelman
and
James K.
McCusker
*
Department of Chemistry, Michigan State University, 578 South Shaw Lane, East Lansing, MI 48824, USA. E-mail: jkm@chemistry.msu.edu
First published on 10th December 2018
In an effort to better define the nature of the nuclear coordinate associated with excited state dynamics in first-row transition metal-based chromophores, variable-temperature ultrafast time-resolved absorption spectroscopy has been used to determine activation parameters associated with ground state recovery dynamics in a series of low-spin Fe(II) polypyridyl complexes. Our results establish that high-spin (5T2) to low-spin (1A1) conversion in complexes of the form [Fe(4,4′-di-R-2,2′-bpy′)3]2+ (R = H, CH3, or tert-butyl) is characterized by a small but nevertheless non-zero barrier in the range of 300–350 cm−1 in fluid CH3CN solution, a value that more than doubles to ∼750 cm−1 for [Fe(terpy)2]2+ (terpy = 2,2′:6′,2′′-terpyridine). The data were analyzed in the context of semi-classical Marcus theory. Changes in the ratio of the electronic coupling to reorganization energy (specifically, Hab4/λ) reveal an approximately two-fold difference between the [Fe(bpy′)3]2+ complexes (∼1/30) and [Fe(terpy)2]2+ (∼1/14), suggesting a change in the nature of the nuclear coordinate associated with ground state recovery between these two types of complexes. These experimentally-determined ratios, along with estimates for the 5T2/1A1 energy gap, yield electronic coupling values between these two states for the [Fe(bpy′)3]2+ series and [Fe(terpy)2]2+ of 4.3 ± 0.3 cm−1 and 6 ± 1 cm−1, respectively, values that are qualitatively consistent with the second-order nature of high-spin/low-spin coupling in a d6 ion. In addition to providing useful quantitative information on these prototypical Fe(II) complexes, these results underscore the utility of variable-temperature spectroscopic measurements for characterizing ultrafast excited state dynamics in this class of compounds.
Recent interest in the creation of molecular functionality based on earth-abundant materials has triggered efforts to develop analogs of compounds like [Ru(bpy)3]2+ but employing the more widely available metals of the first transition series. As is the case for ruthenium, metal polypyridyl complexes have provided a convenient platform for these efforts, with [Fe(bpy)3]2+ being one of the most well-studied as well as serving as an excellent template for illustrating fundamental principles underpinning d6 photophysics as they manifest in the first transition series.4 For this chromophore, absorption of visible light excites the low-spin 1A1 ground state into the singlet metal-to-ligand charge transfer (1MLCT) state, whereupon ultrafast intersystem crossing to the 3MLCT occurs in ∼20 fs.5 In contrast to their heavier group 8 congeners, whose 3MLCT states can last for several microseconds in deoxygenated solvents, deactivation out of the MLCT manifold occurs on the order of 100 fs with near-unit efficiency.6,7 These ultrafast non-radiative decay dynamics occur due to the presence of ligand field states that lie below the MLCT manifold (in contrast to [Ru(bpy)3]2+, in which these relative energetics are reversed). The lowest energy excited state – which for [Fe(bpy)3]2+ is the high-spin 5T2 state – is formed in less than 200 fs through a cascade of processes.8–11 Ground state recovery from this ligand field state occurs on the order of nanoseconds,12 the dynamics of which can be influenced to some extent by the solvent.13 This paradigm is being challenged recently through the work of Wärnmark and co-workers, who have exploited the strong σ-donating properties of N-heterocyclic carbene ligands to destabilize the ligand field states and realize 3MLCT lifetimes on the order of hundreds of picoseconds.14 This groundbreaking work notwithstanding, all known low-spin Fe(II) polypyridyl chromophores undergo ultrafast charge transfer deactivation as just described.
