Comparative Experimental and Theoretical Study of the Fe L2,3

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Comparative Experimental and Theoretical Study of the Fe L2,3Edges X‑ray Absorption Spectroscopy in Three Highly Popular, LowSpin Organoiron Complexes: [Fe(CO)5], [(η5‑C5H5)Fe(CO)(μ-CO)]2, and [(η5‑C5H5)2Fe] Silvia Carlotto,*,† Paola Finetti,‡ Monica de Simone,§ Marcello Coreno,∥ Girolamo Casella,⊥ Mauro Sambi,† and Maurizio Casarin*,†,# Downloaded via UNIV OF LOUISIANA AT LAFAYETTE on April 18, 2019 at 13:56:47 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Via Francesco Marzolo 1, 35131 Padova, Italy Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena, Via Università 4, 41121 Modena, Italy § CNR − IOM, Strada Statale 14 Basovizza, Trieste, Italy ∥ CNR − ISM, Strada Statale 14 Basovizza, Trieste, Italy ⊥ Dipartimento di Scienze della Terra e del Mare, Università degli Studi di Palermo, Via Archirafi 22, 90123 Palermo, Italy # CNR − ICMATE, Via Francesco Marzolo 1, 35131 Padova, Italy ‡

S Supporting Information *

ABSTRACT: The occupied and unoccupied electronic structures of three highly popular, closed shell organoiron complexes ([Fe(CO)5], [(η5C5H5)Fe(CO)(μ-CO)]2, and [(η5-C5H5)2Fe]) have been theoretically investigated by taking advantage of density functional theory (DFT) calculations coupled to the isolobal analogy (Elian et al. Inorg. Chem. 1976, 15, 1148). The adopted approach allowed us to look into the relative role played by the ligand → Fe donation and the Fe → ligand back-donation in title molecules, as well as to investigate how CO- (terminal or bridging) and [(η5-C5H5)]−-based π* orbitals compete when these two ligands are simultaneously present as in [(η5-C5H5)Fe(CO)(μ-CO)]2. Insights into the nature and the strength of the bonding between Fe and the C donor atoms have been gained by exploiting the Nalewajski−Mrozek bond multiplicity index (Nalewajski et al. Int. J. Quantum Chem. 1994, 51, 187), which have been found especially sensitive even to tiny bond distance variations. The bonding picture emerging from ground state DFT results proved fruitful to guide the assignment of original, high-resolution, gas-phase L2,3-edges X-ray absorption spectra of the title molecules, which have been modeled by the two-component relativistic time-dependent DFT including spin orbit coupling and correlation effects and taking advantage of the full use of symmetry. Assignments alternative to those reported in the literature for both [Fe(CO)5] and [(η5-C5H5)2Fe] are herein proposed. Despite the high popularity of the investigated molecules, the complementary use of symmetry, orbital, and spectroscopy allowed us to further look into the metal−ligand symmetry-restricted-covalency and the differential-orbital covalency, which characterize them.

1. INTRODUCTION

theoretical analysis is needed to this end. In fact, besides ligand-field and TM-ligand covalency effects, the spin−orbit (SO) coupling between the possible many final-state multiplets should be taken into account.6 Organoiron derivatives probably outnumber the analogous compounds of any other TM7 due to the easy accessibility of starting materials such as [Fe(CO)5]8 and [(η5-C5H5)2Fe],9,10 very well suited to get organoiron species among which the dimer [(η5-C5H5)Fe(CO)(μ-CO)]2, first synthesized only few years later than [(η5-C5H5)2Fe],11a is one of the most studied.11b Despite the relevance of the closed shell [Fe-

X-ray absorption spectroscopy (XAS) is solidly accepted as a tool able to probe, element-selectively, the molecular unoccupied electronic structure through the excitation of the core electrons of the absorbing species to low-lying empty molecular orbitals (MOs) as well as to the continuum.1 One of the most prominent XAS peculiarities is the localized character of core excitations, which makes K- and L-edge2 spectra sensitive to both the electronic structure and the local surroundings of the target species. Transition metal (TM) L2,3-edges features are determined by electronic states generated by the TM-based, electric-dipole allowed3 2p → 3d excitations,4 and even though a huge amount of chemical information may be mined from them,5 a demanding © XXXX American Chemical Society

Received: January 23, 2019

A

DOI: 10.1021/acs.inorgchem.9b00226 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (CO) 5 ], [(η 5 -C 5 H 5 )Fe(CO)(μ-CO)] 2 , 12,13 and [(η 5 C5H5)2Fe]14,15 complexes (0, I, and II, respectively; see Figure 1),16 no Fe IL2,3-edges XAS study is reported in the

Optimized structures of 0, I, and II needed to run SO RTDDFT calculations have been obtained (optimized Cartesian coordinates are reported in Tables S1−S5 of the Supporting Information) by running ADF numerical experiments substantially homogeneous with those of Atkins et al.30 Nevertheless, as the forthcoming discussion on the Fe-ligand symmetry-restricted-covalency32,33 and differential-orbital-covalency (DOC) 5,34 will exploit fragment-based MOs (FMOs),35 the GS frontier electronic structure of 0, I, and II will be herein reconsidered.

2. EXPERIMENTAL AND COMPUTATIONAL DETAILS X-ray absorption measurements have been carried out on the undulator-based Gas-Phase Photoemission beamline36 at the Elettra synchrotron light source (Trieste, Italy) by exploiting the gratings covering the energy range 200−900 eV. Fe L2,3-edges spectra have been calibrated by means of Xe;37 moreover, the Fe L2,3-edges spectra of 0 and II have been also cross-calibrated by exploiting the outcomes of ISEELS under electric-dipole scattering conditions.38 The photon energy bandwidth was better that 300 meV at the Fe L2,3-edges. Great care has been taken in handling samples to minimize contamination by moisture. To this end, they have been transferred to the sample holder in a glovebag filled with dry nitrogen. Because of the liquid state of 0 at room temperature (RT), the complex has been subjected to several cycles of freezing and pumping in situ to eliminate N2 traces as well as others possible contaminants. Finally, its temperature has been slowly raised and maintained at RT. A similar procedure has been adopted for II, solid at RT but rather volatile (its vapor pressure at 300.17 K is 1.2 Pa),39 thus preventing its direct load into the experimental vacuum chamber. Similarly to 0, vapors of II have been loaded in through a gas line after cycles of cooling and pumping to remove contaminants and residual gases. Fe L2,3-edges spectra of 0 and II have been recorded by using an absorption cell40 operating at a working pressure of ∼6 × 10−1 Pa. Analogously to II, I is solid at RT; nevertheless, the generation of a suitable vapor beam of I implied the insertion of an oven into the experimental chamber, which allowed us to gradually raise T to 365−368 K. No trace of residual H2O or N2 has been observed during XAS measurements recorded by detecting the total-ion-yield (TIY) signal with a channeltron. Geometrical parameters of 0, I, and II have been optimized by using the ADF suite of programs (version 2014.01)31 and by assuming for them the following idealized symmetries: D3h for 0; C2h and C2v for trans-I and cis-I tautomers, respectively; D5h and D5d for eclipsed (EII) and staggered (SII) rotamers of II, respectively.3 GS ADF numerical experiments have been carried out by running allelectron nonrelativistic calculations with generalized gradient corrections self-consistently included through the Becke-Perdew formula41 (BP86) and by adopting a triple-ζ with two polarization function (TZ2P) Slater-type basis set for all the atoms. To favor the comprehension of GS theoretical outcomes, the molecular eigenvalues have been graphically displayed as density of states (DOS) by applying a 0.25 eV Lorentzian broadening factor. These plots, based on the Mulliken’s recipe42 for partitioning the overlap density, allow an easy inspection of the atomic composition of MOs over a broad range of energies. Partial density of states (PDOS) is

Figure 1. Schematic representation of the optimized D3h 0, C2h trans-I and D5h eclipsed-II. In the adopted framework, the C3, C2, and C5 symmetry axes of 0, trans-I, and eclipsed-II, respectively, correspond to the z one. Throughout the text, apical and equatorial (terminal and bridging) CO of 0 (I) are labeled COa and COe (COt and COb), respectively. White, gray, red, and yellow spheres are representative of the H, C, O, and Fe atoms, respectively.

