Analysis of the Relative Stabilities of Ortho, Meta, and Para MClY

Article pubs.acs.org/Organometallics

Analysis of the Relative Stabilities of Ortho, Meta, and Para MClY(XC4H4)(PH3)2 Heterometallabenzenes (M = Rh, Ir; X = N, P; Y = Cl and M = Ru, Os; X = N, P; Y = CO) Majid El-Hamdi,†,‡ Ouissam El Bakouri El Farri,† Pedro Salvador,† Ben Ali Abdelouahid,‡ Mohamed Soussi El Begrani,‡ Jordi Poater,*,† and Miquel Solà*,† †

Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, Universitat de Girona, Campus Montilivi, E-17071 Girona, Catalonia, Spain ‡ Département de Chimie, Faculté des Sciences, Université Abdelmalek Essaâdi, M’Hannech II B.P.2121, C.P. 93002 Tétouan, Morocco S Supporting Information *

ABSTRACT: Density functional theory calculations of the relative stabilities of the ortho, meta, and para MClY(XC4H4)(PH3)2 heterometallabenzenes (M = Rh, Ir; X = N, P; Y = Cl and M = Ru, Os; X = N, P; Y = CO) have been carried out. The ortho isomer is the most stable for X = P, irrespective of the metal M. For X = N and M = Ir, Rh the meta is the lowestlying isomer, whereas for M = Ru, Os the ortho and meta isomers are almost degenerate. The electronic structure and chemical bonding have been investigated with energy decomposition analyses of the interaction energy between various fragments, to discuss the origin of the differences observed. The values of the multicenter index of aromaticity and nucleus-independent chemical shifts indicate that the heterometallabenzenes studied should be classified as aromatic or slightly aromatic. conjugation is weaker than in benzene.12 As to reactivity, metallabenzenes undergo the typical aromatic electrophilic substitutions.17 However, they can also react in unusual ways for aromatic systems.18 A few years before the synthesis of the first metallabenzene, Hoffmann and Thorn analyzed the orbital interactions between a C5H5− ion and a suitable metal fragment, which resulted in the formation of a metallabenzene.19 Defining the z-axis as perpendicular to the ring plane and the x-axis in the direction of the metal−Cpara axis, they suggested that metallabenzenes have 6π-electrons, four of which come from the π-occupied orbitals of the C5H5− ion and two from the occupied dxz metal orbital. Different authors support this point of view.10,14,16 An alternative interpretation was proposed by Schleyer,6,20 who suggested that the occupied dyz metal orbital also significantly contributes to the π-orbital interactions in metallabenzenes, which means that they are actually 8π-electron systems. This proposal, also held by Jia et al.,21 violates the 4n+2 Hückel’s rule 22 for aromatic compounds. However, the orbital interaction between the dyz metal orbital and the 2π and 4π* orbitals of the C5H5− ion has δ symmetry, and thus it fulfills the criteria of Möbius aromaticity.20,23 Finally, there are several authors that consider metallabenzenes as 10π-electron systems.12,13,24 The different electron counting is due to the disputable participation of the metal d orbitals in π-bonding.12

1. INTRODUCTION The chemistry of transition-metal-containing aromatic metallacycles is currently attracting significant attention.1 Among these metallacycles, the so-called metallabenzenes that are formally obtained by substitution of a CH+ group in benzene by an isolobal metal group are of particular interest.2−6 The first example of a stable metallabenzene was reported by Roper in 19827 and was an osmabenzene synthesized by a cyclization reaction involving a thiocarbonyl ligand and two ethyne molecules. The X-ray structural analysis showed an essentially planar metallacycle with delocalized bonding within the ring. Following Roper’s communication, there was a hiatus in the field until the late 1980s, when Bleeke et al. succeeded in synthesizing a stable iridabenzene.8 Metallabenzenes exhibit properties usually associated with aromatic systems, such as deshielded proton resonances in the 1H NMR spectrum, bondlength equalization, and ring planarity.4−6,9 Their aromatic character has been substantiated by theoretical calculations of Bird aromaticity indices,10 aromatic stabilization energies,10−12 chemical hardnesses,10,11 diamagnetic susceptibility exaltations,10 NMR chemical shifts,10 nucleus-independent chemical shifts (NICS),13,14 magnetic susceptibility anisotropies,14 anisotropies of the induced current density (ACID),15 and ring currents.13,16 The comparison made by Fernández and Frenking of the π-bonding strength in metallabenzene compounds and the corresponding acylic reference molecules indicates that metallabenzenes should be considered as aromatic compounds, whose extra stabilization due to aromatic © 2013 American Chemical Society