Despite the knowledge that has been gained from time-resolved optical5 and X-ray measurements9 previously carried out on [Fe(bpy)3]2+, there remain a surprising number of unanswered fundamental questions about this model complex, for instance, although attempts have been made to estimate the driving force (ΔG0) between the ground state and lowest energy excited state (1A1/5T2), a range of values spanning nearly 1 eV (i.e., 2000–9000 cm−1) have been posited in the literature.15–18 The underlying reason for this ambiguity is understandable: whereas steady-state emission spectroscopy and/or electrochemistry can be used to estimate ΔG0 for charge transfer states, the non-emissive, ligand-field nature of the 5T2 → 1A1 transition renders the application of these methods ineffectual. Values for the reorganization energy (λ) that characterizes the 5T2 → 1A1 conversion – a parameter that contains information about the structural distortions relevant for the kinetics of ground state recovery – as well as the magnitude of the electronic coupling between the two electronic states (Hab) have also been estimated but not directly measured. For example, Sutin used the lifetime of the 5T2 excited state of [Fe(bpy)3]2+ in a Marcus-type analysis to suggest ΔG0 = −7300 cm−1, λ = 4800 and Hab = 20–200 cm−1 as reasonable parameters for describing the potential energy surfaces defining the compound's ground state recovery dynamics.15 Soon thereafter, Jortner and co-workers applied second-order perturbation theory to approximate Hab at 170 cm−1.18 Hauser and co-workers studied [Fe(bpy)3]2+ doped into a Zn(II) lattice by variable-temperature time-resolved absorption spectroscopy.17 Using Jortner's estimate of the electronic coupling matrix element, these researchers determined the activation energy (Ea) of ground state recovery to be 364 cm−1 for a driving force of −2000 cm−1. As part of a study on a series of spin-crossover complexes, Conti et al. studied a low-spin Fe(II) complex possessing a relatively long-lived excited state using variable-temperature nanosecond time-resolved transient absorption spectroscopy in solution.19 In contrast to the results of Jortner, the analysis presented by Conti indicated an electronic coupling constant of < 10 cm−1 for the 5T2 → 1A1 conversion, a significant difference given that the rate constant for nonradiative decay scales as the square of this matrix element. While the approach by Conti is promising, a direct application of their methods is not possible in the case of compounds like [Fe(bpy)3]2+ due to the fact that this molecule is not a spin-crossover complex (i.e., ΔG0 ≫ kBT) and therefore not susceptible to environmental perturbations that allow one to quantify these sorts of thermodynamic parameters.
As part of a broader effort to better understand the energetics as well as the nature of the nuclear coordinate(s) that define the photo-induced intramolecular dynamics of low-spin Fe(II)-based chromophores, we sought to develop a more quantitative picture of the solution-phase ground state recovery dynamics of [Fe(bpy)3]2+ and in so doing develop a general methodology for examining in greater detail the factors driving the kinetics of this class of compounds. In this report, we present the results of an ultrafast variable-temperature time-resolved absorption study of a series of Fe(II) polypyridyl chromophores (Chart 1), describing for the first time the activation parameters associated with the ultrafast (i.e., sub-nanosecond) dynamics of this class of compounds. An analysis of the relaxation kinetics has served to quantify activation energies and frequency factors, which in turn provide insights into the electronic coupling and reorganization energy associated with the 5T2 → 1A1 conversion by correlating the experimental Arrhenius parameters to nonradiative decay theory. Specifically, the data indicate that the ligation motif (that is, a tris-bidentate versus bis-tridentate coordination environment) has a measurable effect on the specific vibrational modes that serve to define the nuclear coordinate for ground state recovery, suggesting that variable-temperature ultrafast spectroscopy combined with synthetic design can be a powerful tool for controlling the excited state dynamics of this class of chromophores.
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Chart 1 The four complexes used in these studies. Left: [Fe(bpy′)3]2+ family, in which R = H for [Fe(bpy)3]2+, CH3 for [Fe(dmb)3]2+, and tert-butyl for [Fe(dtbb)3]2+. Right: [Fe(terpy)2]2+. |
For the data presented herein, excitation energy at the sample was ∼5 μJ which yielded signals in the linear response regime. Samples were prepared in CH3CN at concentrations to afford absorbance values of ∼0.7 AU in a 1 cm sample cryogenic cuvette (FireFlySci) at the excitation wavelength of 490 nm. No changes in the absorption spectra acquired before and after the variable-temperature experiments were evident. Pulse characterization was performed within the cryostat via optical Kerr effect (OKE) measurements on neat acetonitrile;24 pump-probe cross-correlation indicated an instrument response function of less than 300 fs. The data presented represent an average of 10 scans; fits of individual scans were statistically indistinguishable from the averaged data. Data fitting was performed using the Igor Pro software, and all error bars reported are the result of propagation of error across multiple data sets.