literature, and the only attempt of a nonqualitative modeling of the Fe 0/IIL2,3-edges XA spectra dates back to a quarter of a century ago.17 As such, it is worthwhile to mention that the need of an updated theoretical investigation of the Fe 0/IIL2,3-edges XAS data has been explicitly called for by Miedema and de Groot in their review specifically devoted to the Fe L-edges.18 In addition, a comparative study of the Fe 0/I/IIL2,3-edges spectra appears particularly intriguing due to the Fe presence in three distinct formal oxidation states in the title complexes.16 This is highly captivating if coupled to the conclusions reported by Grush et al.,19 Carlotto et al.,20a,c−e and Maganas et al.6j about the influence of the TM oxidation state on the TM L2,3-edges XAS features. Original gas-phase Fe L2,3-edges spectra of 0, I, and II are herein presented and discussed by exploiting the results of relativistic time-dependent density functional theory (RTDDFT) including spin orbit (SO) coupling with full use of symmetry and correlation effects.21,22 It is an approach we successfully employed in the past to model literature Ti L2,3edges spectra of the closed shell [TiCl4], [(η5-C5H5)TiCl3], and [(η5-C5H5)2TiCl2] with a relatively low computational effort.24,25 The oscillator strength f as a function of the excitation energy (f(EE)) for the Fe 2p excitations of 0 and II in the gas phase was first recorded by the Hitchcock group in the late 1990 by means of the inner-shell excitation by electron energy loss spectroscopy (ISEELS) under electric-dipole scattering conditions28 and recently revisited by Godehusen et al.29 In this regard, it deserves to be outlined that Atkins et al.30 have recently studied the ground state (GS) properties of title compounds in a series of papers devoted to the modeling of their Fe K-edge features by means of TD-DFT as implemented in the Amsterdam Density Functional (ADF) package.31

PDOSnvS (ε) =

∑ p

f nvS γ π (ε − εp) + γ 2

(1)

and

DOS(ε) =

∑ PDOSnvS (ε) = ∑ v ,n,S

p

gp γ π (ε − εp) + γ 2

(2)

is the Mulliken’s where γ is the Lorentzian broadening factor and population contribution from atom ν, state (nl) to the pth MO of energy εp and degeneracy gp. We are perfectly aware that the Mulliken’s prescription for partitioning the overlap density, even f nvS

B


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Inorganic Chemistry though uniquely defined, is rather arbitrary; nevertheless, it yields at least a qualitative idea of the electron localization. Additional information about the bonding/antibonding character of selected MOs over a broad range of energies has been gained by exploiting the overlap population DOS (often referred to as crystal orbital overlap population − COOP).43 Finally, three-dimensional (3D) contour plots (CPs) have been obtained to further look into the localization and the character of determined MOs. Fe L2,3-edges f(EE) distributions of 0, I, and II have been initially evaluated by using the current DFT/ROCIS method6h we successfully employed to model literature and original TM L2,3 features of several TM complexes.20 These numerical experiments have been carried out by using the popular PBE0 exchange-correlation functional44 and by adopting the def2-TZVP(-f) basis set.45 Despite the apparent excellent agreement between experimental and DFT/ROCIS XAS patterns (see Supporting Information), their detailed analysis (see Supporting Information) induced us to alternatively model the Fe L2,3-edges XAS features through the exploitation of RTD-DFT including SO coupling with full use of symmetry and correlation effects.21,46,47 In general, a particle/hole method like TD-DFT is unable to unravel the complex multiplet structure of the TM L2,3edges XAS features. Nevertheless, in closed-shell systems,24,48 the adopted approach,21 based on the two-component zeroth-order regular approximation (ZORA)46 and a noncollinear exchangecorrelation (XC) functional,49,50 is known to provide good agreement between theoretical and experimental 2p TM photoabsorption spectra. In more detail, two-component ZORA46 SO RTD-DFT calculations have been run by adopting all-electron QZ4P ZORA basis sets for all the atoms;51 moreover, the adiabatic local density approximation52 has been employed to approximate the exchangecorrelation (XC) kernel, while, for the XC potential applied in the self-consistent field calculations, the LB94 functional53 with the GS electronic configuration has been adopted. In this ambit, Fronzoni et al.54 have pointed out that, among approximate XC functionals having the correct asymptotic behavior, a necessary condition for a proper description of high energy virtual orbitals and Rydberg states, the LB94 functional provides a good agreement between theory and experiment. Finally, scaled ZORA orbital energies55 instead of the ZORA orbital energies in the RTD-DFT equations have been employed throughout to improve deep core excitation energies. Simulated spectra have been shifted to superimpose the highest intensity feature of the experimental and simulated L3 spectra, which do not suffer from extra broadening and distortion due to the Coster− Kronig Auger decay process.56 Incidentally, this is needed because absolute theoretical EEs carry errors arising from DF deficiencies in the core region, one-particle basis set restrictions, and inadequacies in the modeling of spin-free relativistic effects.

SALC and the Fe 3dx2−y2/dxy AOs) contributions (see Figure 2).60

Figure 2. COOPs between the Fe 3d AOs and suitable COe-/COabased 5σ (upper panel) and 1π/2π (lower panel) SALCs in 0. In the COOP plots, bonding and antibonding combinations correspond to positive and negative peaks, respectively. Vertical bars represent the HOMO (solid line) and LUMO (dotted line) energies of 0.

At variance to that, the Fe 3dxz and 3dyz AOs,57,58 which strongly (70%) contribute to the 3e″ HOMO−1, may only interact with the COe- and COa-based π SALCs (see Figure 2). As a whole, the 3e″ MO provides a net contribution to the Fe−CO bond because the Fe → COe/a back-bonding significantly exceeds the antibonding interaction with the COe/a-based 1π SALC.61 As far as the fifth Fe 3d-based MO is concerned, the ADF 14a′1 LUMO, significantly localized on the Fe 3dz2 AO (53%), accounts for an antibonding interaction with the CO-based 5σ MO a′1 SALC (see Figure 2). As such, it has to be emphasized that the energy position of the Fe 3dz2based a′1 VMO herein reported is much lower than that estimated by Fronzoni et al.17 (vide infra). It has been already mentioned that one of the major interests of this contribution concerns the TM-ligand symmetry-restricted-covalency32,33 and the DOC.5,34 In this regard, it is worth noting that Fe, C, and O Hirshfeld charges (Q)62 are very similar and close to zero (see Table 1), thus pointing out that the Fe−C Nalewajski−Mrozek bond multiplicity indexes63,64 (NMI, see Table 1) are indicative of a rather strong Fe−CO covalent interaction, prevalently π in nature, associated with the Fe0 → CO back-bonding at which

3. RESULTS AND DISCUSSION 3.1. Ground State Electronic Structures. [Fe(CO)5]. The D3h symmetry3 of 0 prevents the possibility of looking at the Fe 3d-based atomic orbitals (AOs) in terms of t2g- and eg-like sets;57 moreover, the distinction between σ and π contributions to the Fe−CO interaction is in principle hampered by the symmetry allowed mixing between σ and π SALCs of symmetry e′.58 Even though there is no way to get around the former hindrance, the recognition of σ and π contributions to the Fe−CO bonding may be worked out by exploiting the ADF31,59 fragment approach. In 0, the eight Fe valence electrons fulfill the 3d-based 10e′ HOMO and 3e″ HOMO−1.35 The Fe−COe bonding nature of the former is rather complex; in fact, it includes at the same time bonding (between the occupied COe-based 5σ SALC and the empty Fe 4px/4py AOs), back-bonding (between the occupied Fe 3dx2−y2/dxy AOs and the SALC of the empty COebased 2π FMOs), and antibonding (between the COe-based 5σ C


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Inorganic Chemistry

Table 1. Selected Hirshfeld Charges (Q)62 and Nalewajski−Mrozek Bond Multiplicity Indexes (NMI)63 for Title Moleculesa Fe

Q QCCO QOCO QCCp QH Cp Fe−Fe Fe−CO Fe−CCp C−O C−C

0

trans- I

cis- I

S

−0.09 0.10e/0.13a −0.10e/−0.08a

0.00 0.09t/0.04b −0.14t/−0.17b −0.03m

0.00 0.10t/0.04b −0.12t/−0.17b −0.04m

0.01

0.01

−0.06 0.06

−0.06 0.06

0.43 1.18t/0.71b 0.27m 2.39t/2.29b 1.42m

0.44 1.14t/0.72b 0.27m 2.41t/2.29b 1.42m

0.47

0.47

0.83e/0.86a 2.48e/2.46a

E

II

1.39

II

1.39

Superscripts e, a, t, b, and m stand for equatorial, apical, terminal, bridging, and mean value, respectively; Cp stands for [(η -C5H5)]−.