Received: July 1, 2013 Published: August 28, 2013 4892

dx.doi.org/10.1021/om400629w | Organometallics 2013, 32, 4892−4903

Organometallics

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parameter functional (B3)48 and includes a mixture of HF and DFT exchange terms associated with the gradient-corrected correlation functional due to Lee, Yang, and Parr (LYP).49 The all-electron Dunning’s correlation consistent cc-pVDZ basis set50 for nonmetal atoms and the cc-pVDZ-PP basis set51 containing an effective core relativistic pseudopotential for metal atoms were used to perform single-point energy calculations at the optimized BP86/TZ2P molecular geometries. 2.2. Bond Energy Decomposition Analyses. The bonding energy, ΔE, associated with the formation of a given aza(or phospha)metallabenzene from two triplet biradical moieties, namely, an aza(or phospha)ethendiyl fragment A (αα) and a metal fragment B (ββ) (see Scheme 1), was split up into two major components (eq 1):

Depending on the degree of C 2p and metal d orbital mixing, one can consider that metallabenzenes are 6, 8, or 10π-electron species. There are arguments in favor of and against any of these proposals, and the main conclusion is that π-electron counting in these species is not as obvious as it is in classical organic molecules. While considerable progress has been made in the synthesis of metallabenzenes,2,4−6 the heteroatom-containing analogues such as metallapyryliums,25 metallathiabenzenes,26 metallapyridines,27−29 metallapyridiniums,29 metallapyrimidines and metallapyrimidiniums,30 metallapyrroles,31,32 metallafurans,33 metallathiophenes,34 and azametallahelicenes35 are relatively less developed. In almost all heterometallacycles synthesized to date the heteroatom is directly bonded to the metal atom. To our knowledge the only exception is an osmapyridyne in which the N atom is in meta position with respect to the metal.28 Some of us have recently analyzed the relative energy and bonding of the pyridazine and pyrimidine isomers.36 We found that pyrimidine, with the two N atoms in meta position, is about 20 kcal/mol more stable than pyridazine, with N atoms in ortho position. Our results show that the larger stability of pyrimidine comes from the more favorable electrostatics and σorbital interactions involved in the formation of two C−N bonds from azaethendiyl and azabutendiyl fragments in comparison with the generation of C−C and N−N bonds in pyridazine and not from lower Pauli repulsions, as usually assumed, or due to changes in aromaticity.36 In this work, we study the relative stabilities of the ortho, meta, and para MClY(XC4H4)(PH3)2 heterometallabenzenes (M = Ir, Rh; X = N, P; Y = Cl and M = Os, Ru; X = N, P; Y = CO). Our objective is threefold: first, to find the most stable heterometallabenzene isomer in each case; second, to discuss the aromaticity in these compounds; and third, to analyze the chemical bonding to unravel the reasons for the different isomer stabilities. The analysis of the isomerization energies will be carried out with an energy decomposition analysis37,38 and the so-called turn-upside-down approach.36,39,40 There are several theoretical works that discuss the structure, bonding, and aromaticity in metallabenzenes,10−16,18,19,21 but few of them do the same for heterometallabenzenes.24,30 The present paper aims to fill in part this void.

ΔE = ΔEdef + ΔE int

(1)

Scheme 1. Fragments Considered in the EDA for the Formation of the Ortho, Meta, and Para Isomers of MClY(XC4H4)(PH3)2 Complexes (M = Ir, Rh; X = N, P; and Y = Cl and M = Os, Ru; X = N, P; and Y = CO)

