Theoretical Analysis of Fe K-Edge XANES on Iron Pentacarbonyl.

Iron pentacarbonyl (Fe(CO)5) is a versatile material that is utilized as an inhibitor of flame, shows soot suppressibility, and is used as a precursor for focused electron-beam-induced deposition (FEBID). X-ray absorption near-edge structure (XANES) of the K edge, which is a powerful technique for monitoring the oxidation states and coordination environment of metal sites, can be used to gain insight into Fe(CO)5-related reaction mechanisms in in situ experiments. We use a finite difference method (FDM) and molecular-orbital-based time-dependent density functional theory (TDDFT) calculations to clarify the Fe K-edge XANES features of Fe(CO)5. The two pre-edge peaks P1 and P2 are mainly the Fe(1s) → Fe-C(σ*) and Fe(1s) → Fe-C(π*) transitions, respectively. When the geometry transformed from D 3h to C 4v symmetry, a ∼30% decrease of the pre-edge P2 intensity was observed in the simulated spectra. This implies that the π bonding of Fe and CO is sensitive to changes in geometry. The following rising edge and white line regions are assigned to the Fe(1s) → Fe(4p)(mixing C(2p)) transitions. Our results may provide useful information to interpret XANES spectra variations of in situ reactions of metal-CO or similar compounds with π acceptor ligandlike metal-CN complexes.

Introduction

Carbon monoxide (CO) is one of the important ligands that can be a σ donor or a π acceptor in metal–carbonyl complexes so as to own some special characters in chemical bonding, like strong field ligand,[1] semibridging ligand,[2] and cis effect.[3] It plays an important role in organometallic synthesis, catalysis, biological processes, and materials chemistry.[4−9] For example, iron pentacarbonyl (Fe(CO)5) has various applications such as flame inhibition, soot suppressibility,[10−14] and as a precursor for focused electron-beam-induced deposition (FEBID).[15−17] In general, the trigonal bipyramid geometry (D3 symmetry) is the most common structure for gas[18−21] and solid phases of Fe(CO)5[22,23] and the square pyramid geometry (C4 symmetry) is a transition state of Berry pseudorotation.[24,25] However, the C4 and C2 structures may be stabilized by interactions with a solvent molecule located at the trans to rotational axis of a CO ligand.[26−29] In general, infrared spectroscopy is often used to characterize metal–carbonyl complexes. Besides, X-ray absorption spectroscopy (XAS) is another technique to characterize the change of metal sites in such metal–carbonyl complexes due to the element-specific character of XAS. For example, Fe K-edge XAS is utilized to solve the local structure of Fe(CO)5 in a solution state and the C2 structure is obtained in a benzene solvent.[28]

Generally, the metal K-edge X-ray absorption spectrum is divided into two regimes: X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS). The range up to 50–1000 eV above the absorption edge is the EXAFS regime, which is a single-scattering-dominated region. It can provide coordination numbers and distances between absorbing atom and surrounding atoms within 5 Å.[30] The range above the rising edge up to 40 eV including the pre-edge peaks is named XANES. In the XANES regime, the spectrum features are dominated by the contributions of multiple scattering events with many atoms, which is a measurement of high-order atomic correlation functions. Therefore, this spectral region can be also utilized to obtain local structures through XANES fitting. However, to the best of our best knowledge, currently, only XMAN[31,32] and FitIt[33,34] software can achieve XANES fitting. In addition, the pre-edge peaks are attributed to the excitation of core electrons into the unoccupied molecular orbitals (MOs), which can be used to investigate molecular symmetry and metal coordination. Due to these characteristics of XANES, it can even be applied to monitor the variations of the local structure in absorbing atoms during the reaction process. Therefore, Ahr et al. combined picosecond Fe K-edge XAS experiments and theoretical XANES spectra to study the ligand substitution dynamics of Fe(CO)5 in ethanol.[35] The region in front of and behind the white line is divided into three ranges of 7121–7125 eV (measurement 1), 7127–7129 eV (measurement 2), and 7131–7133 eV (measurement 3), and these ranges are monitored during a substitution reaction. The results indicate that measurement 3 is sensitive to the reaction process that is occurring and subsequently observed in measurement 1. In combination with the simulated XANES of Fe(CO)5 and Fe(CO)4EtOH by the FEFF program, where FEFF is an automated program for ab initio calculations of XAS for clusters of atoms based on the multiple scattering theory (MST), the variations of measurements 1 and 3 are interpreted as the excitation of Fe(CO)5 and the formation of Fe(CO)4EtOH, respectively.[35] However, there is no discussion in the pre-edge region that is below 7120 eV.