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Scheme 1 Schematic overview of the variable-temperature apparatus used for time-resolved ultrafast transient absorption spectroscopy. |
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Fig. 1 Ground state electronic absorption spectra of [Fe(bpy)3](PF6)2 (red), [Fe(dmb)3](PF6)2 (green),25 [Fe(dtbb)3](PF6)2 (blue), and [Fe(terpy)2](PF6)2 (purple). All spectra were acquired in CH3CN solution at room temperature. |
The spectral profile of [Fe(terpy)2]2+ is quite different than the [Fe(bpy′)3]2+ family of compounds (although it possesses the same overall oscillator strength when one integrates the entire MLCT envelope). The sharp feature near 560 nm is characteristic of transition metal-terpyridine charge transfer complexes and is a reflection of a decrease in the relative nuclear displacements between the ground and excited state potential energy surfaces afforded by the conjugation of the ligand π-system across the three rings. The extent to which this may play a role in the ultrafast dynamics of these sorts of systems – in particular conversion from the MLCT state(s) to the lower-lying ligand field manifold – is an open question that is being pursued but is beyond the scope of the present study. Notwithstanding these differences, the gross similarities across the spectra of all four compounds allows for time-resolved optical studies to be carried out under essentially identical experimental conditions. This will simplify the process of making comparisons and should allow for any differences noted to be correlated to fundamental distinctions in the molecular origins of the observed dynamics.
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Fig. 2 Single-crystal X-ray structures of the cations of [Fe(dmb)3](PF6)2 (left) and [Fe(terpy)2](PF6)2 (right). Solvent molecules as well as the PF6− counterions have been omitted for clarity. |
Complex | Fe–N distance (Å) | Cis N–Fe–N angle (°) | Trans N–Fe–N angle (°) | Ref. |
---|---|---|---|---|
[Fe(bpy)3](PF6)2 | 1.9670 ± 0.0004 | 81.86–94.31 | 174.61 | 17 |
[Fe(dmb)3](PF6)2 | 1.967 ± 0.006 | 80.92–97.52 | 173.80–176.12 | This work |
[Fe(dtbb)3](PF6)2 | 1.957 ± 0.001 | 81.06–95.84 | 172.62–175.5 | 18 |
[Fe(terpy)2](PF6)2 | 1.881 ± 0.002 | 80.82–99.97 | 161.97–178.83 | This work |
1.976 ± 0.005 |
The effect of temperature on the index of refraction of the sample solution turns out to be a surprisingly significant issue to deal with from an experimental perspective. The temperature dependence of some common solvents – including acetonitrile – has been studied previously.28,29 Specifically, as the temperature decreases, the solvent's refractive index increases. This directly impacts the experiment in two important ways. First, the pump-probe overlap will change with temperature. The perturbation to the propagation of the pump through the sample will be more pronounced than that of the probe in our setup because the pump is oriented at an angle (5–10°) relative to the optical axis of the probe in an effort to minimize scatter reaching the detector. A good solution to this problem is to optimize overlap on the side of the cuvette away from the detector (i.e., where the beams first enter the sample): in this configuration, the probe beam traverses a relatively straight path to the detector, and any beam refraction in the pump due to solvent will occur after the beams have overlapped, thereby minimizing adverse effects on the data. Second, we found that the amount of pump scatter significantly increased with decreasing temperature. The physical origin of this is unclear. All of our measurements were carried out above the freezing point of the solvent, so the effect is not associated with the formation of nucleations within the solution. Pump scatter manifests as a negative signal superimposed on the solute's kinetics, which in turn artificially shortens the observed time constant. Since the magnitude of the effect varies with temperature, failure to account for this results in non-linear Arrhenius plots. The most straightforward way to address this issue would be the incorporation of a monochromator as part of a two-color setup in order to discriminate against pump scatter. The drawback to this approach is the significant loss in light throughput, which impacts sensitivity. Using our bandpass setup, we found that selecting probe wavelengths well-separated spectrally from the excitation wavelength (>50 nm) negated this problem.