a

5

all the occupied Fe 3d AOs participate.65 According to that, the C−O stretching frequency (νCO) is red-shifted upon moving from the free molecule to the coordinated one.66 Incidentally, it deserves to be mentioned that the Fe−COe interaction is herein computed slightly weaker than the Fe− COa one, and, correspondingly, the COe bonding appears slightly stronger than the COa one (see the NMIFe−CO and NM CO I indexes reported in Table 1). Such a result is certainly in contrast with conclusions reported by Jones et al.70 in their contribution devoted to the study of potential constants of 0 from vibrational spectra; nevertheless, it perfectly matches the gas-phase electron diffraction results reported by Davis and Hanson,71 and it is consistent with the molecular structure of 0 recently optimized by Wernet et al.72 at the CASPT2 level.73 [(η5-C5H5)2Fe].74 In a fundamental paper published more than 40 years ago, it has been demonstrated that TM(CO)3, TM(η6-C6H6), and TM′(η5-C5H5)75 conical fragments are isolobal; i.e., “...the number, symmetry properties, extent in space and energy of the frontier orbitals of the fragments are similarnot identical, but similar”.76a The IIFe environment may be then considered pseudo-octahedral independently of the II conformation (E or S), thus allowing us to look at the Fe 3d-based MOs in terms of t2g- and eg-like orbitals. In principle, the electronic properties of II could be tackled by referring to the nonclassical77 super electrophilic [Fe(CO)6]2+ carbonyl cation;78 nevertheless, we chose the [Fe(CN)6]4− anion, isoelectronic with [Fe(CO)6]2+, because the Fe → (CN)− back-bonding has been thoroughly investigated by Solomon and co-workers both experimentally and theoretically.34b,79 Symmetry properties of EII and SII rotamers are described by the D5h and D5d symmetry point groups, respectively.3 EII and SII differ in the presence of the symmetry plane σh in the former and the center of inversion i in the latter; IRs labeled as ′ and ′′ in D5h will then become “g” and “u” in D5d. Moreover, the [(C5H5)2]2− Sπ and Eπ SALCs (bases for the 10-fold reducible representations SΓπ and EΓπ) will span the a1g + a2u + e1g + e1u + e2g + e2u (Sπ1− + Sπ1+ + Sπ2− + Sπ2+ + Sπ3− + Sπ3+, respectively) and a′1 + a″2 + e′1 + e″1 + e′2 + e″2 (Eπ1− + Eπ1+ + Eπ2− + Eπ2+ + Eπ3− + Eπ3+, respectively) IRs.80 Among the irreducible components of SΓπ and EΓπ, the S/Eπ1−, S/Eπ1+, S/E − π2 and S/Eπ2+ SALCs have a DOMO nature, while the S/E − π3 and S/Eπ3+ ones have a VMO character.35 As far as the Fe 3d AOs are concerned, 3dz2, 3dx2−y2 and 3dxy (3dxz and 3dyz) orbitals behave, in the adopted framework (see Figure 1), as t2g- (eg-like) AOs both in SII and EII.81 The Fe 3d PDOS and the Fe−(η5-C5H5)2 COOPs between Fe 3d AOs and π SALCs of the same symmetry are displayed in Figure 3 for SII.82 The inspection of the figure testifies that

Figure 3. Fe 3d PDOS (upper panel) and COOPs between Fe 3d AOs and suitable (η5-C5H5)2-based π SALCs (lower panel) in SII. In the COOP plots, bonding and antibonding combinations correspond to positive and negative peaks, respectively. Vertical bars represent the energies of the 4e2g HOMO (solid line) and 5e1g LUMO (dotted line).82

(i) as expected, t2g-like AOs are quasi-degenerate; (ii) even though both eg- and t2g-like AOs contribute to the Fe−(η5C5H5)2 bonding, the Fe−(η5-C5H5)2 e1g COOP exceeds the Fe−(η5-C5H5)2 e2g one;81,82 (iii) among the Fe t2g-like AOs only two of them, the 3dx2−y2 and 3dxy ones in our framework, may participate to the FeII → [(η5-C5H5)2]2− back-bonding interaction because no (η5-C5H5)-based π SALC of symmetry a1g is empty; (iv) the third t2g-like AO, the 3dz2 one in our D


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Inorganic Chemistry

determined by the assumption of [(η5-C5H5)2M2(CO)4] alternative geometries with the main goal of answering the following question: “What makes a certain electron count opt for one structural type?”.89e In the present contribution, the attention is focused on the CO and [(η5-C5H5)]− π acceptor capability; in particular, on how this is affected by (i) the simultaneous presence of CO and [(η5-C5H5)]− ligands, taking 0 and II as references; (ii) the different (terminal vs bridging) CO coordinative modes. In the adopted framework, the C2 symmetry axis of the transI species is oriented along z with both IFeI ions lying in the xy plane; IFe 3d-based t2g-like (eg-like) orbitals will then be the 3dx2−y2, 3dz2, 3dxz (3dxy, 3dyz) AOs. The dimeric nature of I implies the presence of in-phase (+) and out-of-phase (−) linear combinations of t2g-like (+t2g and −t2g, respectively) and eg-like (+eg and −eg, respectively) orbitals. In addition to this, + t2g/−t2g sets transform in the C2h trans-I as the (2ag + bg)/(au + 2bu) IRs, while the +eg/−eg ones as the (ag + bg)/(au + bu) IRs. The overall number of Fe 3d electrons amounts to 14 (each IFeI ion has a 3d7 configuration); +t2g (the 31ag, 30ag, and 13bg MOs) and −t2g (the 28bu, 27bu and 16au MOs) combinations will then have a DOMO35 nature (+t2g/−t2g PDOS are displayed in the upper panels of Figure 4), while the remaining two electrons fill up the +eg 14bg HOMO (+eg/−eg PDOS are reported in the lower panels of Figure 4), whose 3D plot is displayed in Figure 5 with that of the −eg 29bu LUMO.93 Interestingly, the +eg 14bg HOMO accounts for a multicenter interaction involving the COb 2π FMO lying in the

framework, behaves as a lone-pair. As a whole: (i) the Fe−C NM I of both EII and SII amounts to ∼1/2 of the Fe−C NMI in 0 (see Table 1); (ii) QFe, QC, and QH values are, both in EII and S II, 0.01, −0.06, and 0.06, respectively; (iii) despite the different Fe oxidation number in 0 and II,16 0QFe and IIQFe values are very close to zero. Before going on, let us emphasize that the optimized structures of SII and EII (Tables S4 and S5 of the Supporting Information) numerically agree with neutron diffraction outcomes collected by Takusagawa and Koetzlet83 and theoretical results published by Coriani et al.84 As anticipated, the isolobality exploitation allows us to treat E/S 82 II as a pseudo-octahedral complex whose bonding scheme in general, and back-bonding interactions in particular, could be compared with those characterizing the [Fe(CN)6]4− species.34b,79 In the octahedral [Fe(CN)6]4− anion, each (CN)− participates to the bonding scheme with two π FMOs35 (the 1π and 2π ones), each of them doubly degenerate; moreover, analogously to the isoelectronic CO, the 1π (2π) FMOs are DOMOs (VMOs).35 In the Oh [Fe(CN)6]4−, both 1π and 2π FMOs generate 12 SALCs transforming as the t1g, t2g, t1u, and t2u Oh IRs for a total of 24 SALCs. Two t2g sets of (CN)−-based FMOs are then present, one occupied and the other unoccupied. Hocking et al.34b,79 estimated by means of ADF calculations, carried out by adopting the BP86 XC functional41 and a TZP basis set, that the % of the Fe character in Fe(t2g), Fe(eg), π*(t2g), and πb(t2g)85 amounts to 77, 57, 16, and 8, respectively (see Table 2 of ref 34b). In II, the number of π ligand-based FMOs35 is definitely smaller (10 vs 24), and only three of them (the π1− SALC and the doubly degenerate π3− one) may interact with occupied Fe t2g-like AOs;80,81 moreover, the interaction between the occupied π1− SALC and the Fe 3dz2 AO is negligible (see Figure 3).86 Even though the Fe contribution to the t2g-like 4e2g MOs (80%)81 is slightly larger than that reported for [Fe(CN)6]4− (a further clue86 of a weaker back-bonding interaction in II than in [Fe(CN)6]4−), it is of some relevance to point out that the Fe participation to the 5e2g π*(t2g) orbitals (14%) is rather close to that computed by Hocking et al.34b (16%) for [Fe(CN)6]4−. Similar considerations hold for the Fe contribution to the eg*-like 5e1g MOs (55%)81 (see Table 2 of ref 34b). As a whole, we may conclude that the Fe → ligand back-bonding interaction is less pronounced in II than in [Fe(CN)6]4− as a consequence of two concurrent reasons: (i) the involvement of two, rather than three, TMbased orbitals in the Fe → π* interaction; (ii) the lower participation of ligand-based π* MOs to Fe(t2g) orbitals in II than in [Fe(CN)6]4−. As such and before tackling the IGS, it is worthwhile to mention the quantitative agreement between experimental87 and theoretical ring metal stretches in SII (vide infra).88 trans-[(η5-C5H5)Fe(CO)(μ-CO)]2. A great deal of attention has been devoted until few years ago to the molecular and electronic structure of I,11b,89,90 one of the main issues being the nature of the interaction, if any, between the iron atoms89i,j (X−N deformation density maps obtained for the trans-I tautomer do not show any feature between IFe ions).89d,91 In the early 1980s, Jemmis et al.89e exploited the isolobal analogy76 to investigate the electronic structure of [(η5C5H5)2M2(CO)4] (M = Fe and Mo) complexes by combining the FMO approach with extended Huckel type92 calculations. More specifically, they focused on the electronic perturbations

Figure 4. trans-I Fe 3d PDOS: (upper, left panel) gerade combinations of t2g-like Fe 3d AOs (+t2g); (upper, right panel) ungerade combinations of t2g-like Fe 3d AOs (−t2g); (lower, left panel) gerade combinations of eg-like Fe 3d AOs (+eg); (lower, right panel) ungerade linear combinations of eg-like Fe 3d AOs (−eg). E


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Inorganic Chemistry

Figure 5. 3D CPs of the +eg 14bg HOMO and −eg 29bu LUMO of trans-I.35 Displayed isosurfaces correspond to ±0.04 e1/2 Å−3/2 values.

