Reduction potentials (E0) are highly variable in [FeX4] redox couples. In particular, the redox potentials of [FeCl4]2,1 and [Fe(SCH2CH3)4]2,1 differ by almost 1 V in acetonitrile (E0are0.08 V and1.0 V, respectively). (The vertical ionization energy also excludes energetic effects from geometric distortions upon redox that are important for adiabatic ET. The difference in adiabatic corrections for both species has been calculated at0.2 eV, stabilizing the tetrachloride 702 Spectroscopy and Electronic Structure of [FeX4]n(XẳCl, SR)
relative to the tetrathiolate since the former exhibits more pronounced geometric changes upon redox.) The redox potentials of transition metal complexes are considered from the perspective of oxidation of the reduced (ferrous) species (not including solvent effects). Within this context, contributions can be divided into three intrinsic factors: (i) the effect of the LF on the RAMO, (ii) the energy of the 3d manifold given by the effective nuclear charge of the metal ion within the ligand environment, and (iii) the changes in the electronic and geometric structure on oxidation (i.e., electronic and geometric relaxation, where the latter corresponds to a reorganization energy).
Figure 12 Redox densities for [Fe(SCH3)4]2,1(a) excluding and (b) including the effect of electronic relaxation.
Ψf M
Ψi L
ΨfL Ψi
M
Ψf M
ΨfL Ψk
M
Ψk L
Wf
Wi
Erlx
dn+1L cdn+1L
dn
cdn
Q
∇
i –e–+Q k rlxSA f
Figure 11 VBCI model developed to define electronic relaxation, i.e., the difference between the unrelaxed final state (Koopmans state) and the true relaxed final state.10 The left side of the diagram represents the initial state configuration interaction between thejdniground configuration and thejdnþ1Licharge transfer configuration; these valence bond (VB) states are separated by. The two VB wave functions mix (based upon the mixing parameter, T) to yield the CI-mixed Mi and Li states, split byWiẳ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2þ 4T2
p . To
create the final state wave functions, the metal-based VB configuration (jcdni) is destabilized relative to the CT configuration (jcdnþ1Li) by an amountQ, the magnitude of the 2p–3dhole interaction. These final state VB states also mix through T to give the correct final state wave functions ( Mf and Lf) split by Wf ẳ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðQị2 ỵ 4T2 q
. The unrelaxed final state ( Mk and Lk) is defined by distributing the effect ofQ to each of the CI-mixed wave functions based on the amount of jdni in the original ground state wave functions. The expected intensities of the PES transitions are shown on the far right. Without relaxation, a single peak is expected, corresponding with the energy of the Mk state. Inclusion of relaxation redistributes
the intensity over the Mf and Lf wave functions based on the sudden approximation.
The large difference in E0between the two redox couples is also observed as a large shift in the vertical ionization energies (Ivert) of the RAMO in each species, which indicate the tetrathiolate is 1.4 eV easier to oxidize than the tetrachloride (see Figure 13). The experimentalIvertdemon- strates that there is a large difference in the intrinsic ionization potentials of the two species as contributions from the environment are not included.
LF effects are evaluated by comparison of the LF splitting diagrams for the ferrous species (Figure 8). In these diagrams, the RAMO corresponds the lowest energy 3d orbital. Direct comparison of the RAMO energy (relative to the baricenter of the 3d manifold) indicates that there is very little difference between the two systems; although 10Dqis greater for [FeCl4]2, the axial splitting in [Fe(SR)4]2is larger and results in similar overall energies for the RAMO. From this, the LF effect is negligible and is not expected to play a significant role in defining the reduction potential of the redox couples.
The energy of the Fe 3dmanifold is evaluated by theoretical correlation with experimental core binding energies. X-ray photoelectron spectroscopic (XPS) data for the Fe 2p3/2 core ionization allow us to determine the relaxation-correction core binding energy for each species (see Kennepohl and Solomon10for details). The Fe 2p3/2binding energy for [FeCl4]2is nearly 1.4 eV greater than that for [Fe(SR)4]2indicating that the effective charge on the metal (ZFeeff) is much greater in the tetrachloride. From this, we can estimate that the valence Fe 3dbinding energies differ by1.2 eV (note that the core to valence shifts are 0.9). Valence ionization is thus inherently easier for the tetrathiolate due to its lowerZeffFe; this is a direct result of the greater covalency in the tetrathiolate complex relative to the tetrachloride. This effect clearly represents the dominant contribution to the 1.4 eV difference in Ivertbetween the two redox couples.