![]() | (1) |
Complex | ΔEox (V) | Lifetime at 292 K (ns) | Lifetimea at 235 K (ns) | A (ps−1) | E a (cm−1) |
---|---|---|---|---|---|
a The freezing point of CH3CN is 228 K. | |||||
[Fe(bpy)3](PF6)2 | 0.68 | 1.05 ± 0.02 | 1.52 ± 0.03 | 230 ± 20 | 310 ± 15 |
[Fe(dmb)3](PF6)2 | 0.52 | 1.32 ± 0.02 | 2.01 ± 0.04 | 240 ± 20 | 345 ± 10 |
[Fe(dtbb)3](PF6)2 | 0.53 | 1.07 ± 0.01 | 1.56 ± 0.02 | 230 ± 15 | 315 ± 15 |
[Fe(terpy)2](PF6)2 | 0.72 | 5.2 ± 0.1 | 12.6 ± 1.7 | 150 ± 55 | 755 ± 70 |
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Fig. 4 Arrhenius plot for ground state recovery dynamics of [Fe(bpy)3](PF6)2 in CH3CN solution. The solid line corresponds to a fit of the data to an Arrhenius model (eqn (1)), indicating an activation energy of 310 ± 15 cm−1 and an intercept (i.e., the rate constant in the limit of no barrier) of 230 ± 20 ps−1. |
Analogous data were obtained for the two other 4,4′-di-substituted complexes in the [Fe(bpy′)3]2+ family and are summarized in Table 2. The relaxation kinetics for [Fe(dmb)3]2+ and [Fe(dtbb)3]2+ are generally similar to those obtained for [Fe(bpy)3]2+, however, some interesting features are apparent. Alkyl groups are expected to be electron-donating, a point reflected by the ca. 0.15 V decrease in the Fe(II/III) oxidation potential observed for both [Fe(dmb)3]2+ and [Fe(dtbb)3]2+ relative to [Fe(bpy)3]2+ (Table 2). Oxidation samples the t2g orbitals of the metal, but the multielectronic nature of term states makes it difficult to draw a correlation between shifts in redox potential and the ligand field strength that serves to define term state energies. That being said, we note that the data acquired on [Fe(dtbb)3]2+ are experimentally indistinguishable from those of [Fe(bpy)3]2+, both in terms of the measured Arrhenius barrier as well as the rate constant in the barrierless limit. This suggests that the energetics associated with the potential energy surfaces that define ground state recovery in these two complexes are basically identical. The other member of this series, [Fe(dmb)3]2+, presents a slightly different picture: whereas the intercept of the Arrhenius plot is identical to the other two tris-bidentate complexes, the measured barrier is slightly larger. Admittedly the difference is small given the error bars, but the differences in time constants for ground state recovery are well outside of experimental error. We take this as an indication that a subtle but observable difference exists in the energetics that serve to define the dynamics of [Fe(dmb)3]2+ relative to the other two compounds. Plots for the variable-temperature ground state recovery spectra and Arrhenius fittings for all of the compounds listed in Table 2 can be found in the ESI.†
![]() | (2) |
![]() | (3) |
![]() | (4) |
We consider first the pre-exponential term. As stated above and shown in Table 2, the three tris-bidentate complexes exhibit the same frequency factor within experimental error. Using the value of A = 240 ± 20 ps−1 measured for [Fe(bpy)3]2+, rearrangement of eqn (3) yields Hab4/λ = 1/(30 ± 5). The values of Hab and λ obviously cannot be independently-determined from this expression, however, we can use informed estimates to obtain a range of values that these parameters must fall within to be consistent with experimental data. An initial calculation of Hab for high-spin to low-spin conversion in Fe(II) spin-crossover systems was carried out by Jortner and co-workers based on a second-order perturbation theory treatment of spin–orbit coupling between the S = 0 and S = 2 states.18 Using Hab = 170 cm−1 obtained from that analysis, Hab4/λ = 1/(30 ± 5) affords a physically unrealistic value of ∼3 × 106 eV (25 × 109 cm−1) for the reorganization energy. If we assume values for λ to be in the range of 0.25–2.5 eV (ca. 2000–20000 cm−1) as proposed by various groups,15,30–32 the magnitude of the electronic coupling can only span from ca. 3–5 cm−1 and still be consistent with our experimental data. Indeed, an unrealistically low value of λ = 800 cm−1 yields Hab = 2.3 cm−1, whereas an unrealistically high value of λ = 20
000 cm−1 corresponds to Hab = 5.1 cm−1. This narrow range of possible values for Hab emerging from this analysis is due to the quartic relationship between Hab and λ stemming from eqn (3) and allows for a surprisingly high degree of confidence in the magnitude of Hab that can be obtained from these variable-temperature measurements.