[Fe(μ-CO)]2 plane and, in the selected framework, the IFeI 3dyz-based AOs (see Figure 5). It has also to be remarked that the +eg 14bg HOMO corresponds to the orbital through which the spin pairing between the 3d7 IFeI ions takes place, thus discarding the need for a direct Fe−Fe bond to this end. Incidentally, such a picture of the trans-I bonding scheme perfectly matches the one published by some of us in the late 1980s89f about a series of ligand-bridged iron binuclear complexes investigated by combining gas-phase UV photoelectron spectroscopy (PES) and DV-Xα calculations.94,95 Useful information about the competition between CO and [(η5-C5H5)]− π* FMOs in the Fe → ligand back-bonding may be obtained by referring to the outcomes reported in Table 1, among which a special attention must be paid to (i) the COt NMIFe−CO (NMIC−O) increasing (decreasing) on passing from 0 to I; (ii) the NMIFe−CO/NMIC−O differences between COt and COb; (iii) the dramatic decreasing of the NMIFe−CCp, basically halved, upon moving from II to I. A COt bonding weaker in I than in 0 is consistent with both the conventional89c and the 2D infrared spectroscopy outcomes97a,b pertaining to cis-and trans-I in the CO stretching frequency region. As a matter of fact, infrared evidence indicates that the COt νCO is further66 red-shifted on passing from 0 to I.98 Similar considerations hold for COb, whose s CO a CO ν / ν lie at 1810/∼1777 cm−1 in cis-I89c,99 and at 1781 cm−1 in trans-I.89c,99 Incidentally, these low stretching frequencies are indicative of a rather strong Fe → COb π back-donation, further confirmed by the C and O COb Hirshfeld charges (see Table 1). Before turning our attention to the Fe−[(η5-C5H5)] interaction, let us emphasize that the Fe−COb NMI, significantly smaller than the Fe−COt one, provides theoretical support to the mechanism, first proved by Bullit et al., “whereby cis- and trans-CO-bridged isomers interconvert via non-bridged isomers”.89c,100 It has been already mentioned that, among data reported in Table 1, the most impressive feature is the halving of the NM Fe−CCp I upon moving from II to I. As such, it has to be highlighted that the II → I switching implies a significant lengthening of the Fe−CCp bond distance (numerically reproduced by our optimized structures) and an equally significant reduction of the Fe-ring stretching force constant.101 The inspection of Figure 3 clearly indicates the VMO35 nature of the Fe 3d-based eg*-like MOs (the 5eg orbitals) and their Fe−[(η5-C5H5)] antibonding character. The I I Fe 3d7 configuration implies a DOMO35 character for the +eg 14bg HOMO, which, besides the already mentioned multicenter interaction, is also antibonding with respect to the Fe− [(η5-C5H5)] interaction (see Figures 5 and 6).102 The comparison between Figures 3 and 6 reveals that COOPs

Figure 6. COOPs between Fe eg-/t2g-like AOs and Cp-based π2/π3 FMOs in trans-I. In the COOP plots, bonding and antibonding combinations correspond to positive and negative peaks, respectively. Vertical bars represent the HOMO (solid line) and LUMO (dotted line) energies of trans-I.

between the Fe +eg/−eg sets and the occupied [(η5-C5H5)]based π2 FMOs is rather similar in trans-I and SII (if we exclude the antibonding contribution provided by the +eg 14bg HOMO), while the opposite is true when COOPs between Fe + t2g/−t2g sets and [(η5-C5H5)]-based π3 FMOs is considered. The origin of such a weakening has to be ultimately traced back to the higher π acceptor capability of CO, independently of the terminal or bridging coordination, vs [(η5-C5H5)]− (see Figure 7). As remarkably summarized by Labinger only a few years ago,89j the existence of a direct Fe−Fe bonding in trans-I has been a matter of debate for a long time. Even though the symmetric breaking of the dimer in two radical monomers would suggest the occurrence of a direct Fe−Fe interaction, Labinger also reports experimental,89d conjectural,89i and computational evidence89e−g,103 consistent with the absence of any Fe−Fe direct bond. In this regard, it is of some relevance to point out that Vitale et al.104 proposed to assign the sharp band at 225 cm−1, typifying the Raman spectrum of a cyclohexane solution of I recorded with an irradiation wavelength of 648 nm, to the Fe−Fe stretching mode. TZ2P BP86 IGS results indicate the presence of an ag normal mode at 228.5 cm−1 whose symmetry displacements involve only the COb C atoms. The use of the ADF graphical user interface31 allowed us to associate the corresponding vibrational mode to the in-phase bending of the two Fe−C−Fe bond angles. Moreover, the extended transition state analysis105 ultimately confirmed that the electrons pairing between the radical [(η5C5H5)Fe(CO)2] moieties takes place through back-bonding into COb π* FMOs rather than through a direct Fe−Fe interaction (see the Supporting Information). 3.2. X-ray Absorption Spectra. Dipole allowed transitions imply that3 ΓGS ⊗ Γμ ⊗ ΓES ⊃ ΓSym

(3)

where ΓGS, Γμ, ΓES, and ΓSym correspond to the IR of the electronic GS of 0, I, and II (the totally symmetric F


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Figure 7. COOPs between Fe 3d AOs and π SALCs in trans-I. Bonding and antibonding combinations correspond to positive and negative peaks, respectively, in the COOP plots. Vertical bars represent the HOMO (solid line) and LUMO (dotted line) energies of trans- I.

and L33, respectively, in Figure 9) lying at 709.8, 711.9, and 713.9 eV, respectively. As a whole, the 0L2,3 spectral pattern is

representation as a consequence of the title molecule closed shell nature), the IRs of the dipole moment operator (e′ and a″2 in 0; au and bu in trans-I; a1, b1 and b2 in cis-I; a2u and e1u in S II; e′1 and a″2 in EII), the IR of the electronic excited state (ΓES = Γiso⊗ ΓGS⊗ Γfso = Γiso⊗ Γfso),106 and finally the totally symmetric IR. The already mentioned diamagnetic nature of title compounds allows us to simplify eq 3 in eq 4 Γμ = Γiso ⊗ Γfso

(4)

SO RTD-DFT 0/I/IIf(EE) for allowed excitations are superimposed to corresponding gas-phase Fe L2,3-edges XAS spectra in Figure 8. 0 L2,3-Edges Absorption. The 0L3-edge region includes at least two well evident features and a faint structure (L31, L32,

Figure 9. High-resolution gas-phase Fe L3-edge spectrum (solid line) of 0 superimposed to the SO RTD-DFT 0f(EE) distribution (bars). Blue and red bars correspond to a″2 and e′ 0f(EE), respectively, which have been shifted by 5.52 eV.

very similar to the ISEELS f(EE) distribution obtained by the Hitchcock group28 early in the 1990s as well as to the TIY 0 L2,3-edges XAS recently recorded by Godehusen et al.29 The inspection of Figure 9 and theoretical outcomes collected in Table S6 of the SI107 suggests that electronic states contributing to L32 are associated with two accidentally degenerate transitions108 of symmetry a″2 and e′ (see eq 4) from the 2e5/2 and 1e3/2 levels107 (the Fe 2p3/2-based isos) to the Fe 3dz2-based 14a′1 VMO and to the π* CO-based 4e″ and 12e′ VMOs (the antibonding partners of the 3e″ and 10e′ DOMOs; see Figure 2).109 Results collected in Table S6 of the Supporting Information clearly show that more than one iso → fso transition may contribute to the generation of a particular electronic state. The assignment herein proposed somehow reconciles those reported by the Hitchcock group in refs 28b−28c; as a matter of fact, they suggested in ref 28b to associate the L31 and L32 features to transitions involving what they called “dπ*” and “dσ*” “final orbitals”, respectively, while they proposed in ref 28c to ascribe the most intense L32 peak of the Fe 2p oscillator strength spectrum “...to Fe 2p excitation to the Fe 3d component of the main density of π*(CO) MOs”. Before going on, it has to be underlined that our assignment is also alternative to the one suggested by Fronzoni et al.,17 which