In fact, the resolution of metal K-edge pre-edge features is also important. For instance, carbonmonoxy-myoglobin was investigated by polarized X-ray absorption spectra and it was concluded that the observed two pre-edge peaks were assigned to the transition of Fe(1s) to [Fe(d) + CO(σ)]* and [Fe(d,d) + CO(π*)]*,[36,37] which interprets the reduction of pre-edge absorption in photon-induced lysis of a Fe–CO bond.[38] To analyze the pre-edge transition peaks of K edge XAS by theoretical calculation, the molecular orbital (MO)-based time-dependent density functional theory (TDDFT) calculations can achieve the reasonable pre-edge absorptions using only allowed excitation out of the selected appropriate donor core orbitals into the entire virtual space. The methodology has been applied to analyze pre-edge features of many transition-metal complex studies, such as Ti,[39] V,[40,41] Cr,[42−45] Mn,[45−49] Fe,[50−69] Co,[70,71] Ni,[54,72] Cu,[73−75] and Mo.[76] Through the combination of the high-energy-resolution fluorescence-detected (HERFD) XANES technique[77−80] and MO-based TDDFT calculations, more information of electronic structure can be provided from high-resolution pre-edge of K-edge spectra.[60−62] Atkins and co-workers utilize this methodology to study Fe pre-edge spectra of Fe(CO)5 and interpret that observed first and second pre-edge peaks are caused by Fe(1s) to unoccupied A1′ and to E″/E′ transitions, respectively. The results indicate that Fe(1s) → A1′ and Fe(1s) → E″ transitions are quadrupole-allowed, whereas Fe(1s) → E′ transitions are quadrupole-allowed (74.8%) and dipole-allowed (25.2%).[62] However, the earlier report by Fronzoni and co-workers showed a single pre-edge peak (Fe(1s) → E′ transitions) based on ab initio configuration interaction (CI) calculations.[81] Although HERFD XANES can provide more detailed information about the pre-edge region, such experiments are performed on insertion device (ID) beamline of synchrotron radiation and at low-temperature conditions to avoid radiation damage (using a He cryostat under vacuum condition), which are not easy to access for general users. Here, we re-examine the conventional Fe K-edge XANES of Fe(CO)5 at room temperature in ambient conditions and analyze the XANES features by theoretical calculations.

Through using MST and finite difference method (FDM) to solve the Schrödinger equation, the initial and final states can be calculated to obtain a good XANES simulation beyond the pre-edge region, which indicates the good approximation of Fermi energy and spectral shape. In general, it is hard to describe the pre-edge region very well based on MST or FDM simulation. However, the MO-based TDDFT can calculate the relative pre-edge transition energy quite well but not for the Fermi level and even higher-energy region. Therefore, in this paper, we will combine the advantage of both methods to interpret the pre-edge and XANES transitions.

In this work, the EXAFS was initially used to solve the structure of Fe(CO)5. Subsequently, we used the combination of MO-based TDDFT and FDM calculations—providing good XANES features of the pre-edge region and rising edge up to 40 eV region, respectively—to get a comprehensive insight into the relation between Fe K-edge spectrum and electronic configuration. The XANES spectrum of the C4 structure in the transition state was also simulated. The results can provide more spectral information on the influence of geometric change from D3 to C4 symmetry.

