Bonding in Binuclear Carbonyl Complexes M2(CO)9 (M = Fe, Ru, Os

Jun 14, 2018 - Structures and stabilities of M2(CO)9 complexes (M = Fe, Ru, Os) were ... This holds for the triply bridged D3h structures as well as f...
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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Bonding in Binuclear Carbonyl Complexes M2(CO)9 (M = Fe, Ru, Os) Sudip Pan,† Lili Zhao,*,† H. V. Rasika Dias,*,‡ and Gernot Frenking*,†,§ †

Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China ‡ Department of Chemistry and Biochemistry, The University of Texas at Arlington, Arlington, Texas 76019, United States § Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, Marburg 35032, Germany

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S Supporting Information *

ABSTRACT: Quantum-chemical density functional theory calculations using the BP86 functional in conjunction with a triple-ζ basis set and dispersion correction by Grimme with Becke-Johnson damping D3(BJ) were performed for the title molecules. The nature of the bonding was examined with the quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) methods and with the energy decomposition analysis in conjunction with the natural orbital for chemical valence (EDA-NOCV) analysis. The energetically lowestlying form of Fe2(CO)9 is the triply bridged D3h structure, whereas the most stable structures of Ru2(CO)9 and Os2(CO)9 are singly bridged C2 species. The calculated reaction energies for the formation of the cyclic trinuclear carbonyls M3(CO)12 from the dinuclear carbonyls M2(CO)9 are in agreement with experiment, as the iron complex Fe2(CO)9 is thermodynamically stable in these reactions, but the heavier homologues Ru2(CO)9 and Os2(CO)9 are not. The metal−CO bond to the bridging CO ligands is stronger than the bonds to the terminal CO ligands. This holds for the triply bridged D3h structures as well as for the singly bridged C2 or C2v species. The analysis of the orbital interactions with the help of the EDA-NOCV method suggests that the overall M→CO π backdonation is always stronger than the M←CO σ donation. The bridging carbonyls are more strongly bonded than the terminal CO ligands, and they are engaged in stronger σ donation and π backdonation, but the formation of bridging carbonyls requires reorganization energy, which may or may not be compensated by the stronger metal−ligand interactions. The lower-lying D3h form of Fe2(CO)9 and C2 structures of Ru2(CO)9 and Os2(CO)9 are due to a delicate balance of several forces.

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INTRODUCTION Homoleptic transition-metal carbonyl complexes play a central role in organometallic chemistry and have been widely used as reagents for different transformations.1 Mononuclear carbonyl complexes may be regarded as parent systems in transition-metal chemistry serving as model compounds for the Dewar−Chatt− Duncanson (DCD) bonding model2 and the 18-electron rule.3 In contrast, binuclear carbonyls pose a challenge for classical concepts. The most prominent example is Fe2(CO)9, which is the first homoleptic polynuclear metal carbonyl ever reported.4 The X-ray structure analysis showed that the molecule features two Fe(CO)3 units connected by three bridging CO ligands resulting in a D3h symmetric structure.5 The bonding in Fe2(CO)9 has been a matter of debate for a long time,6 because it appeared to violate the 18-electron rule. The short distance of 2.523 Å between the two Fe centers, which is only slightly longer than the standard value for a Fe−Fe covalent bond (2.32 Å),7 and straightforward electron counting according to the 18electron rule, suggest the formation of a genuine Fe−Fe single bond. However, molecular orbital (MO) analysis and the calculated negative value of the Fe−Fe overlap population suggest that there is no Fe−Fe bond.6b,d−g This is supported by a quantum theory of atoms-in-molecules (QTAIM) analysis, © XXXX American Chemical Society

which shows the absence of an Fe−Fe bond path, and by the analysis of the domain-averaged Fermi holes in Fe2(CO)9.8 The present understanding of the bonding situation in Fe2(CO)9 was recently reviewed by Ding and Hall.9 The 18-electron rule is fulfilled either by assuming an Fe−Fe bond or by formally considering different bonding interactions of the three bridging CO ligands, where one of them engages in a three-center twoelectron bond, while the other two are ketonic groups that are bonded via Fe−C electron-sharing bonds (Figure 1). Figure 1b shows one of three equivalent resonance structures, where the three bridging CO ligands in turn take the role of the threecenter two-electron donor. This model has been discussed in detail by Green et al. in 2012.10 If the three bridging carbonyl ligands donate altogether eight electrons to the two metal atoms, the 18-electron rule is fulfilled. It means that the bridging CO ligands donate on average more electrons to iron than the terminal CO groups. Ding and Hall also present an MO correlation diagram, where the relevant orbitals of Fe2(CO)9 are constructed from scratch, using the orbitals of Fe and CO as building blocks, which eventually lead to the full MO diagram of Received: March 29, 2018

A

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Unlike Fe2(CO)9, its heavier congeners Ru2(CO)9 and Os2(CO)9 are thermally unstable under ambient condition, where they quickly get converted to the more stable trinuclear M3(CO)12 complexes. The adducts Ru2(CO)9 and Os2(CO)9 have only been observed at low temperatures or as short-lived intermediates in the gas phase, where they were identified and characterized via IR spectroscopy.11 The spectroscopic data for the ruthenium and osmium homologues of Fe2(CO)9 indicate significantly different structures compared with the iron species. A C2v symmetric singly CO-bridged structure was deduced from the IR data. The number of theoretical studies on Ru2(CO)9 and Os2(CO)9 reported so far is very limited. The first study was made by Hunstock et al.,6g who calculated the complete series, M2(CO)9 (M = Fe, Ru, Os), where they showed that the C2v isomer is energetically lower-lying than the D3h one for M = Ru and Os. Like for Fe2(CO)9, they obtained negative values for the metal−metal overlap population in Ru2(CO)9 and Os2(CO)9, which suggest the absence of a bond between the metals. More

Figure 1. Schematic view of the bonding situation in Fe2(CO)9 complexes with Lewis structures fulfilling the 18-electron rule. (a) Assuming an Fe−Fe bond; (b) using one bridging CO as three-center two-electron donor and two bridging carbonyls as ketonic groups with Fe−C electron-sharing bonds.

the complex.9 The fairly elaborate analysis shows that the descriptive qualitative MO explanation for the bonding in Fe2(CO)9 is quite complicated.