Figure 8. Fe L2,3-edges XA spectra of 0, I, and II (solid lines) superimposed to SO RTD-DFT f(EE) distributions (bars). Bars in the simulated Fe IL2,3-edges spectra correspond to the trans-I (Ci) and cis-I (C2v) isomers, respectively. Bars in the simulated Fe IIL2,3-edges spectra correspond to the eclipsed EII (D5h) and staggered SII (D5d) rotamers, respectively. Simulated spectra have been shifted by 5.52 eV (0), 4.60 eV (cis-I), 5.68 eV (trans-I), 4.81 eV (SII), and 4.98 eV (EII). G


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K3[Co(CN)6].110−113 In both complexes these two peaks have been assigned to electronic states generated by transitions from the TM 2p-based MOs to the TM 3d-based eg*-like MOs (the former) and to the CN−-based π*(t2g) (the latter).114 The combined use of GS (see Figure 3) and SO RTD-DFT results (see Figures 8 and 10; Tables S9 and S10 of the Supporting Information) makes straightforward the assignment of the IIL2,3-edges spectrum. Both in SII and EII, electronic states contributing to the intense L31 feature are associated with two transitions, rather close in energy, having symmetry a2u/e1u and a″2/e′1 in SII/EII, involving the Fe 2p3/2-based isos (the 2e1/2u and 1e3/2u spinors in SII, see Table S9; the 2e9/2 and 1e7/2 spinors in EII, see Table S10)107 and the Fe 3d-based eg*like VMOs (the 5e1g MO in SII, the 5e″1 MO in EII). Similarly to 0, the inspection of Table S9 (S10) of the Supporting Information clearly indicates that at least two distinct iso→ fso transitions contribute to the generation of both a2u and e1u (a″2 and e′1) electronic states in SII (EII). Elementary symmetry considerations3 (see eq 4 and the upper panel of Figure 3) allow us to predict that only electronic states associated with transitions of symmetry e1u (e′1) should significantly contribute to L32 in SII (EII). According to that, the inspection of Table S9 (S10) of the Supporting Information indicate that the L32 spectral feature in S II (EII) is due to electronic states generated by e1u (e′1) excitations among which the one having the largest f value has the 10e3/2g and 5e5/2g (10e3/2 and 9e5/2) as fsos.107,115 The experimental ΔEE between L32 and L31 (2.51 eV) is underestimated both in SII (1.64 eV) and in EII (1.71 eV); nevertheless, the corresponding relative intensity is satisfactorily reproduced. As such, the less pronounced Fe → ligand back-bonding in II than in [Fe(CN)6]4− as a consequence of (i) the involvement of two rather than three Fe-based AOs in the Fe → π* interaction and (ii) the lower participation of ligand-based π* MOs to Fe(t2g) orbitals in II than in [Fe(CN)6]4− provides a rationale for the opposite L31 and L32 relative intensity in the two species. Moving to the weak features L33 and L34 (see Figure 10), the major contribution to the broad L33 structure is provided in SII (EII) by an a2u(a″2) electronic state associated with an iso → fso transition of the same symmetry involving the 17e1/2g (17e1/2)107 fso (the SR 11a1g (11a′1) VMO, which has a sizable contribution (4%) on the Fe t2g-like 3dz2 AO). Interestingly, only the EII f(EE) distribution include contributions beyond L33. Among electronic states associated with transitions lying in this EE region, the one associated with the excitation (1e7/2 → 15e3/2)107 with the largest f values (3.4 × 10−3) has an a″2 symmetry.116 The experimental L21 − L31ΔEE (12.4 eV) is exactly the same as reported above for 0 and appears satisfactorily reproduced by SO RTD-DFT results (12.0 eV); nevertheless, no detailed assignment of the IIL2 region is herein attempted for the reasons already mentioned. As a whole, the assignment herein proposed for II is substantially in agreement with that reported by Fronzoni et al.,17 while it does not agree with that suggested by the Hitchcock group28c who assumed that electronic states contributing to the L32 peak were generated by Fe2p → e2u(-like), [(η5-C5H5)]−-based π* excitations. I L2,3-Edges Absorption. Similarly to II, the Fe IL3 EE region is typified by the presence of two well-defined peaks centered at 709.4 and 710.9 eV (L32 and L33, respectively, in Figure 11). Moreover, both features are characterized by the presence of an evident shoulder, on the lower EE side of the former (L31),

associated the L31 (L32) feature to electronic states generated by transitions having an e″ (e′) orbital, Fe−CO antibonding in nature, as fso. In addition, Fronzoni et al.17 presumed that the excitation from the Fe2p-based MOs to the Fe3dz2-based VMO (the 14a′1 orbital in our calculations) is “above the ionization threshold” as a consequence of the already mentioned very high energy position of the Fe 3dz2-based VMO.17 Even though SO RTD-DFT results reproduce satisfactorily both the 0L2 − 0L3 ΔEE (12.4Exp vs 12.0Theo eV), and the corresponding relative intensities (see Figure 8), any detailed assignment of the L2 band envelope will be herein avoided as this EE region suffers from extra broadening and distortion due to the Coster−Kronig Auger decay processes. Therefore, it is not unambiguously determined by experiment.6j,56 II L2,3-Edges Absorption.74 SO RTD-DFT IIf(EE) distributions for staggered and eclipsed rotamers of II are separately compared with the high-resolution gas-phase Fe IIL2,3-edges spectra in Figure 10. The Fe IIL3-edge region includes at least

Figure 10. High-resolution gas-phase Fe L3-edge spectrum (solid line) of II superimposed to the SO RTD-DFT IIf(EE) distribution (bars). Blue and red bars correspond to a2u and e1u IIf(EE) for SII(a) and a″2 and e′1 for EII(b), which have been shifted by 4.81 and 4.98 eV, respectively.

two very evident features (L31 and L32 in Figure 10) at 708.9 and 711.3 eV and two weak structures (L33 and L34 in Figure 10) at 713.9 and 716.0 eV, respectively. Analogously to the Fe 0 L2,3 spectral pattern, the Fe IIL2,3 one is very similar to the ISEELS f(EE) distribution obtained by Hitchcock et al.,28 while it has to be noted that the L32 EE reported by Godehusen et al.29 (712.1 eV) is definitely higher than that measured by the Hitchcock group (711.5 eV). The possibility of treating II as a pseudo-octahedral complex whose bonding scheme may be compared with that of the [Fe(CN)6]4− ion by exploiting the isolobal analogy76 has been thoroughly considered in Section 3.1. As such, Solomon and co-workers pointed out in their Fe L-edge XAS study of the back-bonding in K4[Fe(CN)6] that “When π back-bonding is present in a system, there are two major sets of Fe2p → 3d transitions. There are transitions to the eg set, which are also present in the absence of π back-bonding, and there are additional transitions to π* orbitals”.34b According to that, the lower EE region of the K4[Fe(CN)6]34b,110 and K3[Co(CN)6]110,111 TM L2,3-edges spectral patterns is characterized by the presence of two very evident features lying at 710.35 and 712.05 eV in K4[Fe(CN)6] and 782.7 and 785.5 eV in H


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have the following localization percentages: 18au VMO (π*(COt) = 66, π*([(η5-C5H5)]−) = 15, Fe3dxz = 11); 30bu VMO (π*(COb) = 31, π*(COt) = 27, Fe3dx2−y2 = 21; π*([(η5C5H5)]−) = 4%); 33ag VMO (π*(COt) = 78, Fe3dx2−y2 = 8; Fe 3dxy = 3).120 SO RTD-DFT results indicate that only trans-I significantly contributes to L34; more specifically, the quasi-degenerate excitations from the 4e1/2g/4e1/2g*, 5e1/2g/5e1/2g*, and 4e1/2u/ 4e1/2u* isos118 to the 52e1/2g/52e1/2g* and 52e1/2u/52e1/2u* fsos (the SR 18bg and 33bu VMOs, respectively; see Figure 4) provide the major contributions to the generation of the electronic states generating L34. Incidentally, the localization percentages of the SR 18bg and 33bu VMOs are 18bg VMO (π*([(η5-C5H5)]−) = 38, π*(COb) = 32, π*(COt) = 17, Fe3dxz = 6, Fe3dyz = 3); 33bu VMO (π*([(η5-C5H5)]−) = 32, π*(COb) = 29, Fe3dz2 = 12, π*(COt) = 11). Contributions of the C2h tautomer to the L33/L34 band envelope are then mainly generated by the electronic states associated with excitation from 2p3/2 to π*(+t2g)and π*(−t2g) VMOs. The overall participation of COt-/COb-based π* FMOs appears to exceed the one provided by the [(η5-C5H5)]−-based FMOs, thus providing experimental support to the already stressed CO π acceptor capability higher than the [(η5-C5H5)]− one. The experimental L22 − L33ΔEE (12.6 eV, L22 corresponds to the L2 peak lying at the higher EE) is very similar to those measured for 0 and II. Analogously to the mononuclear complexes, no detailed assignment of the L2 region is herein attempted.

