Electronic Structures of the [Fe(N2)(SiPiPr

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Electronic Structures of the [Fe(N2)(SiPiPr3)]+1/0/−1 Electron Transfer Series: A Counterintuitive Correlation between Isomer Shifts and Oxidation States Shengfa Ye,* Eckhard Bill, and Frank Neese Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany S Supporting Information *

ABSTRACT: The electronic structure analysis of the low-spin iron(II/I/0) complexes [Fe(N2)(SiPiPr3)]+/0/− (SiPiPr3 = [Si(o-C6H4PiPr2)3]−) recently published by J. Peters et al. (Nature Chem. 2010, 2, 558−565) reveals that the redox processes stringing this electron transfer series are best viewed as metal-centered reductions, i.e. FeIIN20 → FeIN20 → Fe0N20. Superficially, the interpretation seems to be incompatible with the Mössbauer measurement, because the observed isomer shifts are more negative for the lower oxidation states, whereas typically iron-based reduction tends to increase the isomer shift. To rationalize the experimental findings, we analyzed the contributions from the 1s to 4s orbitals to the charge density at the Mössbauer nucleus and found that the positive correlation between the isomer shift and the oxidation state results from an unusual shrinking of the Fe− N2 bond upon reduction due to enhanced N2 to Fe π-backbonding. The other effects of reduction arising from shielding of the nuclear potential, decreasing covalency, and changes in the 4s population would induce the usual negative correlation. The structure distortion dictates the radial distribution of the 4s orbital and the charge density at the nucleus such that a virtually linear relationship between the isomer shift and the Fe−N2 distance could be identified for this series.

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INTRODUCTION In biology, nitrogenase enzymes are able to efficiently catalyze the production of NH3 from N2 at ambient temperature and pressure,1 whereas rather harsh conditions have to be applied in the industrial Haber−Bosch process to accomplish the same transformation.2 Therefore, it is of great importance to clarify the mechanistic details of the enzymatic N2 fixation. To this end, a range of Mo− and Fe−N2 complexes have been synthesized in the past to mimic and probe the function of Mo and Fe in the nitrogenase FeMo cofactor, the N2-reducing site.3 Some of them have been shown to release NH3 upon protonation.4 Recently Peters and co-workers reported that three different formal oxidation states, namely, + II (1), + I (2), 0 (3, 4, and 5), can be accessed in a series of low-spin Fe−N2 complexes by using the anionic tetradendate tris(phosphino)silyl ligand, SiPiPr3 (SiPiPr3 = [Si(o-C6H4PiPr2)3]−), as sketched in Scheme 1.5 Interestingly, the measured Mössbauer isomer shifts show a positive correlation with the iron oxidation states, whereas typically higher oxidation states tend to exhibit more negative isomer shifts, at least for high-spin and high-valent iron compounds.6 In particular for a series of homologous low spin iron compounds with the iron oxidation state ranging from II to VI, a typical negative correlation between the isomer shift and the oxidation state has been established.7 The trend is known to fade for lower oxidation states and in particular for low-spin complexes, in which the isomer shift is often insensitive to the variation of the oxidation state,6,8 but the opposite trend has © XXXX American Chemical Society

been hardly ever conjectured. Thus, the unusual Mössbauer results found for complexes 1 to 4 would rather point to ligandbased reductions. In fact, N2 is a noninnocent ligand and can exhibit different oxidation states in transition metal complexes such as N20,3,9 N22−,10 and even N23−.11 This would be consistent with the increasingly lengthened N−N bonds found across this redox series 1−4 (1.091−1.147 Å), as well as the considerable red-shift in the N−N stretching frequencies (2143−1891 cm−1) (Table 1). However, the experimentally determined N−N bond lengths in complexes 1−4 fall within the range for other well-characterized Fe−N20 compounds,12 contradicting what would be expected for an N2-based reduction. Thus, the experimental findings provide ambivalent information about the electronic structure of complexes 1−4. Complex 5, generated by addition of trimethylsilyl chloride to 4 (Scheme 1), is presumably isoelectronic with the corresponding diazenido species.5a However, the N−N bond length and the N−N stretching frequency of 5 are intermediate between those found for 3 or 4 and the independently prepared phenyldiazenido derivative [(SiPPh3)Fe(NNPh)] (6, SiPiPh3 = [Si(o-C6H4PiPh2)3]−)) (N−N 1.233(7) Å, νN−N = 1623 cm−1).5a Moreover, in contrast to the N−N−CPh angle of 122.5(5)° observed for 6, the N−N−SiMe3 moiety in 5 is nearly linear (165.6(3)°). This geometric feature significantly deviates from the ideal geometry of a diazenido ligand having Received: December 16, 2015