The effect of electronic relaxation is evaluated using the VBCI model discussed in Kennepohl and Solomon10. From this model, the energy stabilization due to electronic relaxation (Erlx) can be calculated directly for either core or valence ionization (see Figure 11). In the valence region, it is found that Erlx0.4 eV for [FeCl4]2 and 0.6 eV for [Fe(SR)4]2. The influence of relaxation on the absolute ionization energies (and reduction potentials) is, therefore, very large, although the relative influence on Ivert between the tetrathiolate and the tetrachloride is Erlx0.2 eV.
Altogether, the greatest contribution to Ivert between [FeCl4]2,1and [Fe(SR)4]2,1is the effective charge on the metal ion, which is much greater in the tetrachloride due to its lower metal–ligand covalency. Electronic relaxation also plays a significant role in Ivert; the experi- mental data clearly demonstrate the overall importance of relaxation in ionization energies and reduction potentials. Lastly, LF splitting is negligible in these systems, even though LF effects are commonly regarded as influential in defining reduction potentials.
Figure 13 Valence ionization data for [FeCl4]2and [Fe(SR)4]2presented as45 eV25 eVspectra (see Kennepohl and Solomon10for details). The spectra are referenced to the common tetraethyl ammonium counterion core
ionization peaks.
704 Spectroscopy and Electronic Structure of [FeX4]n(XẳCl, SR)
2.59.5.2 Reorganization Energies
The inner-sphere reorganization energy (i) is determined by the intrinsic geometry change that occurs on redox; the metal–ligand bond distance change (rredox) is usually the vibrational mode of greatest importance. From crystallographic data, [FeCl4]2,1 has a much larger geometric change on redox (rredoxẳ0.11 A˚) than [Fe(SR)4]2,1(rredoxẳ0.05 A˚). This correlates with the experimental core Fe 2p3/2 binding energy shift between the reduced and oxidized species (EFe 2predox
3=2), which is much larger for the tetrachloride (2.4 eV) than for the tetrathiolate (0.3 eV) indicating thatqredoxis much larger in the former (see Kennepohl and Solomon11 for details).
This result is also observed in DFT results, which correlate well with the experimental results. The calculatedqredoxfor [FeCl4]2,1is0.2 e, whereas that for [Fe(SR)4]2,1is only 0.1 e. From this, it is concluded thatrredox(and by extension,i) directly correlate withqredoxfor a particular redox couple. This demonstrates that changes in the electrostatic attraction between the metal and the ligands dominate the changes observed in the bond distances on redox. Table 2provides a breakdown of contributions toqredox; the greater covalency of the tetrathiolate, as well as its greater electronic relaxation both contribute to its lowerqredoxrelative to the tetrachloride.
The origin of the smallqredox(and thusrredox) for both species was investigated in detail by generating DFT-calculated potential energy surfaces for each of the species (Figure 14). Import- antly, therredoxcalculated using the BP86 functional are in good agreement with those observed experimentally. (The calculated gas phase bond distances are larger than the experimental crystal- lographic bond distances, which is unsurprising due to the anionic nature of the complexes. The effect is less for the tetrathiolate since the negative is better distributed over the larger complex.) A potential energy surface is also generated for the unrelaxed oxidized species, thus allowing evaluation of the effect of electronic relaxation (see FeIII* in Figure 14). Of great importance is that the rredox without electronic relaxation are predicted to be 0.20 A˚ and 0.17 A˚ for [FeCl4]2,1 and [Fe(SR)4]2,1, respectively. The effect of electronic relaxation is, therefore, extremely important in both cases. The same effect is observed when i is calculated from the surfaces; electronic relaxation decreasesesei from 1.7 eV to 0.8 eV for [FeCl4]2,1and from 0.9 eV to 0.1 eV for [Fe(SR)4]2,1. (The calculated values for the inner-sphere reorganization energy are in good agreement with values obtained from the experimental structures (0.7 eV and 0.3 eV for the tetrachloride and the tetrathiolate, respectively.) Clearly, electronic relaxation has a dramatic effect on the inner-sphere reorganization energy in both redox couples, loweringesei by almost 1 V in each case. For the tetrathiolate redox couple, the final effect is that bothrredoxand esei are inherently very small, allowing for facile ET.