Figure 11. High-resolution gas-phase Fe L3-edge spectrum (solid line) of I superimposed to the SO RTD-DFT If(EE) distribution (bars).117 Blue bars in the panel (a) correspond to the au If(EE) for trans-I; blue, red, and green bars in the panel (b) correspond to the b2, a2, and b1 If(EE), respectively, for cis-I. Bars have been shifted by 5.68 and 4.60 eV in trans-I and cis-I, respectively.

and on the higher EE side of the latter (L34). Besides the asymmetry of the two peaks and their shift (∼0.5 eV) toward higher EE, the most evident difference between the Fe L3-edge spectral patterns of I and II is the reversed relative intensity of the two main peaks. A thorough analysis of the SO RTD-DFT outcomes (see Table S7 of the Supporting Information) pointed out that trans-I118 contributes to the L31 shoulder with electronic states mainly associated with transitions from one of the in-phase combinations of the Fe 2p3/2-based spinors (the 4e1/2g/4e1/2g* isos)119 to the 45e1/2u/45e1/2u* fsos (the SR Fe 3d-based −eg 29bu LUMO; see Figures 4 and 5). Interestingly, electronic states of the C2h conformer118 mainly contributing to the IL32 peak are associated with accidentally degenerate transitions. Both in-phase (the 4e1/2g/ 4e1/2g* and 5e1/2g/5e1/2g* isos) and out-of-phase (4e1/2u/4e1/2u* isos) combinations of Fe 2p3/2-based spinors are involved as isos,119 while the fsos correspond either to the 46e1/2u/46e1/2u* (the SR Fe 3d-based −eg 17au VMO, see Figure 4) or the 46e1/2g/46e1/2g* spinors (the fourth SR Fe 3d-based +eg 32ag VMO, see Figure 4). As a whole, the L31 shoulder and the L32 peak include electronic states associated with Fe-based transitions from 2p3/2 spinors to +eg/−egVMOs. Even if a thorough discussion of the theoretical results pertaining to cis-I is postponed to a forthcoming paper, it can be useful to underline that the inspection of Figure 11b testifies that the C2v tautomer contributes to the L31/L32 band envelope with several closely spaced electronic states of symmetry a1, b1, and b2 (see also Table S8 of the Supporting Information); the rather high intensity of this feature is then not so surprising. In trans-I, the excitations contributing with the largest f values to electronic states associated with L33 (see Table S7 of the SI) have, similarly to those previously described, the inphase and out-of-phase combinations of Fe 2p3/2-based spinors as isos but, as expected, the π*(−t2g) and π*(+t2g) levels as fsos. In more detail, the 49e1/2u/49e1/2u*, 47e1/2u/47e1/2u*, 48e1/2g/ 48e1/2g* spinors (the SR 18au, 30bu and 33ag VMOs; see Figure 4) correspond to the fsos of the just mentioned excitations. Before moving to the analysis of trans-I electronic states contributing to the L34 shoulder, it is worthwhile to mention that the above indicated SR π*(−t2g)/π*(+t2g) combinations

4. CONCLUSIONS The occupied and empty electronic structures of three highly popular, closed shell organoiron complexes ([Fe(CO)5], [(η5C5H5)Fe(CO)(μ-CO)]2, and [(η5-C5H5)2Fe]) have been thoroughly investigated. The title compounds’ ground states have been comparatively studied by exploiting DFT combined with the fragment MO approach, the Nalewajski−Mrozek bond multiplicity index, and the isolobal analogy. The adopted methodology allowed the rationalization of a series of experimental evidence including structural and vibrations parameters; moreover, the use of the Ziegler transition state approach definitively ruled out the need of a direct Fe−Fe bond to justify the diamagnetic nature of trans-[(η5-C5H5)Fe(CO)(μ-CO)]2. With specific reference to trans-[(η5-C5H5)Fe(CO)(μ-CO)]2, the concomitant presence of the [(η5C5H5)]−, COt, and COb ligands allowed us to investigate how their π* orbitals compete for the electronic charge in the Fe → ligand back-donation. Theoretical, structural, and vibrational evidence is consistent with a definitely higher π-acceptor capability of the CO ligand, terminal or bridging, compared to that of the [(η5-C5H5)]− one. This has been further confirmed by exploiting the Fe L2,3-edges XAS data recorded in the gasphase and assigned by employing the SO RTD-DFT method, thus further strengthening the conclusions reported by the Solomon group about the capability of Fe L-edge XAS to provide a direct probe of the metal-to-ligand back-bonding.

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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.9b00226. I


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F.; Wernet, P.; Odelius, M. Ab Initio calculations of x-ray spectra: atomic multiplet and molecular orbital effects in a multiconfigurational SCF approach to the L-edge spectra of transition metal complexes. J. Phys. Chem. Lett. 2012, 3, 3565−3570. (g) Maganas, D.; Roemelt, M.; Hävecker, M.; Trunschke, A.; Knop-Gericke, A.; Schlögl, R.; Neese, F. First principles calculations of the structure and V L-edge X-ray absorption spectra of V2O5 using local pair natural orbital coupled cluster theory and spin−orbit coupled configuration interaction approaches. Phys. Chem. Chem. Phys. 2013, 15, 7260− 7276. (h) Roemelt, M.; Maganas, D.; DeBeer, S.; Neese, F. A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: application to transition metal L-edge X-ray absorption spectroscopy. J. Chem. Phys. 2013, 138, 204101. (i) Maganas, D.; DeBeer, S.; Neese, F. Restricted open-shell configuration interaction cluster calculations of the L-edge x-ray absorption study of TiO2 and CaF2 solids. Inorg. Chem. 2014, 53, 6374−6385. (j) Maganas, D.; Roemelt, M.; Weyhermüller, T.; Blume, R.; Hävecker, M.; Knop-Gericke, A.; DeBeer, S.; Schlögl, R.; Neese, F. L-edge X-ray absorption study of mononuclear vanadium complexes and spectral predictions using a restricted open shell configuration interaction ansatz. Phys. Chem. Chem. Phys. 2014, 16, 264−276. (7) Kerber, R. C. Mononuclear Iron Compounds with η1-η6 Hydrocarbon Ligands. Comprehensive Organometallic Chemistry II 1995, 7, 101−229. (8) Mond, L.; Quincke, F. Note on a Volatile Compound of Iron with Carbon Oxide. J. Chem. Soc., Trans. 1891, 59, 604−607; Ber. Dtsch. Chem. Ges. 1891, 24, 2248−2250. (9) Kealy, T. J.; Pauson, P. L. A New Type of Organo-Iron Compound. Nature 1951, 168, 1039−1040. (10) Wilkinson, G.; Rosenblum, M.; Whiting, M. C.; Woodward, R. B. The Structure of Iron bis-Cyclopentadienyl. J. Am. Chem. Soc. 1952, 74, 2125−2126. (11) (a) Piper, T. S.; Wilkinson, G. Alkyl and Aryl Derivatives of πCyclopentadienyl Compounds of Chromium, Molybdenum, Tungsten, and Iron. J. Inorg. Nucl. Chem. 1956, 3, 104−124. (b) Bitterwolf, T. E. Photochemistry and Reaction Intermediates of the Bimetallic Group VIII Cyclopentadienyl Metal Carbonyl Compounds, (η5C5H5)2M2(CO)4 and Their Derivatives. Coord. Chem. Rev. 2000, 206−207, 419−450. (12) Besides an oxygen carrier, Fe serves multiple purposes among which the generation of carcinogenic free radicals is well-known. Nevertheless, [(η5-C5H5)Fe(CO)2X] complexes (X = halide, NCS, and (η5-C5H5)Fe(CO)2) have been recently found to induce apoptosis in breast cancer and HeLa cell lines without affecting normal cells.13 (13) Poh, H. T.; HO, P. C.; Fan, W. Y. Cyclopentadienyl iron dicarbonyl (CpFe(CO)2) derivatives as apoptosis-inducing agents. RSC Adv. 2016, 6, 18814−18823. (14) [(η5-C5H5)2Fe] and its derivatives are very popular molecules for biological applications and for conjugation with biomolecules.15 (15) Van Staveren, D. R.; Metzler-Nolte, N. Bioorganometallic Chemistry of Ferrocene. Chem. Rev. 2004, 104, 5931−5986. (16) The peculiar labeling of title compounds takes origin from the Fe formal oxidation states in [Fe(CO)5], [(η5-C5H5)Fe(CO)(μCO)]2 and [(η5-C5H5)2Fe], 0, +1, and +2, respectively. (17) Fronzoni, G.; Decleva, P.; Lisini, A.; Ohno, M. 2p→3d Excitations in Transition Metal Compounds. A computational investigation on Fe(CO)5, Fe(C5H5)2 and Cr(CO)6. J. Electron Spectrosc. Relat. Phenom. 1993, 62, 245−262. (18) Miedema, P. S.; de Groot, F. M. F. The iron L edges: Fe 2p Xray absorption and electron energy loss spectroscopy. J. Electron Spectrosc. Relat. Phenom. 2013, 187, 32−48. (19) Grush, M. M.; Muramatsu, Y.; Underwood, J. H.; Gullikson, E. M.; Ederer, D. L.; Perera, R. C. C.; Callcott, T. A. Soft X-ray emission and absorption - A comparative study on the sensitivity to oxidation state and ligand environment of transition metal complexes. J. Electron Spectrosc. Relat. Phenom. 1998, 92, 225−229. (20) (a) Carlotto, S.; Sambi, M.; Vittadini, A.; Casarin, M. Theoretical modeling of the L2,3-edge X-ray absorption spectra of