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DOI: 10.1021/acs.inorgchem.5b02908 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Scheme 1. Structures of Complexes 1−5

Table 1. Comparison of the Key Structural and Spectroscopic Parameters Calculated by Using the TPSSh Functional for Complexes 1−5 with the Experiment Findings5a 1 1 2 2 3 3 4 4 5 5

calcd exptl calcd exptl calcd exptl calcd exptl calcd exptl

Fe−N (Å)

N−N (Å)

Fe−P (Å)

Fe−Si (Å)

δa (mm/s)

ΔEQb (mm/s)

1.887 1.913(2) 1.813 1.8192(15) 1.790 1.795(3) 1.739 1.763(3) 1.673 1.695(2)

1.109 1.091(3) 1.123 1.124(2) 1.132 1.132(4) 1.151 1.147(4) 1.194 1.195(3)

2.446, 2.446, 2.446 2.3922(7), 2.4041(7), 2.3781(7) 2.202, 2.335, 2.308 2.2841(7), 2.2657(5), 2.3244(6) 2.198, 2.199, 2.199 2.1944(10), 2.1954(11), 2.1999(11) 2.215, 2.214, 2.214 2.2029(4), 2.2029(4), 2.2029(4) 2.254, 2.255, 2.251 2.2508(8), 2.2500(8), 2.2577(8)

2.322 2.2978(7) 2.272 2.2713(6) 2.237 2.2365(11) 2.267 2.2526(9) 2.310 2.3104(9)

0.51 0.53 0.38 0.38 0.24 0.27 0.20 0.23 0.14 0.19

−2.12 2.39 −0.61 0.71 +1.02 1.01 +1.15 0.98 +1.45 1.26

ηc 0 0.30 0.02 0.01 0.03

νN−N (cm−1) 2232 2143 2134 2003 2066 1920 1960 1891 1823 1748

a Isomer shifts referenced to α-Fe at room temperature. bThe sign of the quadrupole splitting ΔEQ has not been determined experimentally. cThe asymmetry parameter η of the electric field gradient has not been determined experimentally.

two sp2-hydrized N atoms. Therefore, an intriguing question of how to rationalize the experimental observations arises.

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to the fact that the chemically inert core and semicore (1s, 2s, and 3s) electrons yield an overwhelming constant contribution to the electron density at the nucleus, while the valence 4s electron provides a marginal contribution.22,26 To increase the sensitivity of the slope (α) in the linear regression, C is used to subtract this constant value, similar to the charge density of the reference material used to calibrate the spectrometer in the experiment. The reference material for isomer shift calculations is α-Fe, consistent with the experiment. Quadrupole splittings ΔEQ were obtained from electric field gradients Vij (i = x, y, z; Vii are the eigenvalues of the electric field gradient tensor) by using a nuclear quadrupole moment Q(57Fe) = 0.16 barn:27

COMPUTATIONAL DETAILS

Geometry optimizations were performed with the BP86,13 B3LYP,14 and TPSSh15 density functional. Scalar relativistic effects were taken into account by using the zeroth-order regular approximation (ZORA),16 for which our implementation follows the model potential approximation of van Wüllen.17 The respective def2-ZORA-TZVP(-f) (Fe, N, P, Si, and Na) and def2-ZORA-SV(P) basis sets18 were applied in combination with the auxiliary basis sets def2-TZV/J (Fe, N, P, Si, and Na) and def2-SV/J (remaining atoms).19 The RI20 and RIJCOSX21 approximations were used to accelerate the calculations. The Mössbauer spectroscopic parameters were computed using the same density functional as for the geometry optimization step. The CP(PPP)22 basis set for Fe were employed, the TZVP23 basis set for N, P, Si, and Na were employed, and the SV(P) basis set24 for remaining atoms were used. Isomer shifts δ were calculated from the electron densities ρ0 at the Fe nuclei by employing the following linear regression:

