Article pubs.acs.org/IC
Structure and Properties of Precursor/Successor Complex and Transition State of the FeCl2+/Fe2+ Electron Self-Exchange Reaction via the Inner-Sphere Pathway François P. Rotzinger* Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 6, CH-1015 Lausanne, Switzerland S Supporting Information *
ABSTRACT: The electron self-exchange reaction FeCl(OH2)52+ + Fe(OH2)62+ → Fe(OH2)62+ + FeCl(OH2)52+, proceeding via the inner-sphere pathway, was investigated with quantum chemical methods. Geometry and vibrational frequencies of the precursor/successor complex, (H2O)5FeIIIClFeII(OH2)54+/ (H2O)5FeIIClFeIII(OH2)54+ (P/S), and the transition state, (H2O)5FeClFe(OH2)54+⧧ (TS), were computed with the LC-BOP functional and CPCM hydration. Bent and linear structures were computed for the TS and P/S. The electronic coupling matrix element (Hab) and the electronic energies were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMCQDPT2) and spin−orbit configuration interaction (SO-CI). Since the Fe···Fe distance changes considerably along the electron transfer step, the transformation P → TS → S, equations based on the hypothesis of a fixed donor−acceptor distance cannot be applied. Hence, the rate constant for the electron transfer step (ket) was calculated as described previously (Rotzinger, F. P. Inorg. Chem. 2014, 53, 9923). ket is very fast, ∼9.4 × 108−6.6 × 109 s−1 at 0 °C. The experimental rate constant of the title reaction (k) is much slower and controlled by the formation of the precursor complex. The substitution of a water ligand by FeCl(OH2)52+ at Fe(OH2)62+ is rate-determining.
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INTRODUCTION The electron self-exchange reaction 1 of the CrCl(OH2)52+/ Cr(OH2)62+ couple via the inner-sphere pathway involves the exchange of an electron in an antibonding molecular orbital (MO), dσ*, exhibiting a dz2 shape.1
equations for the calculation of the Gibbs activation energy (ΔGet⧧) for the electron transfer step and λ were introduced.1 In the present study, the electron transfer reaction (eq 2) of the FeCl(OH2)52+/Fe(OH2)62+ couple via the inner-sphere pathway was investigated using the same quantum chemical methods as for eq 1.1 The measured rate constant15,16 of eq 2 is virtually equal to that of eq 1.17,18
CrCl(OH 2)52 + + Cr(OH 2)6 2 + → Cr(OH 2)6 2 + + CrCl(OH 2)52 +
FeCl(OH 2)52 + + Fe(OH 2)6 2 +
(1)
→ Fe(OH 2)6 2 + + FeCl(OH 2)52 +
The substitution reaction leading to the precursor complex (P), (H2O)5CrIIIClCrII(OH2)54+, is very fast due to the high lability of Cr(OH2)62+.2 The electron transfer step (ket = 10−330 s−1 at 0 °C) is rate-determining because of the large reorganizational energy (λ).1 This reaction is adiabatic due to the large electronic coupling matrix element (Hab) giving rise to an electron transmission coefficient (κel) of 1.1 Reaction 1 might proceed via two pathways, the first involving a bent precursor/successor complex (P/S) and transition state (TS), and the second one linear isomers of the P/S and the TS. In the reaction via the bent structures the Cr···Cr distance remains approximately equal in the P/S and TS, allowing the use of common equations3−14 for the treatment of electron transfer reactions. For the linear isomer, the Cr···Cr distance in the TS is considerably shorter than in the P/S (by ∼0.4 Å), precluding the application of equations, which are based on the hypothesis of a constant donor− acceptor distance along the electron transfer step.1 Alternative © 2015 American Chemical Society
(2)
In this reaction, an electron in a nonbonding MO, dπ, exhibiting a dxz or dyz shape, is exchanged. Like reaction 1, reaction 2 might also proceed via bent or linear isomers of the P/S and TS. In contrast to reaction 1, for both isomers, the Fe···Fe distance in the TS is appreciably shorter than in the P/S. Hence, equations derived for a fixed donor−acceptor distance during the electron transfer cannot be used for reaction 2.