Results and Discussion

Berry Pseudorotation of Fe(CO)5

The trigonal bipyramid molecule with a D3 symmetry can exchange molecular orientation through the Berry pseudorotation.[25] The movement that decreasing ∠Cax–Fe–Cax (θ) from 180 to 120° is accompanied by increasing one of the ∠Ceq–Fe–Ceq (ϕ) from 120 to 180° is performed to complete pseudorotation (see Scheme ); the transformation of molecule symmetry is D3 → C4 → D3 through this movement. To examine the effect of structure transformation, the relaxed scan of D3 → C2 → C4 was performed, and the obtained Walsh diagram of occupied MOs is shown in Figure . The energy change of MO 2E″ and 2E′ in the D3 structure, which were split and reformed to MO 1B1 and 3E and 2A1 of the C4 structure along with symmetry exchange, is most obvious. These MOs display π back-donation interaction, which indicates that the metal–ligand π bonding is affected obviously by a symmetry transformation. On the other hand, the Fe(CO)5 of D3 is more stable by 1.59 kcal/mol than that of C4, which is consistent with the activation barrier of ∼2 kcal/mol for Fe(CO)5 pseudorotation reported by previous theoretical[24] and experimental literature studies.[82] This result indicates molecular conformation change is very fast so that EXAFS analysis is used to investigate the main structure of Fe(CO)5 at room temperature.

Scheme 1

(a) D3 and (b) C4 Structures of Fe(CO)5

The Berry pseudorotation is carried out by increasing ∠Ceq–Fe–Ceq (ϕ) and decreasing ∠Cax–Fe–Cax (θ) simultaneously.

Figure 1

Walsh diagrams of occupied MOs in Fe(CO)5. From the D3 structure to the C4 structure, each scan step decreases ∠Cax–Fe–Cax angle by −1.53° and increases that of ∠Ceq–Fe–Ceq by 2.00° simultaneously.

EXAFS Analysis

The best EXAFS fitting result was obtained by the D3 symmetry of Fe(CO)5 as the molecular model. This result is consistent with infrared spectra that the CO stretching modes E′ and A2″ of the D3 structure[83] were observed at 2013.68 and 2034.90 cm–1, respectively (see Figure S1). The fitting parameters and results are shown in Table and Figure . The first shell was fitted with single scattering contributed from the five Fe–C scattering paths at 1.813(3) Å. The second shell was fitted with single scattering contributed from Fe–O (2.957(4) Å) and multiple scattering corresponding to Fe–C–O (2.957(4) Å) and Fe–C–O–C (2.957(4) Å). The single scattering and multiple scattering paths are described in Figure . According to the fitting results, the averaged Fe–C bond length of 1.813(3) Å and C–O bond length of 1.144(7) Å were consistent with the values of 1.806–1.832 Å for Fe–C bond length and 1.127–1.153 Å for C–O bond length reported by single-crystal data[22,23] and electron diffraction experiments.[18−21] Moreover, our EXAFS fitting result is consistent with Robertson’s that, which are 1.813(3) Å for the Fe–C length and 2.948(4) Å for the Fe–O length;[84] the Fe–O lengths are slightly varying and their difference is about 2 standard deviations.

Table 1

Parameters Used in Fitting the EXAFS Data of Fe(CO)5

bond type	N	R (Å)	σ2 (Å2)
Fe–C	5	1.813(3)	0.0018(3)
Fe–O	5	2.957(4)	0.0026(2)
Fe–C–O	10	2.957(4)	0.0026(2)
Fe–C–O–C	5	2.957(4)	0.0026(2)
Δk (Å–1)	[2.2–13.95]
ΔR (Å)	[1.56–3.12]
Rfit	0.8%
ΔE0	1.2(7)

Figure 2

EXAFS fitting results of Fe(CO)5.

Figure 3

Scattering paths of Fe(CO)5.

Simulation and Analysis of Fe K-Edge Spectra

Based on the best-fitting EXAFS result obtained by the D3 structural model, the same model also was used for the Fe K-edge XANES simulation. In addition, the simulation spectra together with experimental results are shown in Figure . In the pre-edge region, two broad peaks at around 7115.3 and 7118.0 eV denoted P1 and P2, respectively, are observed and assigned to 1s → 3d transitions. These absorptions are through quadrupole-allowed and dipolar-forbidden transitions.[85] The white line at about 7128.2 eV (denoted A) is assigned as 1s → 4p dipole-allowed transition. In the multipole scattering region, a very broad peak at about 7151.0 eV (denoted B) is observed. The pre-edge region of our experiment spectrum limited by the intrinsic resolution of conventional K-edge spectra shows lower resolution than that of the HERFD XANES spectrum.[62] However, obtaining HERFD XANES spectra needs the ID beamline of synchrotron radiation, and this resource is not easy to get for general users. Moreover, two pre-edge peaks observed in our experimental data demonstrate a certain extent of quality in the conventional XAS K-edge beamline.