2. THEORETICAL METHODS 2.1. General Procedure. All density functional theory (DFT) calculations were performed with the Amsterdam Density Functional (ADF) program.41 The molecular orbitals (MOs) were expanded in a large uncontracted set of Slater-type orbitals (STOs) of triple-ζ quality containing diffuse functions for all atoms and augmented with two sets of polarization functions, the so-called TZ2P basis set. An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately for each SCF cycle.42 Energies and gradients were computed using the local density approximation (Slater exchange and VWN correlation)43 with nonlocal corrections for exchange (Becke88)44 and correlation (Perdew86)45 included self-consistently (i.e., the BP86 functional). Scalar relativistic effects were considered by means of the zero-order regular approximation (ZORA).46 Calculation of the vibrational frequencies at the optimized geometries showed that most compounds with a planar ring are minima on the potential energy surface. In a few cases we found imaginary frequencies with low wavenumbers. Geometry optimizations of the latter species without symmetry constraints gave energy minima in which the ring moiety deviates slightly from planarity. Isomerization energies were also calculated with the Gaussian 03 program47 with the B3LYP method, which uses Becke’s three-

In this energy decomposition analysis (EDA), the deformation energy ΔEdef is the amount of energy required to deform the separated biradical fragments in their triplet state from their equilibrium structure to the geometry that they acquire in the cyclic molecule. The interaction energy ΔEint corresponds to the actual energy change when the prepared fragments are combined to form the overall molecule. The interaction energy is analyzed in the framework of the Kohn−Sham MO model using a Morokuma-type decomposition of the bonding energy into electrostatic interaction, exchange (or Pauli) repulsion, and orbital interactions (eq 2).37,38,52 4893


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ΔE int = ΔVelstat + ΔE Pauli + ΔEoi

magnetic fields. In this work, we used the NICS, proposed by Schleyer and co-workers,59 as a magnetic descriptor of aromaticity. NICS is defined as the negative value of the absolute shielding computed at a ring center or at some other interesting point of the system. Rings with large negative NICS values are considered aromatic. NICS values were computed at the B3LYP/cc-pVDZ-PP//BP86/TZ2P level of theory through the gauge-including atomic orbital method (GIAO)60 implemented in Gaussian 03. The magnetic shielding tensor was calculated for ghost atoms located at the ring critical point (RCP) of the heterometallabenzenes, the point of lowest density in the ring plane,61 as suggested by Cossió et al.62 These values are denoted as NICS(0). Similarly, NICS values at 1.0 Å above the perpendicular plane of the ring, NICS(1),63 as well as the NICS(1)zz tensor component were calculated. This latter quantity gives probably one of the best measures of aromaticity among the different NICS-related definitions.64 Values of NICS(1) and NICS(1)zz were computed with the aim to measure the aromaticity due to the π-system, sometimes obscured by the σ-current when NICS is calculated in the molecular plane.

(2)

The term ΔVelstat corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the deformed fragments and is usually attractive. The Pauli repulsion ΔEPauli comprises the destabilizing interactions between occupied orbitals. It arises as the energy change associated with going from the superposition of the unperturbed electron densities of the two fragments to the wave function Ψ0 = NÂ [Ψfragment_Aαα·Ψfragment_Bββ], which properly obeys the Pauli principle through explicit antisymmetrization (Â operator) and renormalization (N constant) of the product of fragment wave functions. It comprises the four electron destabilizing interactions between occupied MOs and is responsible for the steric repulsion. The orbital interaction ΔEoi is the change in energy from Ψ0 to the final, fully converged wave function, ΨSCF, of the system. The orbital interactions account for charge transfer (i.e., donor−acceptor interactions between occupied orbitals on one fragment with unoccupied orbitals of the other, including the HOMO−LUMO interactions) and polarization (empty−occupied orbital mixing on one fragment due to the presence of another fragment). The ΔEoi term can be divided into contributions of orbitals having different symmetries (eq 3) using the extended transition state scheme developed by Ziegler and Rauk.38