Figure 2. Calculated geometries of M2(CO)9 (M = Fe, Ru, Os) at BP86-D3(BJ)/def2-TZVPP using different symmetry constraints and relative energies (in kcal/mol). Interatomic distances are given (in Å). The data in parentheses are the experimental values for Fe2(CO)9 taken from ref 5. The values in square brackets give the number of imaginary frequencies i. B

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 1. Calculateda (BP86-D3(BJ)/def2-TZVPP) and Experimentalb C−O Stretching Frequencies of M2(CO)9 Complexes ν(CO) Fe2(CO)9 bridging CO terminal CO

Ru2(CO)9

Os2(CO)9

calc (D3h)

expc

calc (C2)

expd

calc (C2)

expe

1873 (e′, 687), 1898 (a1′, 0) 2019 (e″, 0), 2024 (e′, 1332), 2050 (a2″, 1707), 2092 (a1′, 0)

1814, 1817 (e′), 1891 (a1′) 1990 (e″), 2016, 2020 (e′), 2088 (a2″), 2112 (a1′)

1839 (a, 517) 1992 (a, 1), 1995 (b, 121), 2007 (a, 1377), 2009 (b, 525), 2018 (a, 217), 2019 (b, 1987), 2053 (b, 1118), 2101 (a, 5)

1813, m 2006, vw 2019, s 2029, w 2040, vs 2078, m

1808 (a, 533) 1989 (b, 139), 1991 (a, 14), 2001 (a, 1455), 2005 (b, 640), 2017 (a, 190), 2021 (b, 2067), 2054 (b, 1051), 2103 (a, 4)

1778, m 2000, w 2013, s 2024, m 2038, vs 2080, s

a

Calculated IR intensities are given in parentheses (in km/mol). bExperimental frequencies are given in inverse centimeters. cIR and Raman data from ref 32. dIR data from ref 11a. eIR data from ref 11b. spin, and it is computed by employing Kohn−Sham determinant on the superimposed fragments to obey the Pauli principle by antisymmetrization and renormalization. The ΔEorb originates from the mixing of orbitals, charge transfer, and polarization between two fragments. Lastly, the ΔEdisp represents the dispersion interaction between the two fragments. The EDA-NOCV16 calculation combines charge and energy decomposition schemes to divide the deformation density Δρ(r) associated with the bond formation into different components (σ, π, δ) of a chemical bond. From the mathematical point of view, each NOCV,15 ψi is defined as an eigenvector of the deformation density matrix in the basis of fragment orbitals.

recently, Schaefer and co-workers found that the C2 isomer of Os2(CO)9 is slightly lower in energy than the C2v structure.12 Bin et al. lately reported that the dissociation of the C2v symmetric species Ru2(CO)9 into Ru(CO)4 + Ru(CO)5 requires less energy than the dissociation of one CO.13 In this work we present a comprehensive theoretical study of the structures, stabilities, vibrational spectra, and bonding analysis of the binuclear carbonyl complexes M2(CO)9 (M = Fe, Ru, Os) using density functional theory (DFT). The nature of the bonding is examined with an energy decomposition analysis (EDA)14 in conjunction with the natural orbital for chemical valence (NOCV)15 scheme. The EDA-NOCV method16 provides quantitative information about the bonding interactions, which gives detailed insights into the strength and nature of the interactions. We particularly focus on the different metal−CO interactions of the bridging and terminal carbonyl ligands. The EDA-NOCV method was proven to be a powerful tool for analyzing different types of chemical bonds.17

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ΔP ψi = vi ψi In the EDA-NOCV, ΔEorb is given by the following equation N /2

ΔEorb =

∑ ΔEkorb = ∑ νk[−F −TSk +FkTS] k

k=1

(3)

TS are diagonal Kohn−Sham matrix elements where −FTS −k and Fk corresponding to NOCVs with the eigenvalues −νk and νk, respectively. The ΔEorb k terms are assigned to a particular type of bond by visual inspection of the shape of the deformation density Δρk. The EDANOCV scheme thus provides both qualitative (Δρorb) and quantitative (ΔEorb) information about the strength of orbital interactions in chemical bonds. More details about EDA-NOCV can be found in recent reviews.31

THEORETICAL METHODS

The geometries of the studied systems were fully optimized at the BP86-D3(BJ),18 PBE-D3(BJ),19 and M06-L-D320 levels in conjunction with def2-TZVPP21 basis sets using the Gaussian 09 program.22 Scalarrelativistic effective core potentials were used for the core electrons of Ru and Os.23 The nature of the stationary points, the zero-point energy (ZPE) corrections, and the thermochemical parameters were evaluated by performing the harmonic vibrational frequency calculations. The partial charges on each atom of the complexes and the Wiberg bond order (P)24 were computed via natural bond orbital (NBO) analysis using the NBO 6.0 program.25 QTAIM26 calculations were performed with the AIMALL program.27 The EDA-NOCV analysis was performed using the ADF (2017.101) program package28 at the BP86-D3(BJ)/ TZ2P29//BP86-D3(BJ)/def2-TZVPP level, where scalar relativistic effects were considered for the metals using the zeroth-order regular approximation (ZORA).30 The frozen core approximation was not employed in these computations. In the EDA14 method, the interaction energy (ΔΕint) between two fragments is decomposed into four energy terms, specifically, the electrostatic interaction energy (ΔEelstat), the Pauli repulsion (ΔEPauli), the orbital interaction energy (ΔEorb), and the dispersion interaction energy (ΔEdisp). Therefore, the interaction energy (ΔΕint) between two fragments can be defined as ΔEint = ΔEelstat + ΔE Pauli + ΔEorb + ΔEdisp