Unfortunately, the same level of precision is not possible when extracting information about the driving force and reorganization energy associated with ground state recovery dynamics. The problem arises due to the fact that the experimentally-determined activation energy reflects a convolution of ΔG0 and λ, whereas the pre-exponential term convolves λ and Hab. Absent an independent determination of one of these three variables, this is an analytically unsolvable problem and therefore can only be addressed numerically, which in turn requires that certain assumptions be introduced.
The most direct means for assessing ground state/excited state energetic differences is emission spectroscopy. Unfortunately, the fact that the 1A1 and 5T2 terms are characterized by ΔS = 2 means that radiative coupling between these two states is effectively zero. For excited states that are charge transfer in nature, electrochemical methods can often be used to gauge excited state energetics even in cases where the state is non-emissive because the energy of the state is correlated to the redox properties of the components;4 however, since ligand field states derive from excited configurations within the d-orbital of the metal (and therefore do not have a redox-based equivalent descriptor), electrochemistry cannot provide the same insight into energetics for this class of excited states.
One approach for assessing relative ligand field-state energetics across a series is to use electrochemical information in conjunction with an assumed value for a reference compound. Given all of the previous work that has been carried out on [Fe(bpy)3]2+, we could in principle write the following expression,
![]() | (5) |
Bearing this in mind, a value of ΔG0 = −7300 cm−1 originally cited by Sutin15 for [Fe(bpy)3]2+ falls well within the range that has been suggested over the years. We can therefore use this free energy difference as a reference point for obtaining estimates for the other Marcus parameters across our series of compounds. In order to factor in some degree of uncertainty in this value, we have included an error bar of ± 10% on the value of ΔG0 and propagated this through the analysis described below. The choice of the magnitude of uncertainty is somewhat arbitrary but does correspond to approximately one standard deviation across the range of values most commonly cited in the literature. At the same time, it is not so large as to obscure any differences between complexes in the Marcus analysis that the experimental data clearly establish. Further details concerning this issue can be found in the ESI.†
The first set of Marcus parameters we will discuss are those for [Fe(bpy)3]2+. The measured activation energy for this compound is 310 ± 15 cm−1: assuming ΔG0 = −7300 ± 730 cm−1, the two possible values for λ stemming from the quadratic nature of eqn (4) are 4800 ± 500 cm−1 and 11000 ± 1000 cm−1. We note that the former value is essentially identical to the estimate provided by Sutin,15 however, since the two values obtained from eqn (4) place the dynamics of ground state recovery on either side of the apex of the Marcus curve, it is important to consider which value is more physically realistic in order to properly conceptualize the photophysical processes occurring in this system.
The high-spin to low-spin conversion in a d6 metal ion represents one of the largest intramolecular structural changes one can come across in the transition block: the change from a to
configuration results in a ∼15 cm3 mol−1 volume contraction of the compound37 due primarily (though not exclusively) to a ca. 10% reduction in metal–ligand bond length that accompanies depopulation of the σ* orbitals. Unfortunately, the only quantitative information available in the literature pertaining to reorganization energy in Fe-based complexes comes from self-exchange measurements. Since self-exchange is an electron transfer process, the measured reorganization energy would be expected to include outer-sphere contributions that will be significantly attenuated in the ground state recovery dynamics of [Fe(bpy)3]2+. Moreover, self-exchange in cases such as [Fe(H2O)6]2+/3+ or [Fe(CN)6]4−/3− do not involve a high-spin/low-spin conversion, which is obviously a critical factor in the present setting.