δ = α(ρ0 − C) + β

ΔEQ =

1 1 eQVzz 1 + η2 2 3

(2)

Here η = (Vxx − Vyy)/Vzz is the asymmetry parameter. All computations in this work were carried out with the ORCA program package.28

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RESULTS AND DISCUSSION The electronic structures of complexes 1− 5 were calculated by using the BP86,29 B3LYP,30 and TPSSh31 density functionals. Comparison of the theoretical results summarized in Table 1 and Table S1 (Supporting Information) shows that TPSSh is the only functional that is able to successfully predict both the experimental structures and the spectroscopic parameters within the computational uncertainty. Thus, the TPSSh results are used for the following discussion. Benchmark calculations reveal that for a strong metal−ligand bond, for instance, the

(1)

Here C is a prefixed value, and α and β are the fit parameters. Their values for different combinations of the density functionals and basis sets can be found in our earlier work (BP86, α = −0.425, β = 7.916, C = 111810; B3LYP, α = −0.366, β = 2.852, C = 111810; TPSSh, α = −0.376, β = 4.130, C = 111810).25 The absolute value of the electron density at the Mössbauer nucleus is typically over 10000 au−3, whereas its variation that dictates the isomer shift is about few au−3. This is due B


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Inorganic Chemistry

S2, complex 2 consists of a low-spin FeI ion (SFe = 1/2) coordinated to an N20 ligand, and complexes 3 and 4 are best formulated as low-spin Fe0 centers (SFe = 0) bound to N20. Of this electron transfer series, the iron-to-N2 π-backbonding interaction strengthens as the iron oxidation state decreases as evidenced by the gradually increased weight of the N2 π*orbitals in the Fe-dxz/yz-centered molecular orbitals upon going from complex 1 to 4 (Figure 1, and Figures S2 and S3Supporting Information). The degree of the π-backbonding peaks in complex 5, in which the π- and π*-MOs with respect to the Fe−N2 interaction contain nearly even contributions from the Fe dxz/yz and N2 π* fragment orbitals (Figure 2). Therefore, the rather covalent metal−ligand interaction makes the unambiguous assignment of the iron physical oxidation state impossible.35b As depicted in Figure 2, the doubly occupied N−N σ- and π-bonding molecular orbitals are largely intact. The SiMe3+ group primarily interacts with the sp-hybridized orbital of the distal N atom, and the predominant N-character in the bonding molecular orbital (N 80% vs Si 20%) indicates that this interaction is a dative bond in nature. Thus, one may propose a resonance electronic structure between N20 and N24− for the N2 ligand in complex 5, consistent with the slightly bent arrangement of the N−N−SiMe3 moiety. The redox processes connecting complexes 1 to 5 are best rationalized to be metal-centered reductions, because the Fe dxy/x2‑y2-based e-set functions as the electron accepting orbital. As such, the Fe dxz/yz orbitals become more and more energetically close to the N2 π*-orbitals due to the gradually attenuated effective nuclear charge of the Fe center, hence resulting in increasingly pronounced iron to N2 π-backdonation. This strengthens the Fe−N2 bonds and simultaneously weakens the N−N bonds as suggested by the steadily shortened Fe−N2 and lengthened N−N bond lengths, as well as the considerable red-shift in the N−N stretching frequencies across this redox series. The geometric changes found for complexes 4 and 5 relative to complex 3 can be readily rationalized by the further enhanced π-accepting ability of the N2 ligand arising from its interaction with Na+ and Me3Si+, respectively. Why does the metal center reduction lead to the more negative isomer shift? As elaborated elsewhere,22,26 the variation in the isomer shift mainly originates from the change in the 4s-electron contribution to the electron density ρ0 at the Mössbauer nucleus, because 1s, 2s, and 3s electrons are core or semicore electrons that in general do not respond to chemical bonding for all iron compounds of interest. As a result, their contributions to the electron density at the nucleus are almost constant (Table 2). Upon going from complex 1 to more reduced 2 and 3, the effective 3d population increases (Table 2), in accord with the metal-center reduction. This would result in a more positive isomer shift, as usual, because the enhanced shielding effect of the extra 3d charge “pushes” the 4s electrons farther away from the nucleus and the isomer shift coupling constant α in eq 1 is negative for 57Fe.36 Simultaneously, the diminished effective nuclear charge enlarges the energy gap between the Fe 4s orbital and the totally symmetric combination of the ligand σ-donating orbitals, so that the total 4s population declines throughout the series. This covalency effect would also point to the usual direction for the isomer shift correlation with the oxidation state, opposite to the trend found experimentally. In addition to the dependence on the oxidation state, the isomer shift correlates more strongly