(2)

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GEOMETRIES AND ENERGIES Figure 2 shows the calculated BP86-D3(BJ) geometries of the dinuclear complexes M2(CO)9 (M = Fe, Ru, Os), using different symmetry constraints, whereas those obtained at the PBED3(BJ) and M06-L-D3 levels are displayed in Figure S1 in Supporting Information. As all the considered levels give the same trend in their relative stability, henceforth we will only discuss BP86-D3(BJ) results. The triply bridged energy minimum structure of Fe2(CO)9 has D3h symmetry, which conforms with the X-ray structure analysis.5 The calculated bond lengths are in good agreement with the experimental data. In contrast to the Fe2(CO)9 analogue, the energetically lowestlying energy minima of the heavier homologues Ru2(CO)9 and Os2(CO)9 are the singly carbonyl-bridged structures with C2 symmetry. Calculations of the latter complexes with enforced D3h symmetry give for Ru2(CO)9 a slightly (1.1 kcal/mol) higher-lying energy minimum form, whereas the Os2(CO)9 species exhibits two imaginary frequencies and is 8.5 kcal/mol less stable than the C2 form. The singly carbonyl-bridged structures with enforced C2v symmetry of all three systems

(1)

ΔEelstat is computed classically by taking the two fragments at their optimized positions but considering the charge distribution is unperturbed on each fragment by other one. The next one is ΔEPauli, which appears as the repulsive energy between electrons of the same C

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry possess one imaginary mode. They are only slightly higher in energy than the respective equilibrium structures, and the bond lengths are nearly the same. Experimental geometries for Ru2(CO)9 and Os2(CO)9 are not available. From the IR spectrum of Os2(CO)9, it was concluded that the structure is considerably different from Fe2(CO)9, whereas the structure of Ru2(CO)9 could not be deduced.11b Our calculation of Os2(CO)9 showing the C2 form as energetically lowest-lying form is in agreement with the theoretical result of Schaefer et al.12 Previous theoretical studies of Ru2(CO)9 considered only the C2v isomer.13 We think that the C2 structure of the ruthenium species, which is reported here for the first time, is the energetically lowest-lying isomer of Ru2(CO)9. Table 1 shows the calculated and experimental vibrational frequencies of the C−O stretching mode of the M2(CO)9 complexes. The theoretical data for Fe2(CO)9 agree quite well with the observed IR and Raman wavenumbers.32 Note that the calculated CO stretching frequencies of transition-metal carbonyls at BP86 were found to agree quite well with the experimental values.33 The calculations suggest that the vibrational spectra of Ru2(CO)9 and Os2(CO)9 possess one IR active mode of the bridging CO and six vibrational modes with moderate to high IR intensity of the terminal carbonyls. Experimentally, the bridging CO and four modes of terminal CO were identified.11 It seems possible that the missing frequencies are concealed by signals of other metal carbonyls, since the vibrational spectra of the volatile complexes M2(CO)9 (M = Ru, Os) could only be recorded in the presence of other carbonyls.11 Considering the experimental conditions, the agreement between the calculated and experimental vibrational spectra is quite good. They leave no doubt that the dinuclear complexes Ru2(CO)9 and Os2(CO)9 exhibit a singly carbonyl-bridged equilibrium geometry. The volatility of Ru2 (CO)9 and Os2 (CO) 9 and the comparatively high stability of Fe2(CO)9 pose the question about the thermodynamic stability of the compounds. We calculated several reaction energies, which shed light on the reactivity of the complexes. Table 2 shows the numerical results of the calculations. Reaction 1 is the dissociation of dinuclear M2(CO)9 into the mononuclear complexes M(CO)5 + M(CO)4 (see Figure S2 for the geometries of M(CO)5 and M(CO)4). The calculations suggest that the reaction energies are not very different for the three metals. The M2(CO)9 compounds are stable at room temperature, the free dissociation energy ΔG298 is between 16.8 kcal/mol (M = Ru) and 18.5 kcal/mol (M = Os). The calculated values for loss of one CO ligand from M2(CO)9 exhibits also no significant differences between iron and the heavier homologues (Reaction 2, see Figure S2 for the geometries of M2(CO)8). Reaction 3 features the substitution of one CO ligand of M2(CO)9 by M(CO)4 and the concomitant formation of the cyclic trinuclear carbonyl complexes M3(CO)12 (see Figure S3 for the geometries of M3(CO)12). The reaction is exergonic for the three metals in the order Fe < Ru < Os. A drastic difference between Fe and the heavier metals is calculated for the energies of reactions 4 and 5. The formation of the trinuclear complexes M3(CO)12 by adding M(CO)5 to M2(CO)9 and loss of two CO ligands is energetically unfavorable for M = Fe, but it is favorable for M = Ru, Os. The same holds true for the disproportionation of binuclear M2(CO)9 to trinuclear M3(CO)12 with the loss of CO ligands (reaction 5). We think that the latter reaction is the thermodynamic driving force for the stability of Fe2(CO)9 and the instability of Ru2(CO)9 and Os2(CO)9 in a condensed

Table 2. Calculated Reaction Energies Including Zero-Point Energy Contributions (D0) and Free-Energy Changes of the Reactions at 298 K (ΔG298) of the Most Stable Isomer of M2(CO)9 Complexesa reaction M2(CO)9 → M(CO)5 +

M(CO)4b

No.