Figure 4

Experimental and theoretical simulation of Fe K-edge spectra. The top curve is the second derivative of the experimental spectrum (second curve). The third, fourth, and fifth curves are simulated with muffin-tin (MT) approximation and full potentials of Xα and Hedin–Lundqvist (HL), respectively. The XANES features are labeled as P1, P2, and A based on the second derivative of the experimental spectrum.

In general, both the calculations of full potential and MT potential reproduce the features of peaks A and B, but peak B in MT potential approximation simulation has a larger deviation from the experimental result than that of full potential. In two full potential simulations, two pre-edge peaks, which are consistent with the experimental result, can be observed. On the other hand, HL exchange potential demonstrated that the pre-edge peaks at 7115.2 and 7117.9 eV (separated by 2.7 eV) are in more agreement with the experimental result than those of the Xα exchange potential (pre-edge peaks at 7112.8 and 7116.5 eV, separated by 3.7 eV). Comparing to the experimental spectrum, the HL potential calculation provides better XANES features that will be used for further analysis.

The densities of states (DOSs) of Fe and C atoms are shown in Figures and 6, respectively. In these figures, the top plot shows the total DOS, and the projection of specific orbital angular moment is displayed in the following plots. For example, the p, p, and p orbitals (l = 1) correspond to m = −1, 0, and 1, respectively. The d, d, d, d, and d orbitals (l = 2) correspond to m = −2 to 2, in turn. The first pre-edge peak P1 is mainly contributed from the Fe(d) orbital (Figure b) together with some hybridization of Cax(p), Ceq(p), and Ceq(p) orbitals, which implies that peak P1 is related to σ* antibonding of the Fe–C bond. The second peak P2 is the linear combination of Fe(d), Fe(d), Fe(d), and Fe(d) orbitals together with slight hybridization of p orbitals of carbon atoms. In general, the intensity of the quadrupolar transition (Δl = ±2) is much weak. Later, more details will be discussed through molecular orbital calculations.

Figure 5

(a) p DOS of Fe and (b) d DOS of Fe.

Figure 6

p DOS plots of (a) axial and (b) equatorial carbon atoms.

Take a closer to look at the features of peak A, the population of Fe(p) orbitals is observed in the 7125–7135 eV region in Figure a. This observation is consistent with the assignment of the 1s → 4p dipolar-allowed transition (Δl = ±1). On the other hand, in the region of 7130–7133 eV beyond the maximum of peak A, the contribution of Fe(p) can be observed at ∼7131.5 eV and Cax(p) owns more the contribution of ∼7136 eV than Cax(p) and Cax(p) (see Figure a). These results indicate that the absorption peak of 7130–7135 eV is mainly related to the bonding between Fe and COax, which is consistent with Ahr’s report that the XANES spectrum of 7131–7133 eV is sensitive to the COax substitution by methanol.[35]

To gain more insight into final-state orbitals, the MO-based TDDFT calculations are performed to fit pre-edge peaks P1 and P2 by B3LYP of origin (20%) and 30% exact exchange (see Figure S3). The spectrum simulated by B3LYP of 30% exact exchange can reproduce the apparent two pre-edge peaks better than that of 20%, which shows a good agreement with the experimental result. These fitting results and its associated molecular orbitals are displayed in Figure . Peak P1 is caused by transition 1 of Fe(1s) → 2A1′(94%; 58% of Fe(d) in 2A1′), and the result of 1s → d transition is consistent with FDMNES calculations. In addition, 2A1′ displays antibonding interaction between 58% of Fe(d) orbitals and 39% of CO(σ) bonding so that this transition is assigned as Fe(1s) → Fe–C(σ*) antibonding character. Peak P2 is a linear combination of four transitions of 1s to Fe–C(π*)-related MOs. The two strongest transitions 4 and 5 at 7118.3 eV are Fe(1s) → 4E′a(76%)/3E′a(18%) and Fe(1s) → 4E′b(76%)/3E′b(18%), respectively. These final states (4E′a, 3E′a, 4E′b, and 3E′b) have dominated contributions derived from CO(π*) of around 71–87%, and the others are mainly the contributions derived from Fe(d) and Fe(d). At 7117.9 eV, the weaker transitions 2 and 3 are Fe(1s) → 3E″b(78%)/3E″a(22%) and Fe(1s) → 3E″a(78%)/3E″b(22%), respectively, which consist of Fe(d)/Fe(d) (∼25%) and CO(π*) (∼75%). Among these final states, the 3E″a, 3E″b, 4E′a, and 4E′b MOs are the major contributions of these four transitions, which indicate that π antibonding character between Fe d orbitals and CO(π*) is related to peak P2. On the other hand, the dipole and quadrupole contributions to transition intensity are presented in Table S1, and transitions 1, 2, and 3 are quadrupole-allowed and transitions 4 and 5 are dipole-allowed (60.5 and 36.3%) and quadrupole-allowed (36.3 and 45.6%). These results are consistent with a previous report by Atkins.[62] Moreover, the calculation without quadrupole contribution in earlier literature show only one pre-edge peak caused by transitions to E′ orbitals.[81] However, based on the study by Atkins et al.,[62] different exchange functionals (BP86 and B3LYP) can provide quite different results on the interpretation of pre-edge peaks. To avoid such uncertainty, we first apply the finite difference method (FDM) to simulate the XANES well and then TDDFT calculations on the same geometric structure are used to complement the relation between pre-edge peaks and chemical bonding.