Fe−N2 and N−N interactions in the present case, the computed metal−ligand bond distance has a standard deviation of around 0.02 Å.32 A larger error range of 0.05 Å is often observed for weak metal−ligand bonds, such as the Fe−P and Fe−Si bond distances in the present case. In comparison with the crystal structures, the computations accurately reproduce the N−N and Fe−N bond lengths, and the larger deviations are found for the Fe−P and Fe−Si bonds with the mean error of only ∼0.04 Å. The calculated isomer shifts (δ) and quadrupole splittings (ΔEQ) are in excellent agreement with experiment. Typically, the estimated isomer shifts and quadrupole splittings have a standard deviation of 0.1 and 0.5 mm/s, respectively.25,27,33 The calculations also suggest a substantial red-shift in the N−N stretching frequencies upon going from 1 to 5, in accord with experiment. The slight overestimation of the frequency is not considered to be critical (Figure S1, Supporting Information), because computed harmonic frequencies that are compared to experimental fundamentals lack non-negligible negative anharmonic corrections.34 Using the notation Γ(X)n, where Γ denotes the irreducible representations of C3v point group, X the predominant character of the orbital, and n the occupation number of the orbital, the orbital occupation pattern of the ground state for complex 1 can be described as e(Fe dxz/yz)4-e(Fe dxy/x2‑y2)2a1(Fe dz2)0 (Figure 1) due to its trigonal bipyramidal

Figure 1. Schematic MO diagram for complex 1, in which localized quasi-restricted molecular orbitals35 were employed.

coordination geometry. Specifically, two π-bonding molecular orbitals that are predominantly of Fe dxz/yz character are doubly occupied; accordingly, their antibonding partners that are mainly N2 π*-orbitals in nature are vacant. These four MOs signify the π-backdonation from the iron center to N2. The equatorial Fe dxy/x2‑y2-based MOs weakly interact with the lone pairs of the three P atoms and are singly occupied. Because of the strong metal−ligand σ-interaction, the Fe 3dz2-based molecular orbital is unoccupied. Thus, the bonding situation of complex 1 is best described as an intermediate-spin ferrous center (SFe = 1) interacting with a neutral N20 ligand. Analogous bonding situations were obtained for complexes 2−4 except for the number of electrons residing in the Fe dxy/x2‑y2-based molecular orbitals. As shown in Figures S1 and C


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Inorganic Chemistry

Figure 2. Schematic MO diagram for complex 5, in which localized quasi-restricted molecular orbitals35 were employed.

Table 2. Effective 4s and 3d Populations and Breakdown of the Contributions to the Electron Density at the Iron Nucleus (ρ0) Derived from the TPSSh Calculations a

4s population 3d populationa ρ0(1s) (au−3) ρ0(2s) (au−3) ρ0(3s) (au−3) ρ0(4s) (au−3) ρ0 (au−3) δ exptlb (mm/s) δ calcdc (mm/s)