M

D0

ΔG298

1

Fe Ru Os Fe Ru Os Fe Ru Os Fe Ru Os Fe Ru Os

32.4 28.4 30.2 29.3 26.8 29.6 −27.0 −40.2 −46.4 20.3 −5.8 −9.4 25.7 −17.7 −25.5

17.6 16.8 18.5 16.4 16.5 19.4 −22.6 −33.5 −40.4 13.0 −9.7 −13.5 7.9 −26.4 −35.5

M2(CO)9 → M2(CO)8 + CO

2

M2(CO)9 + M(CO)4 → M3(CO)12 + CO

3

M2(CO)9 + M(CO)5 → M3(CO)12 + 2CO

4

3M2(CO)9 → 2M3(CO)12 + 3CO

5

a

At the BP86-D3(BJ)/def2-TZVPP level. The energies are in kilocalories per mole. bThe equilibrium structure is a triplet (3B2) for M = Fe and a singlet (1A1) M = for Ru, Os).

phase. The calculated energies for reaction 5 concur with the different stabilities of the M2(CO)9 species.

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BONDING ANALYSIS We first present and discuss the results of a conventional analysis of the electronic structure of the M2(CO)9 species complexes. Table 3 shows the calculated partial charges q and Wiberg bond order P of the molecules at their energetically lowest-lying equilibrium structures, that is, triply bridged Fe2(CO)9 (D3h) and singly bridged Ru2(CO)9 and Os2(CO)9 (C2). The results for the singly bridged C2v structure of Fe2(CO)9 are also given. According to the NBO calculations, the metal atoms carry negative partial charges in the order Fe > Ru > Os. The bridging carbonyl ligands in triply bridged Fe2(CO)9 (D3h) possess a small positive charge, whereas the CObridge groups in the singly bridged structures of all systems M2(CO)9 are negatively charged. The terminal CO ligands of all three metal carbonyls carry small positive charges. The bond order P(CO) of the bridging CO groups is smaller compared with P(CO)terminal, which agrees with the finding that the bond lengths of the bridging CO ligands are longer than the terminal CO groups (Figure 2). All bond orders for the carbonyl ligands are smaller than for free CO, which has P(CO) = 2.30. The very small bond order P(M−M) does not agree with a genuine metal−metal bond. The bond orders P(M−C) of the bridging CO ligands are clearly smaller than the values for the terminal CO species, which also concurs with the calculated bond lengths. Note that there are two M−C bonds for each bridging CO but only one for each terminal CO. Table 3 gives also the partial charges q(M) and q(CO) that come from the QTAIM calculations, which are substantially different from the NBO charges. According to the NBO calculations, the metal atoms receive electronic charge from the ligands, and they are thus electron acceptors. The QTAIM calculations suggest that the metals are donor species, where all CO ligands carry negative charges. Accordingly, the M←CO σ donation is suggested by the NBO analysis to be larger than the M→CO π backdonation, except for the bridging CO ligands in D

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 3. NBO Partial Charges q(e) and Wiberg Bond Orders P of M2(CO)9 at the BP86/def2-TZVPP Levela complex q(M) q(CO)bridge q(CO)terminal P(CO)bridge P(CO)terminal P(M−M) P(M−Cbridge) P(M−Cterminal)

Fe2(CO)9 (D3h)

Fe2(CO)9 (C2v)

Ru2(CO)9 (C2)

Os2(CO)9 (C2)

−0.71 (0.80) 0.06 (−0.27) 0.21 (−0.13) 2.02 2.18 0.11 0.40 0.60

−0.58 (0.72) −0.08 (−0.31) 0.11−0.17 (−0.13 to −0.16) 2.01 2.14−2.16 0.10 0.38 0.60−0.70

−0.42 (0.67) −0.14 (−0.32) 0.10−0.15 (−0.11 to −0.15) 1.98 2.13−2.17 0.10 0.42 0.65−0.74

−0.19 (0.86) −0.26 (−0.39) 0.05−0.10 (−0.15 to −0.18) 1.94 2.12−2.14 0.12 0.46 0.74−0.83

a

The values for the partial charge q in parentheses come from QTAIM calculations.

Table 4 gives the numerical results for the D3h structures, where one bridging CO and the remaining M2(CO)8 fragment in the

the singly bridged species. On the other hand, the QTAIM charges indicate that M→CO π backdonation is always stronger than M←CO σ donation, particularly for the bridging carbonyl ligands. We will see below which charge analysis agrees better with the energy decomposition analysis. Figure 3 shows the plots of the Laplacian distribution ∇2ρ(r) of the M2(CO)9 complexes in the plane that contains a bridging

Table 4. EDA-NOCV Results for Triply Bridged (D3h) M2(CO)9 Complexes at the BP86-D3(BJ)/TZ2P//BP86D3(BJ)/def2-TZVPP Level Taking M2(CO)8 in the Singlet Excited State and One Bridging CO in Singlet Ground State as Interacting Fragmentsa complex fragments ΔEint ΔEPauli ΔEdispb ΔEelstatb ΔEorbb ΔEorb(1)c [M]→(CO)←[M] π|| backdonation ΔEorb(2)c [M]←(CO)→[M] σ donation ΔEorb(3)c [M]→(CO)←[M] π⊥ backdonation ΔEorb(4)c CO σ interaction ΔEorb(rest)c

Fe2(CO)9 (D3h)