ΔEoi = Σ ΓΔE Γ

3. RESULTS AND DISCUSSION This section is divided into two subsections. In the first, we analyze the isomers of the 18-electron complexes MCl2(XC4H4)(PH3)2 with M = Ir, Rh and X = N, P. In the second, the isomers of the 16-electron species MCl(CO)(XC4H4)(PH3)2 with M = Os, Ru and X = N, P are discussed. Previous studies pointed out that there is little difference in the aromaticity of the 4d (Rh, Ru) and 5d (Ir, Os) metallabenzenes.12,13 However, since the 5d complexes are more stable,4−6 we restrict our discussion to irida- and osmapyridines and iridaphosphinines, and the results concerned with osmaphosphinines and rhoda- and ruthenapyridines and phosphinines are collected in the Supporting Information. We do not discuss the optimized geometries because the focus of this work lies on the relative stabilities and bonding situation of the heterometallabenzenes studied. Liu et al. reported that the triplet state of an osmapyridine was marginally more stable than the singlet state.29 For this reason, for all systems studied, we have optimized the singlet and triplet electronic states, and we have found that the ground state is the singlet (see Table S13 in the Supporting Information), the triplet being less stable by 3.9 (o-IrN) to 28.6 kcal/mol (mOsP). In this work we use the nomenclature o-IrN to refer to the ortho-iridapyridine IrCl2(NC4H4)(PH3)2 species or m-OsP to denote the meta-osmaphosphinine OsCl(CO)(PC4H4)(PH3)2 compound. The Cartesian coordinates and figures with the geometries of all complexes studied are available in the Supporting Information. 3.1. MCl2(XC4H4)(PH3)2 Complexes with M = Ir, Rh and X = N, P. We start our study with the iridapyridine IrCl2(NC4H4)(PH3)2 compounds. The π-MOs having relevant contributions from the NC4H4− fragment, depicted in Figure 1 for meta-iridapyridine, are not different from those found by Fernández and Frenking for RhCl2(C5H5)(PH3)2.12 Although the π-electron count in these systems is questionable,16 these MOs indicate that this 18-electron complex has 10π-electrons, thus following Hückel’s rule in agreement with previous results.12,13,24 Defining the z-axis as perpendicular to the ring plane and the x-axis in the direction of the Ir−Cpara axis, the 5d orbitals of the Ir metal that intervene in the π-MOs are the dxz (π3 bonding and π4 antibonding) and dyz (π2 bonding and π5 antibonding). The π1 orbital corresponds basically to the lowest-lying in-phase π-MO of the NC4H4− fragment. The πMOs for the rest of complexes analyzed in this work are similar. It is worth mentioning that in these 5π-MOs the contribution

(3)

In planar systems with a clear σ/π separation, this symmetry partitioning proved to be very useful. In the EDA of the bonding energy, open-shell fragments were treated with the spin-unrestricted formalism, but, for technical reasons, spin-polarization was not included. This error causes the studied bond to become on the order of a few kcal/mol too strong. The correction factor is in the range 0.91−0.99 in all model systems (with only three minor exceptions with values close to 0.9) and does not affect trends. With respect to the so-called turn-upside-down approach,36,39,40 for each pair of systems analyzed (ortho vs meta or meta vs para), in addition to the EDA applied to the relaxed systems, we also apply EDA to the corresponding deformed systems referred to as a and b (as subindex) as intermediate steps between the two relaxed systems (vide inf ra). 2.3. Descriptors of Aromaticity. The multicenter index of aromaticity (MCI) was used as an electronic index of aromaticity. MCI is derived from the Iring index that was defined by Giambiagi53 as OCC

∑

Iring(A) =

Si1i2(A1) Si2i3(A 2 )...Sini1(A n)

i1, i2 , i3 ,...in

(4)

where Sij(Ak) is the overlap between MOs i and j within the domain of atom Ak. In this formula it is considered that the ring is formed by atoms in the string {A} = {A1, A2, ... An}. Extension of this Iring index of Giambiagi by Bultinck and co-workers resulted in the so-called MCI index:

MCI(A) =

∑ Iring(A)= P(A) OCC

=

∑ ∑ P(A) i1, i2 , i3 ,...in

Si1i2(A1) Si2i3(A 2 )...Sini1(A n) (5)

where P(A) stands for the n! permutations of the elements in the string {A}. The MCI index has been successfully applied to a broad number of situations, from simple organic compounds to complex allmetal clusters with multiple aromaticity.54 For planar species, Sij(Ak) = 0 for i ∈ σ and j ∈ π orbital symmetries; thus the MCI can be exactly split into σ- and π-contributions, namely, MCIσ and MCIπ, respectively. The numerical integrations over the atomic domains were carried out within the “fuzzy atom” framework55 using the Beckeρ partitioning scheme56 with the APOST-3D program.57 The Iring and MCI indices were obtained with the ESI-3D program.58 Magnetic indices of aromaticity are based on the electron ring currents that are induced when the system is exposed to external 4894