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COMPUTATIONAL DETAILS
Calculations were performed using the GAMESS19,20 programs. Karlsruhe def2-SV(P), def2-SVP, and def2-TZVP basis sets,21−23 modified as described previously1 and denoted as sv(p), svp, and tzvp, were used. Figures 1−7 were generated with MacMolPlt.24 Received: August 20, 2015 Published: October 19, 2015 10450
DOI: 10.1021/acs.inorgchem.5b01916 Inorg. Chem. 2015, 54, 10450−10456
Article
Inorganic Chemistry
Figure 4. Structure of the TS (isomer 1, Id mechanism, remote attack) for the formation of the bent precursor complex with imaginary mode (105i cm−1) (LC-BOP-CPCM/tzvp calculation). The colors have the same meaning as in Figure 1.
Figure 1. Structure of the bent (a) and linear (b) TS with imaginary mode (reaction coordinate) and MO of the electron being transferred (LC-BOP-CPCM/tzvp calculation). The Fe, Cl, O, and H atoms are represented in dark red, green, light red, and gray, and the MOs in purple/gold.
Figure 5. Structure of the TS (isomer 2, D mechanism, remote attack) for the formation of the bent precursor complex with imaginary mode (69i cm−1) (LC-BOP-CPCM/tzvp calculation). The colors have the same meaning as in Figure 1.
Figure 2. Structure of the IAR (LC-BOP-CPCM/tzvp calculation). The colors have the same meaning as in Figure 1.
Figure 6. Structure of the TS (D mechanism, adjacent attack) for the formation of the linear precursor complex with imaginary mode (66i cm−1) (LC-BOP-CPCM/tzvp calculation). The colors have the same meaning as in Figure 1.
Figure 3. Structure of the TS (D mechanism, adjacent attack) for the formation of the bent precursor complex with imaginary mode (102i cm−1) (LC-BOP-CPCM/tzvp calculation). The colors have the same meaning as in Figure 1. All of the computations were performed for the high-spin state (S = 4.5). Geometries and vibrational frequencies were computed for the hydrated systems with spin-unrestricted density functional theory (DFT) using the LC-BOP functional25 with the default parameter for the long-range correction scheme (μ = 0.33) and a grid finer (NRAD = 120 and NLEB = 770) than the default (NRAD = 96 and NLEB = 302). The Hessians were calculated numerically (based on analytical gradients) using the double-difference method and projected to eliminate rotational and translational contaminants.26 Total energies were also calculated with (spin-restricted) wave function theory (WFT) to take into account near-degeneracy, state−
Figure 7. Structure of the TS (D mechanism, remote attack) for the formation of the linear precursor complex with imaginary mode (102i cm−1) (LC-BOP-CPCM/tzvp calculation). The colors have the same meaning as in Figure 1. state interactions, and spin−orbit coupling (SOC). For the six-state averaged complete active space self-consistent-field calculations, 6stCASSCF(11/10), an active space of 11 electrons in the 10 3d MOs of Fe was used. For the P/S and TS, the energy was averaged over the six 10451
DOI: 10.1021/acs.inorgchem.5b01916 Inorg. Chem. 2015, 54, 10450−10456
Article
Inorganic Chemistry
Table 1. Imaginary Mode (ν⧧) and Selected Bond Lengths and Angles of the Transition State (H2O)5FeClFe(OH2)54+⧧ metal−ligand bond lengths, Å functional/basis set
Fe−Cl
Fe−Oax
LC-BOP/sv(p) LC-BOP/svp LC-BOP/tzvp
2.335, 2.336 2.331, 2.332 2.318, 2.319
LC-BOP/sv(p) LC-BOP/svp LC-BOP/tzvp
2.339, 2.337 2.334, 2.333 2.320, 2.320
(i) Bent TS Structure 2.052, 2.052 2.001−2.163 2.057, 2.058 2.005−2.163 2.069, 2.069 2.010−2.165 (ii) Approximately Linear TS Structure 2.098, 2.100 2.033−2.053 2.102, 2.103 2.036−2.053 2.112, 2.111 2.039−2.053
states with a dπ7dσ*4 electron configuration. Dynamic electron correlation was computed based on the 6st-CASSCF(11/10) wave function with six-state extended general multiconfiguration quasidegenerate second-order perturbation theory including spin-polarization (6st-XGMC-QDPT2, using kxgmc = .t., krot = .t., kszdoe = .t., and thrde = 0).27−31 The 3s and 3p MOs of Fe were included in the PT2 treatment. SOC was calculated with spin−orbit configuration interaction, 10st-SO-CI(11/10), based on the 6st-CASSCF(11/10) wave function involving all 10 states with S = 4.5. The corrections due to SOC were small, ≤0.1 kJ mol−1 for ΔGet⧧, ≤0.3 kJ mol−1 for ΔGsub⧧, and