Ru2(CO)9 (D3h)

Os2(CO)9 (D3h)

Fe2(CO)8 (S) + CO (S) −86.0 152.8 −7.3 (3.1%) −105.1 (44.0%) −126.4 (52.9%) −53.8 (42.6%)

Ru2(CO)8 (S) + CO (S) −85.1 152.3 −7.5 (3.1%) −104.4 (44.0%) −125.5 (52.9%) −57.2 (45.6%)

Os2(CO)8 (S) + CO (S) −94.2 175.1 −7.5 (2.8%) −119.1 (44.2%) −142.7 (53.0%) −64.3 (45.1%)

−46.6 (36.9%)

−43.9 (35.0%)

−51.2 (35.9%)

−15.4 (12.2%)

−14.1 (11.2%)

−15.2 (10.7%)

−6.7 (5.3%) −3.9 (3.1%)

−7.0 (5.6%) −3.3 (2.6%)

−8.4 (5.9%) −3.6 (2.5%)

a

Energy values are in kilocalories per mole. bThe value in parentheses gives the percentage contribution to the total attractive interactions (ΔEelstat + ΔΕorb + ΔEdisp). cThe value in parentheses gives the percentage contribution to the total orbital interactions ΔΕorb.

Figure 3. Plot of the Laplacian distribution ∇2ρ(r) of the M2(CO)9 complexes at the BP86-D3(BJ)/def2-TZVPP/WTBS level. Red dashed lines indicate areas of charge concentration (∇2ρ(r) < 0), while solid blue lines show areas of charge depletion (∇2ρ(r) > 0). The solid lines connecting the atomic nuclei are the bond paths. Green dots are bond critical points; the red central dot in Fe2(CO)9 is a cage critical point.

electronic singlet reference states35 are used as interacting species. The data in Table 4 show that the intrinsic interaction energy ΔEint between the bridging CO and the M2(CO)8 fragment has the order Fe ≈ Ru < Os. The same order is computed for the orbital interactions ΔEorb, which may, therefore, be used to analyze the differences between the three metal systems. The total metal−CO bonding has a more covalent than electrostatic character. The contribution of dispersion interactions is small, but it is not negligible. The most important information of the EDA-NOCV calculations comes from the breakdown of the orbital term ΔEorb into pairwise orbital interactions. There are four contributions ΔEorb(1)−ΔEorb(4) that account for ∼97% of ΔEorb, which can be identified with the help of the associated deformation densities Δρ(1)−Δρ(4) and the connected occupied and vacant fragment orbitals shown in Figure 4. The

CO. There are two M−C bond paths to the bridging CO groups and one M−C bond path to each terminal CO, but there is no M−M bond path in the three complexes. For Fe2(CO)9, this has been reported before.8d Although the nonappearance of a bond path may not be taken as proof for the absence of a chemical bond,34 the shape of the Laplacian distribution between the metal atoms and the lack of a bond critical point suggest that there is no bonding electron pair between the metal atoms. More detailed information about the nature of the metal−CO interactions is provided by the EDA-NOCV method. We compare the triply bridged D3h structures and the singly bridged C2v or C2 species of the M2(CO)9 complexes separately to evaluate the differences between the metals on equal footing. E

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 4. Plot of the deformation densities Δρ and the associated most important occupied and vacant orbitals of the pairwise orbital interaction in the triply bridged D3h structures between one bridging CO and (a) Fe2(CO)8, (b) Ru2(CO)8, (c) Os2(CO)8. For numerical details see Table 4. F

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry contributions ΔEorb(1)−ΔEorb(3) are easily assigned to the classical DCD terms. The strongest orbital interaction of the bridging CO ligand ΔEorb(1) comes in all complexes from the [M]→(CO)←[M] π|| backdonation of the metals into the inplane π||* orbital of carbonyl ligand, where the plane is defined by the M2Cbridging atoms. The [M]←(CO)→[M] σ donation of the highest occupied molecular orbital (HOMO) of CO to the metal atoms, ΔEorb(2), is a bit weaker. The third term, ΔEorb(3), can be attributed to the out-of-plane [M]→(CO)←[M] π⊥ backdonation into the π⊥* orbital of CO. The π⊥ backdonation is much weaker than the π|| backdonation and the σ donation. The fourth term, ΔEorb(4), is not considered in the DCD model. Inspection of the associated orbitals (Figure 4) shows that it comes from a polarization of the σ charge of CO and concomitant charge alteration within the M2(CO)8 fragment. The net result is a charge accumulation in the M−C(O)−M bonding region, which signals some M−M bonding. It can be considered as nonclassical σ interaction, which is small but not negligible. The EDA-NOCV results for the bridging CO ligand in the D3h structures can be compared to the values for the terminal carbonyls, which are given in Table 5. The associated