Information about reorganization energies associated with the excited states of [Ru(bpy)3]2+ are known,38 but we believe that a better comparison is afforded from self-exchange measurements of Co(III) complexes where reduction of a low-spin d6 complex typically yields a high-spin species as the product. Hamann et al. have in fact recently published a study of the self-exchange parameters of various Co(III) complexes in the context of their work on Co-based redox shuttles for use in dye-sensitized solar cells.39 These researchers report a reorganization energy associated with self-exchange of [Co(bpy)3]2+ of 3.21 eV. A detailed accounting of outer-sphere contributions enabled them to specify a value for the inner-sphere component of 2.63 eV, or ∼1.3 eV (∼10500 cm−1) per Co ion. Although the force constants associated with ligand binding to Co(III) are expected to be somewhat larger than for Fe(II), the structural rearrangement in the Co(III/II) self-exchange is more analogous to that of the high-spin to low-spin conversion in Fe(II) polypyridyls, making the 10
500 cm−1 value a more reasonable touchstone for [Fe(bpy)3]2+. We therefore assert that, within the limits imposed by our estimate of ΔG0, 11
000 ± 1000 cm−1 represents a reasonable value for the reorganization energy associated with ground state recovery in [Fe(bpy)3]2+ and places the dynamics of this system firmly within the Marcus normal region.
We can now use the results just described for [Fe(bpy)3]2+ as a reference point for interpreting the data we have obtained for the other two members of the [Fe(bpy′)3]2+ series. In order to do this, we must reconcile two somewhat conflicting pieces of information, namely the (essentially) identical oxidation potentials of the metal measured for [Fe(dmb)3]2+ and [Fe(dtbb)3]2+ and the differing activation parameters obtained for the two complexes from our variable-temperature measurements (Table 2). If we employ eqn (5), that is assume that the change in ΔG0 tracks the energy of the t2g orbitals as measured by the Fe(II/III) oxidation potential, one must also assume a reduction in the magnitude of the reorganization energy for [Fe(dtbb)3]2+ relative to [Fe(bpy)3]2+. Indeed, using eqn (5) and the measured activation energy for [Fe(dtbb)3]2+, a value of λ ≈ 9500 cm−1 is obtained. The electrochemical data clearly indicate that the metal center in [Fe(dtbb)3]2+ is more electron-rich than in [Fe(bpy)3]2+; although we would not expect 4,4′-tert-butyl substituents to play a role in the reorganization of the primary coordination environment about the Fe(II) center, they could impact outer-sphere contributions.13,40 Alternatively, if we instead assume that the reorganization energy for [Fe(dtbb)3]2+ is the same as what we determined for [Fe(bpy)3]2+, the experimental activation energy affords a value of ΔG0 = −7300 cm−1, i.e., identical to that of [Fe(bpy)3]2+. The available data do not allow us to differentiate between these two possibilities, but the fact that the variable-temperature kinetic data for [Fe(bpy)3]2+ and [Fe(dtbb)3]2+ are identical in all respects compels us to favor the latter analysis. We would therefore suggest that in the case of [Fe(dtbb)3]2+, the destabilization of the t2g orbitals indicated by the negative shift in the Fe(II/III) potential is offset by a corresponding destabilization of the orbitals, leading to nearly identical ligand field splittings (and correspondingly similar variable-temperature ground state recovery dynamics) for the two compounds.