1

2

3

4

5

0.47 (0.44) 6.71 (6.52) 10703.90 973.95 137.86 3.93 11819.64 0.53 0.51

0.44 (0.37) 6.92 (6.67) 10703.85 973.94 137.94 4.25 11819.98 0.38 0.38

0.42 (0.33) 7.05 (6.75) 10703.80 973.93 138.04 4.58 11820.36 0.27 0.24

0.42 (0.38) 7.02 (6.73) 10703.79 973.93 138.07 4.66 11820.45 0.23 0.20

0.42 (0.38) 6.95 (6.66) 10703.77 973.91 138.14 4.80 11820.62 0.19 0.14

a The values without parentheses are obtained by the Löwdin population analysis, and those in parentheses are obtained from the Mulliken population analysis. bThe values are obtained from ref 5a. cThe isomer shift was computed by using eq 1, in which α = −0.376, β = 4.130, C = 111810. The standard deviation of the estimated isomer shift is 0.08 mm/s.24

with the metal−ligand distances,22,26 because they dictate the radial extension of the 4s-wave function and hence the varying electron density at the nucleus. As shown in Table 2, the variation of the valence 4s contribution indeed follows the trend of the differential Fe−N2 bond lengths. Despite the decreased total 4s population, the contraction of the Fe−N2 bond drives the 4s orbital toward the core and increases the electron density ρ0(4s) at the nucleus; therefore, a more negative isomer shift results. Consequently, of the three competing factors controlling the isomer shift, the shortened metal−ligand bond length dominates the other two, thereby leading to the observed unusual isomer shift−oxidation state correlation. Complexes 3−5 are found to possess nearly identical 3d as well as 4s populations, yet exhibit different isomer shifts. This further corroborates the notion that the Fe− N2 bond length is the major determinant that modulates the isomer shift cross this series. In line with this analysis, we found that the isomer shift appears to correlate essentially linearly with the Fe−N2 distances for all complexes under consideration (R2 = 0.92 for the experimental data and R2 = 0.91 for the computed data) (Figure 3), whereas no apparent correlations

between the isomer shift and the Fe−Si and Fe−P distances can be identified. A similar linear correlation between the isomer shifts and the Fe−C distances (Figure S4, Supporting Information) is observed for the CO derivatives, [Fe(CO)(SiPiPr3)]+/0/−.37 In support, we computed hypothetical isomer shifts for the one-electron reduced forms of 1 at the fixed geometry of 1 and found that the value (0.62 mm/s) is considerably larger than that observed for 1. Iron-based reductions usually lead to a considerable increase in the isomer shifts, because they are accompanied not only by the enhanced 3d shielding and the reduced 4s population as calculated for complexes 1−3 but also, more importantly, by appreciable metal−ligand bond lengthening. This suggests that the counterintuitive isomer shift correlation with the oxidation state found here mainly stems from the overwhelming πbackbonding interaction. Therefore, we hypothesize that such a positive isomer shift correlation can be observed only for lowvalent iron complexes involving strong π-acceptors, whereas for compounds containing σ- and/or π-donors, the isomer shiftoxidation state correlation likely follows the usual trend with a negative slope. D


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Inorganic Chemistry

neglected. In contrast, the point charge contributions, which are often considered to be the dominant lattice contribution for a low-spin Fe(II) center with a formally closed t2g-subshell configuration, are 1 order of magnitude lower than the former two contributions. It is thus clear that simple crystal field arguments cannot be applied here to explain the change in the quadrupole splittings observed for complexes 1−5, because crystal field theory only considers valence d-orbital contributions, which would vanish for complex 1. In fact, because of anisotropic covalency the local d-shell contribution for 1 is so far from zero that the bonding orbitals provide a dominant negative contribution. Upon going from complex 1 to 2 to 3, the absolute magnitude of the quadrupole splitting first decreases and then increases, because the sign of the main component of the electric field gradient tensor, Vzz, changes. Moreover, adding an electron into the Fe dxy/x2‑y2 orbitals (from 1 to 2) leads to an increase of only ∼1 mm/s in the quadrupole splitting, far below 4.5 mm/s, the value predicted by crystal field theory for the quadrupole splitting difference caused by a complete valence d-electron.41 The computed asymmetry parameters are close to zero for all complexes except 2, consistent with their effective C3v symmetry. The electron configuration of approximately e(Fe dxz/yz)4-e(Fe dxy/x2‑y2)3 found for complex 2 suggests that this complex likely undergoes a (pseudo) Jahn−Teller distortion, in line with the three different Fe−P bond lengths found in its crystal structure and the optimized geometry (Table 1). This distortion lowers the axial symmetry of the compound and leads to a finite asymmetry parameter of the electric field gradient at the iron center.