The data in Table 5 suggest that the weaker bonding of the CO ligand in the ruthenium complex than the others comes from the Pauli repulsion. The attractive forces ΔEelstat and ΔEorb in Ru2(CO)9 are stronger than in Fe2(CO)9.37 The pairwise orbital interactions ΔEorb(1)−ΔEorb(4) in Tables 4 and 5 exhibit some differences between the relative contribution of the σ donation and π backdonation. The (CO)→[M] σ donation, ΔEorb(1), of the terminal CO is the strongest single contribution to ΔEorb providing ∼40% of the covalent bonding, which indicates a higher relative contribution than for the bridging CO. Examination of the two components of the π backdonation to the terminal and bridging CO reveals that their strength in the former ligand (ΔEorb(2) and ΔEorb(3) in Table 5) has a comparable size. In contrast, the in-plane and outof-plane components of the bridging CO (ΔEorb(1) and ΔEorb(3) in Table 4) significantly differ from each other. This can be explained with the arrangement of the terminal and bridging CO ligands in the complexes. The combined strength of the in-plane (π||) and out-of-plane (π⊥) components of the π backdonation for the terminal CO ligands is a bit smaller than for the bridging CO. Note that the absolute and relative contribution of the nonclassical σ interaction ΔEorb(4) to the bonding of the terminal CO is larger than for the bridging CO. The most important result is that the bridging CO ligands in the D3h structures of M2(CO)9 are significantly stronger bonded than the terminal carbonyls, but the strongest carbonyl bonds of both types are found in the osmium complex and not in the iron adduct. The finding that the bridging CO ligands are more strongly bonded than the terminal carbonyls conforms with the request that in M2(CO)9 the bridging ligands donate more electrons to the metal atoms than the terminal CO. The stronger M←CO σ donation of the bridging carbonyls than the terminal CO groups is revealed by comparing the [M]←(CO)→[M] values ΔEorb(2) in Table 4 with the (CO)→[M] values ΔEorb(1) in Table 5. The stronger M←CO σ donation of the bridging carbonyls is masked by the concomitant increase of the M→CO π backdonation. In the absence of M−M bonding, the three bridging CO formally donate eight electrons, while the three terminal CO donate six electrons to the M(0) atoms.9,10 But the formation of bridging CO ligands requests a structural rearrangement of the metal fragments, which is compensated by the stronger bonding in the iron complex Fe2(CO)9 but not in the ruthenium and osmium species Ru2(CO)9 and Os2(CO)9. The preference of the triply bridged iron complex Fe2(CO)9 and the singly bridged species Ru2(CO)9 and Os2(CO)9 is the result of a delicate balance between stronger bonding of bridging CO and distortion of the remaining metal−carbonyl fragments. We also analyzed the nature of the metal−CO bonding to the bridging and terminal carbonyl ligands in the singly bridged structures. For Ru2(CO)9 and Os2(CO)9, we took the energetically lowest-lying C2 species, and for Fe2(CO)9, we took the C2v structure, because it is the only optimized form that can be compared with the heavier homologues. Figure 2 shows that the energy differences between the C2v and C2 structures of Ru2(CO)9 and Os2(CO)9 are very small, and it may safely be assumed that the differences between their bonding situations are negligible. This is supported by EDA-NOCV calculations of the C2v structures of Ru2(CO)9 and Os2(CO)9, which give essentially the same results as for the C2 form (Tables S1 and S2, Supporting Information). Table 6 shows the numerical results for the bridging CO in the singly bridged structures. The interaction energies ΔEint are smaller compared with the triply bridged structure (Table 4).

Table 5. EDA-NOCV Results for Triply Bridged (D3h) M2(CO)9 Complexes at the BP86-D3(BJ)/TZ2P//BP86D3(BJ)/def2-TZVPP Level Taking M2(CO)8 and One Terminal CO in Singlet Ground Electronic States as Interacting Fragmentsa complex fragments ΔEint ΔEPauli ΔEdispb ΔEelstatb ΔEorbb ΔEorb(1)c OC→[M] σ donation ΔEorb(2)c OC←[M] π|| backdonation ΔEorb(3)c OC←[M] π⊥ backdonation ΔEorb(4)c CO σ interaction ΔEorb(rest)c

Fe2(CO)9 (D3h)

Ru2(CO)9 (D3h)

Os2(CO)9 (D3h)

Fe2(CO)8 (S) + CO (S) −48.7 158.1 −5.4 (2.6%) −111.6 (53.9%) −89.9 (43.5%)

Ru2(CO)8 (S) + CO (S) −40.7 181.7 −5.3 (2.4%) −124.7 (56.1%) −92.3 (41.5%)

−36.2 (40.3%)

−36.2 (39.2%)

Os2(CO)8 (S) + CO (S) −50.3 226.5 −5.4 (2.0%) −155.9 (56.3%) −115.5 (41.7%) −46.8 (40.5%)

−22.1 (24.6%)

−22.0 (23.8%)

−25.8 (22.3%)

−19.9 (22.1%)

−19.7 (21.3%)

−23.2 (20.1%)

−9.4 (10.5%)

−12.8 (13.9%)

−17.6 (15.2%)

−2.3 (2.6%)

−1.6 (1.7%)

−2.1 (1.8%)

a

Energy values are in kilocalories per mole. bThe value in parentheses gives the percentage contribution to the total attractive interactions (ΔEelstat + ΔΕorb + ΔEdisp). cThe value in parentheses gives the percentage contribution to the total orbital interactions ΔΕorb.

deformation densities of the orbital interactions are shown in Figure 5. The numerical results in Table 5 suggest that the terminal CO ligands are much weaker bonded than the bridging carbonyls. The interaction energies ΔEint of the terminal carbonyls are between −40.7 kcal/mol for Ru2(CO)9 and −50.3 kcal/mol for Os2(CO)9, much less than ΔEint values of the bridging CO (Table 4). The strength of the ΔEint values has the order Ru < Fe < Os. Note that the ΔEorb values exhibit a different trend for the orbital interactions, that is, Fe < Ru < Os. This is an example for the finding that the trend of a bond strength is not always determined by the orbital interactions.36 G

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 5. Plot of the deformation densities Δρ and the associated most important occupied and vacant orbitals of the pairwise orbital interaction in the triply bridged D3h structures between one terminal CO and (a) Fe2(CO)8, (b) Ru2(CO)8, (c) Os2(CO)8. For numerical details see Table 5. H