While [Fe(dmb)3]2+ and [Fe(dtbb)3]2+ exhibit very similar oxidation potentials, the Arrhenius parameters of these two complexes are more disparate. The data for [Fe(dmb)3]2+ display an increase in the measured activation energy, which implies a decrease in ΔG0 and/or an increase in λ for ground state recovery relative to [Fe(bpy)3]2+. As with the introduction of the tert-butyl group in [Fe(dtbb)3]2+, it is difficult to envision how incorporation of a methyl group on the periphery of the ligand will have a significant impact on the inner-sphere reorganization energy associated with dynamics within the ligand field manifold. That being said, regardless of whether one assumes a value of ΔG0 = −6000 ± 600 or λ = 11000 cm−1, the experimental data for [Fe(dmb)3]2+ necessitate a reduction in the effective ligand field strength of dmb relative to bpy when bound to Fe(II) (Table 3). Methyl groups are well-documented σ-donors and therefore should destabilize the
orbitals (although, as in case of [Fe(dtbb)3]2+, we have no direct experimental probe of these energetics). The measured oxidation potential for [Fe(dmb)3]2+ clearly reveals a destabilization of the t2g orbitals; the more negative reduction potential for dmb versus bpy indicates that the former is more electron-rich which will make it both a better π base and a weaker π acid.41 Previous soft X-ray data on an analogous Fe(II) complex has demonstrated that the electron-donating ability of the bipyridine ligand is also intrinsically tied to the nature of the electronic state.42 Specifically, it was observed that in the 5T2 excited state, both σ-donation from and π-backbonding to the ligand are significantly attenuated relative to the 1A1 ground state. We cannot easily disentangle these various contributions a priori, but the variable-temperature time-resolved absorption data support an interpretation in which dmb presents a slightly diminished ligand field overall as compared to bipyridine.43 We point out that our conclusion, which follows directly from the experimental data provided in Table 2, is consistent with recent theoretical work by Jakubikova and co-workers suggesting a more significant role for ligand π-donation in polypyridyl complexes of Fe(II).44
Complex | H ab 4/λ | H ab (cm−1) | ΔG0a (cm−1) | λ (cm−1) | ΔG0b (cm−1) |
---|---|---|---|---|---|
a Calculated from the Fe(II/III) oxidation potentials (ΔEox) and eqn (5).
b Calculated assuming a value for λ of 11![]() |
|||||
[Fe(bpy)3](PF6)2 | 1/(30 ± 5) | 4.4 ± 0.2 | −7300 ± 730 | 11![]() |
−7300 ± 730 |
[Fe(dmb)3](PF6)2 | 1/(33 ± 4) | 4.2 ± 0.1 | −6000 ± 600 | 9700 ± 900 | −7100 ± 710 |
[Fe(dtbb)3](PF6)2 | 1/(29 ± 4) | 4.3 ± 0.2 | −6100 ± 610 | 9500 ± 900 | −7300 ± 490 |
[Fe(terpy)2](PF6)2 | 1/(14 ± 9) | 6.2 ± 1.2 | −7600 ± 760 | 14![]() |
−5200 ± 480 |
Lastly, we note that despite the subtle differences in activation energies and driving forces across these three complexes, the pre-exponential term and therefore the Hab4/λ ratios are relatively constant (Table 2). The extent to which this may be providing insight into the nature of the nuclear coordinate that defines the trajectory for excited state dynamics in this class of compounds is highlighted by the results obtained on [Fe(terpy)2]2+ described below.
As with the analysis of the data for the bpy′ series, we cannot analytically solve for the three Marcus parameters for [Fe(terpy)2]2+ but we can evaluate the data numerically in order to identify a range of values that are physically reasonable. Focusing first on the pre-exponential term, if we assume that the electronic coupling between the 5T2 and 1A1 states is the same as what was determined for the [Fe(bpy′)3]2+ series, a value of ∼5000 cm−1 is found for the reorganization energy. [Fe(terpy)2]2+ exhibits relaxation along a multimode coordinate, one of which is a change in metal–ligand bond length similar to that observed for [Fe(bpy)3]2+ as evidenced by time-resolved X-ray spectroscopy.46 Moreover, recent calculations from Nance et al. identify a rocking motion of the terpy ligand to be an important vibrational mode associated with conversion from the high-spin to low-spin state.47 Based on these considerations, it seems likely that the reorganization energy for ground state recovery in [Fe(terpy)2]2+ should be at least as large if not larger than what we determined for [Fe(bpy)3]2+, which in turn implies that the magnitude of Hab must be larger for [Fe(terpy)2]2+ than what was found for the [Fe(bpy′)3]2+ series.