DFT/ROCIS numerical experiments and extended transition state results. Tables S1−S5: TZ2P DFT BP86 optimized coordinates of [Fe(CO)5], cis- and trans-[(η5-C5H5)Fe(CO)(μ-CO)]2, eclipsed- and staggered-[(η5-C5H5)2Fe]; Tables S6−S10: SO ZORA RTD-DFT compositions, f × 103 and EE values of transitions associated with electronic states generating the L3 spectral features in [Fe(CO)5], cis- and trans-[(η5C5H5)Fe(CO)(μ-CO)]2, eclipsed- and staggered-[(η5C5H5)2Fe] (PDF)

AUTHOR INFORMATION

Corresponding Authors

*(M.C.) E-mail: [email protected]. *(S.C.) E-mail: [email protected]. ORCID

Marcello Coreno: 0000-0003-4376-808X Mauro Sambi: 0000-0002-7105-4001 Maurizio Casarin: 0000-0002-3347-8751 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Computational Chemistry Community (C3P) of the University of Padova is kindly acknowledged. This work was supported by the University of Padova (Grant P-DISC #CARL-SID17 BIRD2017-UNIPD, Project CHIRoN).

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Inorganic Chemistry

(CO)2]2 Complexes (M = Fe, Ru). Struct. Bonding (Berlin, Ger.) 2004, 106, 153−172. (i) Green, J. C.; Green, M. L. H.; Parkin, G. The occurrence and representation of three-centre two-electron bonds in covalent inorganic compounds. Chem. Commun. 2012, 48, 11481− 11503. (j) Labinger, J. A. Does cyclopentadienyl iron dicarbonyl dimer have a metal−metal bond? Who’s asking? Inorg. Chim. Acta 2015, 424, 14−19. (90) Trans89a,d and cis89b CO-bridged tautomers interconvert through nonbridged isomers.89c (91) GS state calculations and the modeling of the Fe IL2,3-edges spectra have been carried out for both tautomers; nevertheless, the detailed description of GS properties has been herein limited to transI. (92) (a) Hoffmann, R.; Lipscomb, W. N. Theory of Polyhedral Molecules. I. Physical Factorizations of the Secular Equation. J. Chem. Phys. 1962, 36, 2179−2189. (b) Hoffmann, R. An Extended Hückel Theory. I. Hydrocarbons. J. Chem. Phys. 1963, 39, 1397−1412. (93) The latter +eg (−eg) orbital is the 32ag (17au) VMO. (94) (a) Baerends, E. J.; Ellis, D. E.; Ros, P. Self-consistent molecular HartreeFockSlater calculations I. The computational procedure. Chem. Phys. 1973, 2, 41−51. (b) Dunlap, B. I.; Connolly, J. W. D; Sabin, J. R. On some approximations in applications of Xα theory. J. Chem. Phys. 1979, 71, 3396−3402. (c) Van Alsenoy, C. Ab initio calculations on large molecules: The multiplicative integral approximation. J. Comput. Chem. 1988, 9, 620−626. (95) The ionization energy of the trans-I 14bg HOMO, estimated by exploiting the Slater transition state method96 applied to the herein optimized structure, (7.20 eV) is in excellent agreement with the gasphase lowest lying PE band (6.95 eV).89f (96) Slater, J. C. Quantum Theory of Molecules and Solids. The SelfConsistent-Field for Molecules and Solids; McGraw-Hill: New York, 1974, Vol. 4. (97) (a) Yang, F.; Yu, P.; Zhao, J.; Shi, J.; Wang, J. Ultrafast vibrational and structural dynamics of dimeric cyclopentadienyliron dicarbonyl examined by infrared spectroscopy. Phys. Chem. Chem. Phys. 2015, 17, 14542−14550. (b) Anna, J. M.; King, J. T.; Kubarych, K. J. Multiple Structures and Dynamics of [CpRu(CO)2]2 and [CpFe(CO)2]2 in Solution Revealed with Two-Dimensional Infrared Spectroscopy. Inorg. Chem. 2011, 50, 9273−9283. (98) The symmetric/asymmetric COt νCO (sνCO/aνCO) infrared absorption bands of cis-I in CCl4 (CH2Cl2) lie at 2004.3/1963.2 (1996.9/1956.2) cm−1, while aνCO = 1958.8 (1954.6) cm−1 in trans-I. Corresponding analytical values are sνCO/aνCO = 1994.0/1956.3 cm−1 in cis-I; aνCO = 1950.7 cm−1 in trans-I. (99) Analytical values of sνCO/aνCO lie at 1813.6/1789.4 cm−1 in cisI, while aνCO is computed at 1795 cm−1 in trans-I. (100) The trans tautomer is herein estimated to be more stable than the cis one by less than 2 kcal/mol. Even though this in contrast with literature data (Bullit et al.89c estimated cis-I more stable than trans-I by ∼1 kcal/mol), the ΔE trifle has to be highlighted. (101) Diana, E.; Rossetti, R.; Stanghellini, P. L.; Kettle, S. F. A. Vibrational Study of (η5-Cyclopentadienyl)metal Complexes. Inorg. Chem. 1997, 36, 382−391. (102) The +eg 14bg IHOMO is mainly localized on the Fe 3dyz AOs (32%), the COb π* FMOs (22%) and the Cp π2-based FMOs (21%) having a node in the σh plane (see Figure 5). (103) (a) Bénard, M. Theoretical ab Initio Calculations of Deformation Densities in Some Binuclear Metal Complexes. J. Am. Chem. Soc. 1978, 100, 7740−7742. (b) Bénard, M. Molecular Orbital Analysis of the Metal-Metal Interaction in Some Carbonyl-Bridged Binuclear Complexes. Inorg. Chem. 1979, 18, 2782−2785. (c) Bursten, B. E.; Cayton, R. H. Electronic Structure of Piano-Stool Dimers. 3. Relationships between the Bonding and Reactivity of the Organically Bridged Iron Dimers [CpFe(CO)]2(μ-CO)(μ-L) (L = CO, CH2C = CH2CH+)1. J. Am. Chem. Soc. 1986, 108, 8241−8249. (d) Bursten, B. E.; Cayton, R. H.; Gatter, M. G. Electronic Structure of Piano-Stool Dimers. 5. Relationships between the π-Acidity and Electrochemistry in a Series of Isoelectronic Compounds of the Type Cp2M2L4 (L = CO, NO)1. Organometallics 1988, 7, 1342−1348.