Figure 7

Experimental (open circle) and TDDFT-calculated (red dot and line) pre-edge of Fe K-edge XANES for D3 Fe(CO)5. The theoretical calculated transition peaks are shown in the vertical line. All transitions have been convoluted with a pseudo-Voigt function with 1:1 ratio of Lorentzian to Gaussian and 1.3 eV half-width to account for experimental and core hole broadening. The TDDFT transition energy is shifted by 11.6 eV for comparison.

Based on the above analysis, peaks P1 and P2 are assigned as Fe(1s) → Fe–C(σ*) and Fe(1s) → Fe–C(π*) transitions, respectively. The consistent assignments were reported for the pre-edge peaks of carbonmonoxy-myoglobin (six coordination of the Fe porphyrin system) in photon-induced lysis of the Fe–CO bond experiment by Della Longa et al.[36,38] In general, a phenomenon can be summarized that the observation of two pre-edge peaks in K-edge XANES may imply that one is related to σ bonding and the other is related to π bonding interactions between metals and ligands.

To understand the molecular geometric influence on the Fe K-edge spectrum, MO-based TDDFT calculations of the C4 structure were also carried out. However, because of the resolution limit of the dynamic experiment, the transition state of C4 structure is hard to distinguish by only a little variation of the general Fe K-edge XANES spectrum. The calculated pre-edge spectrum of the C4 symmetry is displayed in Figure by blue lines. Overall, the intensity of peak P2 of the C4 structure is weaker than that of the D3 structure. Take a closer look at the feature of peak P2 of the C4 structure, transitions 2 (Fe(1s) → 3A1(96%)), 3 (Fe(1s) → 2B1(99%)), 4 (Fe(1s) → 5Ea(56%)/5Eb(26%)/4Ea(9%)/4Eb(7%)), and 5 (Fe(1s) → 5Eb(56%)/5Ea(26%)/4Eb(9%)/4Ea(7%)) compose this absorption. Transitions 4 and 5 are degenerate. Moreover, the MO 5Ea and 5Eb are the main contributions of peak P2, which are related to Fe–C(π*) orbitals. The intensities of transitions 4 and 5 are obviously weaker than that of the D3 structure so that the intensity of peak P2 is reduced in the C4 structure. This result indicates that π antibonding between Fe and CO is sensitive to changes in geometry, which is consistent with the observation in the Walsh diagram (Figure ). In the Walsh diagram of occupied MOs, π bonding between Fe and CO is affected obviously by a symmetry transformation. In peak P1, the simulated intensity result of the C4 structure is very similar to that of the D3 structure, but transition 1 (Fe(1s) → 3B2(79%)/2B2(18%)) of C4 looks more like a nonbonding interaction between Fe(d) and CO(π*). In addition, the simulation results display that peak P2 intensity of the D3 structure is ∼30% greater than that of the C4 structure. These differences may be observed in the resonance inelastic X-ray scattering (RIXS) spectrum at Fe K-edge, which can be further applied to monitor the in situ reaction.