To understand what an increase in Hab tells us about the energetics of [Fe(terpy)2]2+, we need to consider the origin of Hab for the high-spin to low-spin conversion in Fe(II). The 5T2 → 1A1 transition is one that involves a net spin change of two units (i.e., S = 2 to S = 0). There is no matrix element that directly couples two states for which ΔS = 2, so the avoided crossing on the lowest-energy potential surface for Fe(II) polypyridyl complexes arises due to a higher-order interaction.48 Specifically, mixing can occur between the 5T2 and lowest-energy S = 1 excited state (i.e., 3T1) as well as between the 1A1 and 3T1 states via second-order spin–orbit coupling. The 3T1 state therefore serves as a common link between the high-spin and low-spin configurations to yield a small but non-zero degree of electronic coupling between the S = 0 and S = 2 manifolds. Whether a second-order perturbation treatment is valid for these sorts of systems is open to debate,48 however, the extent of mixing between the 5T2 and 3T1 states will still be inversely proportional to their energy separation. An increase in Hab in this circumstance is therefore indicative of a decrease in the 3T1–5T2 energy gap which, for compounds such as [Fe(terpy)2]2+ where the 5T2 state is the lowest-energy excited state of the system, can only arise from an increase in ligand field strength.49
Using the experimental activation parameters in Table 2, the data acquired on [Fe(terpy)2]2+ are consistent with a slightly larger free energy difference of ΔG0 = −7600 ± 760 cm−1, an electronic coupling of Hab = 6.2 ± 1.2 cm−1, and a reorganization energy of 14100 ± 1200 cm−1 (Table 3). The dynamics of ground state recovery for [Fe(terpy)2]2+ are therefore still in the Marcus normal region, with the slight increase in ligand field strength being offset by a larger increase in the magnitude of the reorganization energy. An increased reorganization energy associated with ground state recovery in [Fe(terpy)2]2+ compared to [Fe(bpy)3]2+ is consistent with a more complex nuclear coordinate that possibly incorporates a Fe–N bending mode.45,46 Given the fact that the ground-state geometry surrounding the central metal ion in [Fe(terpy)2]2+ is more strongly distorted from pseudo-octahedral symmetry than what is found for [Fe(bpy)3]2+ (and therefore presumably leading to less favorable orbital overlap from the ligating nitrogen atoms), we suggest that the modest increase in ligand-field strength for terpy relative to bpy is due to an attenuation of π-donation effects from the former.
Perhaps the most significant take away from the variable-temperature data stems from the constancy in the ratio of the electronic coupling to the reorganization energy for the [Fe(bpy′)3]2+ family of complexes and the fact that this ratio changes significantly for [Fe(terpy)2]2+. Specifically, the increase in reorganization energy that we infer for [Fe(terpy)2]2+ lends support to the experimental46 and theoretical47 findings implicating a distinct and possibly more complex nuclear coordinate for the 5T2 → 1A1 conversion in this compound as compared to [Fe(bpy)3]2+-based complexes. With only the single data point of [Fe(terpy)2]2+ in hand it is difficult to generalize these results with regard to nuclear coordinate trajectories for bis-tridentate versus tris-bidentate binding motifs. It makes sufficient intuitive sense that changes in the nature of the primary coordination sphere could have a particularly significant impact on the mechanism of excited state dynamics involving ligand field states to warrant further study of these types of systems. In this regard, the fact that we are able to identify differences in the nature of the reaction coordinate from variable-temperature optical pump-probe spectroscopy hints at the potential for such measurements to provide insight into the dynamics of a much wider range of chemical systems.
Finally, an important caveat to the conclusions drawn from this work lies in the estimation of ΔG0, the driving force for ground state recovery. We strove to be as forthright as possible with regard to the potential errors that stem from the inability to directly measure the free energy difference for this doubly-spin forbidden, non-emissive process, but we acknowledge the shortcomings inherent in having to approximate ΔG0 in this way. Efforts to overcome these difficulties to allow for an unambiguous determination of all of the parameters necessary for characterizing the excited state dynamics are already well underway and will form the basis of a future report.
Footnote |
† Electronic supplementary information (ESI) available. CCDC 1810752 and 1810753. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c8sc04025g |
This journal is © The Royal Society of Chemistry 2019 |