Octahedral Superelectrophilic Metal Carbonyl Cations of Iron(II), Ruthenium(II), and Osmium(II). Part 2: Syntheses and Characterizations of [M(CO)6][BF4]2 (M = Fe, Ru, Os). Inorg. Chem. 2005, 44, 4206−4214. (79) GS ADF numerical experiments herein reported for II differ from those carried out by Hocking et al.34b to investigate the Fe → (CN)− back-bonding in K4[Fe(CN)6] for the absence of the frozen core approximation and the use of a TZ2P rather than a TZP basis set. (80) In the D 5h [C5 H5 ]− anion, the 5-fold Γ π reducible representation includes the following IRs: a″2, e″1, and e″2. They correspond to the SALCs herein labeled as π1, π2, and π3, respectively. (81) In the D5d (D5h) group the t2g-like AOs transform as a1g + e2g (a′1 + e′2), while the eg-like AOs transform as e1g (e″1). (82) EII PDOS and COOP are basically indistinguishable from those pertaining to SII. (83) Takusagawa, F.; Koetzle, T. F. A Neutron Diffraction Study of the Crystal Structure of Ferrocene. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1979, 35, 1074−1081. (84) Coriani, S.; Haaland, A.; Helgaker, T.; Jørgensen, P. The Equilibrium Structure of Ferrocene. ChemPhysChem 2006, 7, 245− 249. (85) π*(t2g) MOs account for the antibonding interaction between t2g Fe 3d AOs and the empty t2g (CN)−-based 2π SALCs, while πb(t2g) MOs account for the bonding interaction between t2g Fe 3d AOs and t2g (CN)−-based 1π SALCs. (86) Symmetry properties of II set that only two Fe t2g-like orbitals (the3dx2−y2 and 3dxy AOs)81 may participate to the FeII → [(C5H5)2]2− back-bonding because no π SALC of a1g symmetry is empty.81 Accordingly, the contribution of the IIFe 3dz2 AO to the third t2g-like orbital of symmetry a1g amounts to 88%. The Fe-ligand back-bonding interaction may be then foreseen weaker in II than in [Fe(CN)6]4−. (87) Lippincott, E. R.; Nelson, R. D. The vibrational spectra and structure of ferrocene and ruthenocene. Speotrochim Acta 1958, 10, 307−329. (88) Symmetric and antisymmetric ring metal stretches have been assigned by Lippincott and Nelson to the A1g and A2u fundamental modes of the Raman and infrared bands lying at 303 and 478 cm−1, respectively.87 The corresponding ADF analytical values are 305 and 463 cm−1, respectively. (89) (a) Bryan, R. F.; Greene, P. T. Metal-Metal Bonding in Coordination Complexes. Part IX. Crystal Structure of trans-Di-μcarbonyl-dicarbonyldi-π-cyclopentadienyldi−iron (Fe-Fe), a Redetermination. J. Chem. Soc. A 1970, 0, 3064−3068. (b) Bryan, R. F.; Greene, P. T.; Newlands, M. J.; Field, D. S. MetaI-Metal Bonding in Co-ordination Complexes. Part X. Preparation, Spectroscopic Properties, and Crystal Structure of the cis-Isomer of Di-μ-carbonyldicarbonyldi-π-cyclopentadienyldi-iron (Fe-Fe). J. Chem. Soc. A 1970, 0, 3068−3074. (c) Bullitt, J. G.; Cotton, F. A.; Marks, T. J. Structural and Dynamic Properties of the Pentahaptocyclopentadienylmetal Dicarbonyl Dimers. Inorg. Chem. 1972, 11, 671−676. (d) Mitschler, A.; Rees, B.; Lehmann, M. S. Electron Density in Bis(dicarbonyl-π-cyclopentadienyliron) at Liquid Nitrogen Temperature by X-Ray and Neutron Diffraction. J. Am. Chem. Soc. 1978, 100, 3390−3397. (e) Jemmis, E. D.; Pinhas, A. R.; Hoffmann, R. Cp2M2(C0)4−Quadruply Bridging, Doubly Bridging, Semibridging, or Nonbridging? J. Am. Chem. Soc. 1980, 102, 2576−2585. (f) Andreocci, M. V.; Bossa, M.; Cauletti, C.; Paolesse, R.; Ortaggi, G.; Vondrak, T.; Piancastelli, M. N.; Casarin, M.; Dal Colle, M.; Granozzi, G. Molecular orbital analysis of some ligand-bridged iron binuclear complexes by UV photoelectron spectroscopy and DV-Xα calculations. J. Organomet. Chem. 1989, 366, 343−355. (g) Granozzi, G.; Casarin, M. Multicentered Interactions in Bi- and Trinuclear Organometallic Carbonyls by UV-PE Spectroscopy and DV-Xα Quantum Mechanical Calculations. In Topics in Physical Organometallic Chemistry; Gielen, M., Ed.; Freund Publishing House, 1989; Vol. 3, pp 107−162. (h) Jaworska, M.; Macyk, W.; Stasicka, Z. Structure, Spectroscopy and Photochemistry of the [M(η5-C5H5)M


Article

Inorganic Chemistry (104) Vitale, M.; Lee, K. K.; Hemann, C. F.; Hille, R.; Gustafson, T. L.; Bursten, B. E. Resonance Raman Studies of [CpFe(CO)2]2 and [Cp*Fe(CO)2]2: A Probe of Photoreactive States and Intermediates. J. Am. Chem. Soc. 1995, 117, 2286−2296. (105) Ziegler, T.; Rauk, A. On the calculation of bonding energies by the Hartree Fock Slater method. Theor. Chim. Acta 1977, 46, 1− 10. (106) Acronyms iso and fso stand for initial spin orbital and final spin orbital. (107) The spinor labeling is the one reported by Jacobs, P. W. M. Group Theory With Applications in Chemical Physics; Cambridge University Press: Cambridge, 2005; p. 450. (108) BP86 and PBE0 0GSs (see Supporting Information) are characterized by different LUMOs: the Fe 3dz2-based 14a′1 VMO in the former case, the 2π CO-based 4e″ VMO in the latter. As such, the BP86 0GS quasi-degeneracy of the 4e″ (−2.599 eV) and 14a′1 (−2.602 eV) VMOs is worthy of note. (109) States at lower EE and generated by transitions with f values not reported in Table S6 but displayed in Figure 9 imply excitation from the Fe2p3/2 (2e5/2 and 1e3/2)107 levels to fsos related to the 4e″, 11e′, and 14a′1 frontier VMOs. (110) (a) Peng, G.; van Elp, J.; Jang, H.; Que, L., Jr; Armstrong, W. H.; Cramer, S. P. L-Edge X-ray Absorption and X-ray Magnetic Circular Dichroism of Oxygen-Bridged Dinuclear Iron Complexes. J. Am. Chem. Soc. 1995, 117, 2515−2519. (b) Collison, D.; Garner, C. D.; McGrath, C. M.; Mosselmans, J. F. W.; Roper, M. D.; Seddon, J. M. W.; Sinn, E.; Young, N. A. Soft X-ray photochemistry at the L2,3edges in K3[Fe(CN)6], [Co(acac)3], and [Cp2Fe][BF4]. J. Synchrotron Radiat. 1999, 6, 585−587. (c) Kitajima, Y.; Nanba, Y.; Tanaka, M.; Koga, Y.; Ueno, A.; Nakagawa, K.; Tokoro, H.; Ohkoshi, S.-i; Iwazumi, T.; Okada, K.; Isozumi, Y. Observation of π backbonding features appearing in Fe 2p X-ray absorption spectra and Fe 1s-4p-1s resonant X-ray emission spectra of RbMn[Fe(CN)6]. J. Phys.: Conf. Ser. 2013, 430, 012082. (111) The L2,3-edges XAS features of [Co(CN)6]3−, isoelectronic with [Fe(CN)6]4−, have been recently modeled by Lalithambika et al.,112 by exploiting the DFT/ROCIS approach. (112) Lalithambika, S. S. N.; Atak, K.; Seidel, R.; Neubauer, A.; Brandenburg, T.; Xiao, J.; Winter, B.; Aziz, E. F. Chemical bonding in aqueous hexacyano cobaltate from photon- and electron-detection perspectives. Sci. Rep. 2017, 7 (7), 40811. (113) In K4[Fe(CN)6] the peak at the lower EE is less intense than that lying at the higher EE (see Figure 1d of ref 110b),114 while the opposite is true in K3[Co(CN)6] (see Figure 3c of ref 110b). Original TZ2P GS numerical experiments indicate that the contribution of the TM 3d AOs to π*(t2g) MOs in [Fe(CN)6]4− and [Co(CN)6]3− amounts to 16% and 10%, respectively. (114) In ref 34b Hocking et al. pointed out that “the back-bonding allows the π* transition to ‘borrow’ intensity from the intense metalbased eg transitions”. (115) In SII (EII), the 10e3/2g and 5e5/2g (10e3/2 and 9e5/2) spinors correspond to the scalar relativistic (SR) [(η5-C5H5)]−-based π*(t2g) 5e2g (5e′’2) VMOs. (116) The 15e3/2 spinor is related to the SR 8e″1 VMO, which corresponds to a high-lying [(η5-C5H5)]−-based MO with a minor contribution from Fe 3dyz AO. (117) The SO RTD-DFT f(EE) distribution for trans-I has been evaluated by assuming a Ci symmetry because the C2h point group is not implemented for spin−orbit coupled excitations.31 (118) The detailed analysis of the cis-I L2,3-edges spectral pattern will be presented in a forthcoming paper together the SR RTD-DFT modeling of gas-phase K-edge spectra of title molecules. (119) Different contributions to transitions collected in Tables S7 of the Supporting Information have been labeled according to the IRs of the Ci′ double group.117 Spinors of trans-I have been labeled in the text by referring to the C2h′ double group.107 (120) cis-I electronic states mainly contributing to IL33 are generated by two quasi-degenerate excitations of symmetry a1 and b2 (see Figure 11 and Table S8 of the Supporting Information) having the largest f

values. The b2 excitation implies a transition involving the SR 15a2 VMO, almost completely localized (90%) on π*([(η5-C5H5)]−) FMOs with minor contributions from Fe 3dxy (5%) and 3dyz (1%). As far as the a1 excitation is concerned, it implies a transition involving the SR 31b1 VMO, which has the following localization percentages (π*([(η5-C5H5)]−) = 46%, π*(COt) = 10%, π*(COb) = 17%; Fe 3dx2−y2 = 7%; Fe 3dz2 = 7%).

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Comparative Experimental and Theoretical Study of the Fe L2,3

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