Figure 8

Comparing TDDFT-calculated pre-edge of Fe K-edge XANES of C4 (blue dot and line) and D3 Fe(CO)5 (red dot and line). The theoretically calculated transition peaks are shown in the vertical line. All transitions have been convoluted with a pseudo-Voigt function with 1:1 ratio of Lorentzian to Gaussian and 1.3 eV half-width to account for experimental and core hole broadening. The TDDFT transition energy is shifted by 11.6 eV for comparison.

Conclusions

In our studies, the D3 structure of Fe(CO)5 is confirmed by EXAFS characterization. Based on the combination with the results of FDM and MO-based TDDFT and DFT calculations, we can provide a detailed information about Fe K-edge XANES features of the d8-system iron complex. The pre-edge P1 and P2 peaks are mainly the transitions of Fe(1s) → Fe–C(σ*) and Fe(1s) → Fe–C(π*), respectively. Based on the TDDFT calculations and symmetry considerations, the pre-edge peaks are dominated by the quadrupole transition. However, the MOs of A1′, E″, and E′ are the hybridization of ligand p orbitals and metal 3d orbitals. Peak A is assigned to the 1s → 4p transition, and the region of 7130–7135 eV is related to the bonding between Fe and axial CO. When Fe(CO)5 is in the C4 structure, the intensity of pre-edge P2 will be decreased by ∼30% because the absorption intensities of transitions 4 and 5 leading to peak P2 are weakened. This result, which corresponds to the observation of occupied frontier orbitals from the Walsh diagram, indicates that π bonding of Fe and CO is sensitive to changes in geometry. Additionally, the variation of pre-edge P2 should be observed in the RIXS spectrum at Fe K-edge. Our results may provide useful information to monitor the in situ reaction of metal–CO or similar compounds with π acceptor ligands like metal–CN complexes. On the other hand, we also provide a methodology that can be utilized by more general users working on metal K-edge XANES research, where the same structure model is used for EXAFS fitting, XANES simulation, and pre-edge analysis.

Experimental and Computational Section

X-ray Absorption Spectrum Measurements

The X-ray absorption spectrum of Fe K-edge was taken at the Taiwan Light Source (TLS) BL17C wiggler beamline at the National Synchrotron Radiation Research Center (NSRRC), Hsinchu, Taiwan. A double-crystal Si(111) monochromator was installed, and the energy resolution (ΔE/E) was about 2 × 10–4. High harmonics were rejected by Rh-coated mirrors. The spectra were recorded in fluorescent mode and measured by a Lytle detector. The data collection range was from 6.9 to 8.1 KeV. A reference spectrum of Fe foil was always measured simultaneously, and its first inflection point at 7112.0 eV was used for energy calibration. Two drops of liquid Fe(CO)5 were first dropped on the center of filter paper (made by α cotton cellulose, ADVANTEC, Toyo Roshi Kaisha, Ltd.) and waited for the diffusion of liquid Fe(CO)5 on cotton cellulose to almost complete by visualization. Then, we cut this filter paper in a suitable size for measurements at room temperature. This implies what we measured are those liquid Fe(CO)5 drops dispersed on the surface of cotton cellulose so that the self-absorption effects of X-ray photons can also be reduced.[60]

EXAFS Data Analysis

The data analysis procedure basically follows the previous report by Hsu et al.[30] The obtained XAS data were corrected for background and normalized by the AUTOBK program,[86] and χ(k) function of EXAFS was determined by χ(k) = [μ(k) – μ0 (k)]/Δμ0(0), where μ(k) is the measured absorption coefficient, μ0(k) is the background, Δμ0(0) is the edge jump, and k is the wave vector of the photoelectron, followed by the definition of .

Based on the local maxima of the first derivative of the XANES spectra (dμ/dE), E0 was set at 7125.5 eV. The experimental χ(k) in the EXAFS region 2.20 ≤ k ≤ 13.95 was further weighted by k3 and then Fourier-transformed into the R-space as FT[k3χ(k)]. The theoretical EXAFS signals χ(k) were calculated by FEFF8.4, according to the structural model of Fe(CO)5.