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 6. EDA-NOCV Results for Singly Bridged (C2v) Fe2(CO)9 Complex and (C2) Ru2(CO)9 and Os2(CO)9 Complexes at the BP86-D3(BJ)/TZ2P//BP86-D3(BJ)/ def2-TZVPP Level Taking M2(CO)8 in Singlet Excited State and One Bridging CO in Singlet Ground State as Interacting Fragmentsa complex fragments ΔEint ΔEPauli ΔEdispb ΔEelstatb ΔEorbb ΔEorb(1)c [M]→(CO)←[M] π|| backdonation ΔEorb(2)c [M]←(CO)→[M] σ donation ΔEorb(3)c [M]→(CO)←[M] π⊥ backdonation ΔEorb(4)c CO σ interaction ΔEorb(rest)c a

Fe2(CO)9 (C2v)

Ru2(CO)9 (C2)

Os2(CO)9 (C2)

Fe2(CO)8 (S) + CO (S) −81.5 144.9 −7.5 (3.3%) −95.3 (42.1%) −123.6 (54.6%) −53.7 (43.4%)

Ru2(CO)8 (S) + CO (S) −74.4 198.6 −2.3 (0.8%) −126.5 (46.4%) −144.1 (52.8%) −63.7 (44.2%)

Os2(CO)8 (S) + CO (S) −87.9 223.8 −3.4 (1.1%) −141.7 (45.4%) −166.7 (53.5%) −74.4 (44.6%)

−44.9 (36.3%)

−51.6 (35.8%)

−60.9 (36.5%)

−13.7 (11.1%)

−14.5 (10.1%)

−15.3 (9.2%)

−7.6 (6.1%) −3.7 (3.0%)

−9.3 (6.5%) −5.0 (3.5%)

−10.9 (6.5%) −5.2 (3.1%)

Table 7. EDA-NOCV Results for Singly Bridged (C2v) Fe2(CO)9 Complex and (C2) Ru2(CO)9 and Os2(CO)9 Complexes at the BP86-D3(BJ)/TZ2P//BP86-D3(BJ)/ def2-TZVPP Level Taking M2(CO)8 and One Terminal CO in Singlet Ground Electronic States as Interacting Fragmentsa complex fragments ΔEint ΔEPauli ΔEdispb ΔEelstatb ΔEorbb ΔEorb(1)c OC→[M] σ donation ΔEorb(2)c OC←[M] π|| backdonation ΔEorb(3)c OC←[M] π⊥ backdonation ΔEorb(4)c CO σ interaction ΔEorb(rest)c a

Fe2(CO)9 (C2v)

Ru2(CO)9 (C2)

Os2(CO)9 (C2)

Fe2(CO)8 (S) + CO (S) −62.2 165.7 −4.9 (2.2%) −120.0 (52.7%) −103.0 (45.2%) −40.9 (39.7%)

Ru2(CO)8 (S) + CO (S) −47.4 204.5 −2.3 (0.9%) −142.7 (56.7%) −106.8 (42.4%) −41.6 (39.0%)

Os2(CO)8 (S) + CO (S) −59.8 242.6 −2.8 (0.9%) −171.6 (56.7%) −128.0 (42.3%) −51.4 (40.2%)

−30.1 (29.2%)

−28.9 (27.1%)

−33.4 (26.1%)

−20.6 (20.0%)

−20.2 (18.9%)

−23.3 (18.2%)

−9.4 (9.1%)

−14.6 (13.7%)

−18.0 (14.1%)

−2.0 (1.9%)

−1.5 (1.4%)

−1.9 (1.5%)

b

Energy values are in kilocalories per mole. The value in parentheses gives the percentage contribution to the total attractive interactions (ΔEelstat + ΔΕorb + ΔEdisp). cThe value in parentheses gives the percentage contribution to the total orbital interactions ΔΕorb.

b

Energy values are in kilocalories per mole. The value in parentheses gives the percentage contribution to the total attractive interactions (ΔEelstat + ΔΕorb + ΔEdisp). cThe value in parentheses gives the percentage contribution to the total orbital interactions ΔΕorb.

occupation of the valence orbitals. For example, BH 3 spontaneously dimerizes to B2H6, because the vacant 2p orbital of boron is partially filled by bridging B−H bonds. But there are numerous multinuclear boranes BnHm, where the electron demand of boron is satisfied by different arrangements of bridging B−H and B−B bonds. Various types of structures are possible, whose stabilities can be estimated with rules,38 but the actual electronic structures are quite complicated, and the delocalized electrons pose a problem for conventional descriptions of covalent bonding. A related situation is given here, which is further complicated by the concomitant occurrence of σ donation and strong π backdonation. The bonding situation in Ru2(CO)9 and Os2(CO)9 may be sketched as in Figure 6b,c, which shows only the M←CO σ donation. The bridging CO ligand serves like the bridging B−H in B2H6 as electronic source for filling the valence shell of the metals. The triply bridged structure of Fe2(CO)9 (Figure 6a) has three CO ligands, which donate charge to the iron atoms but at the expense of the terminal CO ligands, which are weaker donors in the triply bridged structures than in the singly bridged isomers (Tables 5 and 7). The relative energies of the singly and triply bridged species depend on the factors such as π backdonation, electrostatic interactions, structural reorganization, and Pauli repulsion. The final outcome of the competing interactions is clearly beyond the interpretative power of the 18-electron rule.