Figure 3. Variation of the isomer shift as a function of the Fe−N2 bond distance for complexes 1−5. The standard deviation of the measured isomer shift was assumed to be 0.03 mm/s.

Positive correlations between the isomer shift and the oxidation state have been also observed for low-valent iron− carbonyl complexes with the related tri(silyl)methyl ligand,38 and for dinuclear iron complexes involving metal−metal bonding.8 Furthermore, nearly the same isomer shifts have been measured for a pair of homologous {Fe(NO)2}9,10 species,39 and of closely related iron(II/IV) complexes with vinyl and alkylidenes ligands.40 Both observations have been elegantly explained by the effect of iron−ligand bond lengths. The large variation of the measured quadrupole splitting for complexes 1−5 indicates a considerable change in the electric field gradient at iron and in particular its main component Vzz. As shown in Table 3 and Figure S5, Supporting Information, the computed quadrupole splitting ranges from −2 to +1 mm/ s. The dominant contributions originate from the valence dshell and its ligand-centered bonding orbitals. In fact, the tradeoff between them determines the final sign of the quadrupole splitting. The contributions arising from the core polarization and the two-center bonds are sizable and hence cannot be

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CONCLUSION

In conclusion, a detailed analysis of the electronic structures of the iron−dinitrogen compounds [Fe(N2)(SiPiPr3)]+/0/− reveals that the redox processes threading this electron-transfer series are best viewed as metal-centered reductions, i.e. FeIIN20 → FeIN20 → Fe0N20. On the basis of the proposed electronic structures, the seemingly incompatible experimental findings can be readily explained. In particular, the calculations demonstrate that, in addition to the usual correlation with the iron physical oxidation state, the metal−ligand bond length

Table 3. Breakdown of the Contributions to the Main Component Vzz of the Electric Field Gradient Tensor from the TPSSh Calculations, and the Measured and Computed Quadrupole Splittings valence Fe-dxz,yz (au−3) valence Fe-dxy,x2‑y2 (au−3) d-shell (au−3) Fe-dxy,x2‑y2 bonding orbital (au−3) Fe-dz2 bonding orbital (au−3) local valence core polarization (Fe-2p, 3p) (au−3) two-center point charge (lattice) (au−3) two-center bond (au−3) total (au−3) |ΔEQ| exptla (mm/s) ΔEQ calcdb (mm/s) η calcdc

1

2

3

4

5

−2.16 +3.84 +1.68 +0.66 −3.42 −1.08 +0.23 −0.07 −0.41 −1.33 2.39 −2.12 0

−3.80 +5.86 +2.06 +0.88 −3.18 −0.24 +0.23 −0.05 −0.33 −0.39 0.71 −0.61 0.30

−3.46 +6.52 +3.06 +1.12 −3.50 +0.68 +0.16 −0.04 −0.21 +0.59 1.01 +1.02 0.02

−2.84 +6.38 +3.54 +0.86 −3.84 +0.56 +0.34 +0.02 −0.21 +0.71 0.98 +1.15 0.01

−1.17 +5.85 +4.68 +0.77 −4.39 +1.06 +0.40 −0.12 −0.21 +1.03 1.26 +1.45 0.03

The values are obtained from ref 5a, and the sign of ΔEQ has been determined experimentally. bThe quadrupole splitting was computed by using eq 2, in which e = 1.60 × 10−19 C, Q = 0.16 × 10−28 m−2, conversion factors, 1 au−3 = 9.717 × 1021 V·m2, 1 mm/s = 11.6248 MHz. The standard deviation of the calculated quadrupole splitting is 0.5 mm/s.27 cη has not been determined experimentally. a

E


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Inorganic Chemistry

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has a much stronger influence on the Mössbauer isomer shift. The unusual positive isomer shift correlation with the oxidation state of compounds 1−5 can be traced back to the contraction of the Fe−N2 bond length due to steadily enhanced πbackdonation in the course of the successive metal-centered reductions.

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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.inorgchem.5b02908. Supporting tables and figures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support from the MaxPlanck Society. REFERENCES

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Electronic Structures of the [Fe(N2)(SiPiPr

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