2.59.5.3 Electronic Coupling Matrix Element
From Marcus-Hush theory, the electronic coupling matrix element (HDA) is critically important in defining the rate of ET. For Rd, a structural model of the active site was constructed to include the surrounding protein fold and H-bonding interactions that directly influence the iron tetra- thiolate active site in order to properly describe the electronic structure of the active site within the protein. (As shown previously, the electronic structure of these systems is highly dependent on the orientation of the thiolate.) From full DFT calculations on this structural model, the RAMO (Figure 15) is mostly Fe 3dz2 in character (85%) with contributions from the S pseudo- and the SCligand orbitals. Note that the 3dx2y2 RAMO obtained for the [Fe(SCH3)4]2,1model (and seen inFigure 12) differs from that calculated for Rd due to differences in the orientation of the C in the thiolate ligands between the model and the protein active site. The 3dz2 Rd RAMO is poorly oriented with respect to the protein surface such that direct overlap of the Fe 3dz2 for electron self-exchange (ese) is not possible. Superexchange through to the cysteinate ligands is, therefore, required to allow for ese. The formalism developed by Newton (modified from McConnell) was used to determine HDA0 , the matrix element for direct interaction of two Rd
Table 2 Charge decomposition of ionization process for [FeCl4]2 and [Fe(SR)4]2.10,22
Species qion qrlx qredox
[FeCl4]2,1 þ0.90 0.70 þ0.20
[Fe(SR)4]2,1 þ0.85 0.75 þ0.10
∂V/∂r
∂V/∂r*
∂V/∂r
∂V/∂r
FeIII*
FeII FeIII
FeIII*
FeII FeIII
* (a)
(b)
Energy (eV)
rFe-L (A)˚
2.0 2.5 3.0 3.5
2.0 2.5 3.0 3.5
8 10
6 4 2 0 –2 10 8 6 4 2 0 –2 –4
Figure 14 DFT-calculated potential energy surfaces for (a) [FeCl4]2,1and (b) [Fe(SCH3)4]2,1 for the reduced (FeII), unrelaxed oxidized (FeIII*), and relaxed oxidized (FeIII) sites. The solid lines are Morse
potential fits to the calculated points at several Fe—L bond distances.
Figure 15 RAMO calculated for Rds from a truncated computational model from ADF using the VWN-BP86 functional.11
706 Spectroscopy and Electronic Structure of [FeX4]n(XẳCl, SR)
active sites.HDA0 is calculated to be250 cm1assuming a purely one-electron process. Electronic relaxation on redox decreasesHDA0 to 200 cm1, indicating that relaxation is not as influential for HDA0 as it is for esei and E0 (vide supra). This large coupling term results in an electron transmission that is0.5, suggesting that direct S–S overlap of the thiolates of two Rd sites would result in near-adiabatic ese in Rd.
Application of the Beratan-Onuchic model for coupling over protein structures allows the creation of a surface map that indicates regions of the protein that have similar ese properties.
The map is simplified such that each region (Rn) consists of areas on the surface that are n effective-bonds away from the active site, resulting inFigure 16. RegionsR0R3correspond to the active site itself, as well as the-methylenes on the two surface-exposed cysteinate ligands.
Within these regions, electronic coupling for self-exchange is reasonable (>10 cm1) but the overall surface area is small (<4%). RegionR4(HAD4 cm1) is distinguished by a large surface area (7%) and is dominated by solvent-exposed amide oxygens that are connected to the active site through H-bonds to the cysteinate sulfurs (OẳCNHS). Electron self-exchange between regions at five effective-bonds and beyond (R5þ) correspond to very small coupling (<1 cm1) and should contribute little to the overall rate constant.
Using the Marcus-Hush equation for ET, and defining the overall rate as the integral over all possible Rn!Rm pathways (as defined above), a rate constant for ese of Rd is calculated at infinite ionic strength yieldingk1exeẳ1.7106M1s1, in fortuitous agreement with experimental results (k1exe2106M1s1). Of greater importance, however, is the relative effectiveness of the different pathways to the overall rate constant. As expected from theHDAanalysis above, regions R0R4(corresponding to 10% of the total surface area) are responsible for 90% of the rate constant. As a result, ET in Rd is highly localized to areas very near the active site and is limited to specific pathways shown in Figure 17: (A) through the -methylenes of the surface-exposed cysteinate ligands and (B) through H-bonds to the surface-exposed (B1) and buried (B2) cysteinate sulfurs to the surface-exposed backbone amide oxygens.