The trend of the ΔEint values in the singly bridged complexes has the order Ru < Fe < Os. In contrast, the orbital interaction ΔEorb values exhibit the sequence Fe < Ru < Os. The breakdown of the orbital term into pairwise contributions of the bridging CO shows similar features for the singly and triply bridged systems (Tables 4 and 6). The shape of the deformation densities in the two sets of complexes is also very similar. The deformation densities Δρ(1)−Δρ(4) and the connected occupied and vacant fragment orbitals for the bridging CO in the singly bridged complexes are shown in Figure S4 of Supporting Information. Finally, we present the EDA-NOCV results for the terminal CO ligands in the singly bridged species. The numerical results are given in Table 7. Unlike the bridging CO ligands, the interaction energies ΔEint of the terminal CO are bigger than in the triply bridged structures (Table 5). They exhibit the trend Ru < Os < Fe (Table 7), which is different from the ΔEint values in Table 5. However, the bond strength of the terminal CO in the singly bridged structures remains smaller than those of the bridging ligands. The bridging CO ligands are always significantly stronger bonded than the terminal CO groups. The values for the orbital interactions ΔEorb in Table 7 possess a different trend than the overall interaction energies. The deformation densities Δρ(1)−Δρ(4) and the connected occupied and vacant fragment orbitals for the terminal CO in the singly bridged complexes are shown in Figure S5 of Supporting Information. The EDA-NOCV results demonstrate the difficulty of explaining the bonding situation in the binuclear systems M2(CO)9 in terms of the 18-electron rule, which relies on a rather crude bonding model and considers only integral numbers of electrons. The physical origin of the 8, 18, and 32 rules rests on the stabilization of atoms in a molecule due to the

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SUMMARY AND CONCLUSION The theoretical results of this work give detailed information about the stability, electronic structures, and nature of the bonding in the title compounds. The energetically lowest-lying form of Fe2(CO)9 is the triply bridged D3h structure, whereas the most stable structures of Ru2(CO)9 and Os2(CO)9 are singly bridged C2 species. The triply bridged D3h structures of I

DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 6. Schematic view of the metal−CO interactions in the global energy minima of M2(CO)9 complexes showing only the M ← CO σ donation.

Ru2(CO)9 and Os2(CO)9 are 1.1 and 8.5 kcal/mol higher in energy than the C2 form, respectively. The C2v species of all three metals are transition states that are slightly higher in energy than the lowest-lying structures. The calculated reaction energies for the formation of M3(CO)12 from M2(CO)9 via reactions 4 and 5 (Table 2) show that Fe2(CO)9 is thermodynamically stable in these reactions, but the heavier homologues, Ru 2(CO)9 and Os2(CO)9, are exergonically transformed to their trinuclear analogues. This is in agreement with the experimental observations. In both triply bridged (D3h) and singly bridged (C2v and C2) species, the metal−CO bond to the bridging CO is stronger than the bonds to the terminal CO ligands. The analysis of the orbital interactions with the help of the EDA-NOCV method reveals that the combined M→CO π backdonation is always stronger than the M←CO σ donation. Although the degree of M←CO σ donation of the terminal CO is higher than for the bridging CO, the M→CO π backdonation is the source of dominant orbital interaction. The stronger M→CO π backdonation agrees with the calculated charge distribution in the QTAIM method, which suggests negative partial charges for all CO ligands, the bridging CO possessing a larger negative charge. The NBO method gives positive charges for terminal CO in all complexes and in the bridging CO of the energetically lowestlying D3h form of Fe2(CO)9. This may be related to the preselection of the NBO algorithm, which treats only the (n)s and (n − 1)d functions but not the (n)p functions of the transition metals as genuine valence orbitals.39 The relative stabilities of triply and singly bridged structures of the three group 8 metals cannot be ascribed to a single factor. The overall metal−CO interactions may not always correlate with the orbital interactions. The lower-lying D3h form of Fe2(CO)9 and C2 structures of Ru2(CO)9 and Os2(CO)9 are due to a delicate balance of several forces. The bridging carbonyls are more strongly bonded than the terminal CO ligands, and they are engaged in stronger σ donation and π backdonation, but the formation of bridging carbonyls requires reorganization energy, which may or may not be compensated by for the stronger metal−ligand interactions.

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M2(CO)8. EDA-NOCV results for singly bridged (C2v) structures of Ru2(CO)9 and Os2(CO)9 and the Cartesian coordinates of the studied complexes (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (L.Z.) *E-mail: [email protected]. (H.V.R.D.) *E-mail: [email protected]. (G.F.) ORCID

Lili Zhao: 0000-0003-2580-6919 H. V. Rasika Dias: 0000-0002-2362-1331 Gernot Frenking: 0000-0003-1689-1197 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.P. thanks Nanjing Tech Univ. for the postdoctoral fellowship and the High Performance Computing Center of Nanjing Tech Univ. for supporting the computational resources. L.Z. and G.F. acknowledge the financial support from Nanjing Tech Univ. (Grant Nos. 39837123 and 39837132) and SICAM Fellowship from Jiangsu National Synergetic Innovation Center for Advanced Materials, Natural Science Foundation of Jiangsu Province for Youth (Grant No. BK20170964), and National Natural Science Foundation of China (Grant No. 21703099). H.V.R.D. thanks the financial support by the Robert A. Welch Foundation (Grant No. Y-1289).

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REFERENCES

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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.8b00851. Calculated geometries of M2(CO)9 (M = Fe, Ru, Os) at PBE-D3(BJ)/def2-TZVPP and M06-L-D3/def2-TZVPP levels, the geometries of M(CO)4, M(CO)5, M2(CO)8, and M3(CO)12 (M = Fe, Ru, Os) complexes, plot of the deformation densities and the associated pairwise orbital interactions in the singly bridged (C2v ) Fe2 (CO) 9 complex and (C2) Ru2(CO)9 and Os2(CO)9 complexes between one bridging CO or one terminal CO and J

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DOI: 10.1021/acs.inorgchem.8b00851 Inorg. Chem. XXXX, XXX, XXX−XXX