The EXAFS data analysis was done according to the formulawhere F(k) is the backscattering amplitude from each of the N atoms in the shell at distance R (relative to the absorbing atom), exp(−2k2σ2) is the Debye–Waller factor with a mean-squared displacement σ2, S02 is the amplitude reduction factor, δ(k) is the total phase shift, and λ(k) is the photoelectron mean free path. We fitted FT[k3χ(k)] in the range of Table with the structural parameters varied the bond distance (R) and the bond variance σ2, which is related to the Debye–Waller factor resulting from thermal motion, and the pairwise static disorder of the absorbing and scattering atoms, the nonstructural parameter E0 (the energy at which k = 0) was also allowed to vary but was restricted to a common value for every component in a given fit, then the S0 value was set at 0.88 for the entire course of the fit, and coordination numbers were systematically varied in the course of the fit but were fixed within a given fit by FEFFIT program.[87] The data fitting quality was evaluated with the goodness-of-fit factor, defined aswhere χ ~ = k3χ and n is the number of evaluations of f, with f = χ ~data – χ ~model minimized in the nonlinear least-squares fitting algorithm.

Geometry Optimization and Electronic Structure Calculations

The calculations of geometry optimization for iron pentacarbonyl were carried out by spin-restricted DFT-B3LYP with the combination of a triple-ζ basis set 6-311G(d,p) for the iron atom and a double-ζ basis set 6–31G(d,p) for other atoms. The frequency calculations were performed to confirm that the molecules locate at minimum or transition state, and 0 and 1 of the imaginary frequency are obtained for D3 and C4 structures, respectively. These results indicate that the D3 structure is minimum and the C4 structure is the transition state. Gaussian 09 (ver. A.02) software[88] is used to complete the above calculations.

In general, the local coordinates were set so that the Fe atom is at the origin and the z axis is parallel to the C3/C4 rotational axis (see Scheme ). The x axis of the D3 structure is aligned with one of equatorial CO (COeq; axial CO is denoted COax) and that of the C4 structure is set as bisecting the ∠C–Fe–C. The electronic structure and MO-based TDDFT calculations of these structures were performed by the ORCA4.0.1 package.[89] The B3LYP of origin (20%) and 30% exact exchange were used together with the same basis set as used in geometry optimization. The relativistic effect is considered by zeroth-order regular approximation (ZORA). For the TDDFT calculations, both dipole and quadrupole transitions are included and the calculations involved 150 transitions from Fe(1s). The Löwdin population analysis was used to obtain the contributions of atomic orbitals in each MO. For comparing the experimental data to theoretical calculations, the calculated transition peaks are shifted by +11.6 eV, where such constant shift of energy has also been reported by DeBeer George and others, which demonstrated that no extra error was included.[69] When the 1s electron is excited, the energy of d orbitals decreases due to the formation of a core hole.[81] This may be one of reasons to cause such energy shift in TDDFT calculations.

XANES Simulations

Full multiple scattering (FMS) and FDM were used to simulate Fe K-edge XANES spectra by solving the Schrödinger equation. FMS within the muffin-tin (MT) approximation—the potential is spherical shape around the atoms and is constant in the remaining space—is performed by the FEFF8.4 program.[90] FDM within full potential, which considers no approximation on the form of the potential, is carried out by the FDMNES (ver. 2nd of August 2018) program.[91] In FDM calculations, both Hedin–Lundqvist (HL) and Xalpha (Xα; parameter is 1/3) exchange–correlation potentials were used in the self-consistent calculations and the HL potential is in better agreement with experimental data in both pre-edge and near-edge structures. Moreover, the electronic configurations of Fe, C, and O used in FDM calculation are [Ar]3d54s24p1, 1s22s22p2, and 1s22s22p4, respectively. To simulate the XANES features, the calculation is performed including all atoms within 3.0 Å away from the central Fe atom and both dipolar and quadrupolar transitions are included in the calculation. The energy steps used in the calculations are 0.1, 0.01, 0.2, 1.0, and 2.0 eV for energy ranges [−10.0, −5.0], [−5.0, 6.0], [6.0, 15.0], [15.0, 40.0], and [40.0, 60.0], respectively. The calculation results are convoluted by an arctangent function to obtain the final spectrum. The five convolution parameters of the spectrum in the HL potential, which are the core-level width, the Fermi energy, the center and the width of arctangent function, and the width of the final state, were set as 0.5, −4, 20, 45, and 25 eV, respectively; the setting combination of 1.25, 5, 30, 60, and 15 eV was used for Xα potential. The overall simulated spectra are shifted to align their first-derivative maximum with that of experimental spectra.