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Table 1. BP86/TZ2P and B3LYP/cc-pVDZ-PP//BP86/ TZ2P Relatives Energies of MClY(XC4H4)(PH3)2 Complexes (M = Ir, Rh; X = N, P; Y = Cl and M = Ru, Os; X = N, P; Y = CO) Considered in This Study (units are kcal/ mol), BP86/TZ2P ∠MCCC(X) Dihedral Angles (in deg), and MCI Values (in electrons) and NICS(1)zz (in ppm) Values Both Calculated at the B3LYP/cc-pVDZ-PP//BP86/ TZ2P Level of Theory

Figure 1. Contour plot of the valence π orbitals of the metairidapyridine IrCl2(NC4H4)(PH3)2 compound (energies in au).

of the metal is never higher than 60% (see Table S14), and therefore, none of these MOs belong exclusively to the d orbitals of the metal. This makes us consider these compounds as 10π-electron systems. Table 1 gathers the BP86/TZ2P and B3LYP/cc-pVDZ-PP// BP86/TZ2P relative energies of the 24 ortho, meta, and para heterometallabenzenes studied in this work, together with their ∠MCCC(X) dihedral angles and their values for two indicators of aromaticity, namely, NICS(1)zz and MCI. Relative energies obtained at the BP86/TZ2P and B3LYP/cc-pVDZ-PP//BP86/ TZ2P levels of theory differ by less than 1.1 kcal/mol in all cases. The results indicate that the meta isomers are the most stable for the IrN and RhN species by about 10 kcal/mol, as compared to the ortho and para ones, while the ortho species are the lowest-lying in energy for all metallaphosphinines studied by ca. 20 kcal/mol. Finally, the ortho and meta are almost isoenergetic for the RuN and OsN complexes. With the exception of o-IrN and o-IrP, all heterometallabenzenes studied are planar or almost planar. A slight deviation from planarity was already observed in some iridabenzenes5,14 and was attributed to a sum of steric and electronic (better overlap with the dz2 orbital) effects.21 In the particular case of the o-IrN species, the planar o-IrN is only 0.9 kcal/mol less stable than the optimized nonplanar system. The aromaticity of the singlet ground state of the different isomers is supported by the negative values of the out-of-plane component of the NICS indicator of aromaticity (o-IrN: NICS(1)zz = −5.7 ppm; m-IrN: NICS(1)zz = −8.8 ppm; pIrN: NICS(1)zz = −12.1 ppm) and the positive value of the electronic delocalization multicenter index (o-IrN: MCI = 0.027; m-IrN: MCI = 0.024; p-IrN: MCI = 0.029) calculated at the B3LYP/cc-pVDZ-PP//BP86/TZ2P level. As a reference, benzene has NICS(1)zz = −28.9 ppm and MCI = 0.056 at the

compound

ΔE(BP86)

ΔE(B3LYP)

∠MCCC(X)

NICS(1)zz

MCI

o-IrN m-IrN p-IrN o-IrP m-IrP p-IrP o-RhN m-RhN p-RhN o-RhP m-RhP p-RhP o-OsN m-OsN p-OsN o-OsP m-OsP p-OsP o-RuN m-RuN p-RuN o-RuP m-RuP p-RuP

10.20 0.00 8.87 0.00 21.38 19.22 9.67 0.00 10.31 0.00 23.15 20.57 0.00 0.81 5.89 0.00 16.79 16.17 0.01 0.00 6.45 0.00 18.57 17.41

10.34 0.00 9.60 0.00 20.35 18.30 9.59 0.00 11.26 0.00 22.59 20.06 0.00 1.48 6.18 0.00 16.63 16.13 0.00 0.32 7.52 0.00 18.68 17.78

13.7 0.0 0.0 2.2 0.0 0.0 0.0 0.0 0.0 0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

−5.7 −8.8 −12.1 −5.9 −6.3 −5.5 −10.9 −10.2 −13.0 −7.3 −7.9 −6.9 −10.4 - 9.5 −13.4 −9.2 −7.7 −7.2 −11.0 −10.1 −13.9 −10.1 −8.7 −7.9

0.027 0.024 0.029 0.024 0.023 0.022 0.023 0.023 0.028 0.023 0.022 0.021 0.022 0.024 0.026 0.027 0.021 0.023 0.023 0.024 0.028 0.028 0.022 0.023

same level of theory. These results are in line with those reported by Fernández and Frenking, who found that the stabilization by aromaticity in a series of ruthenabenzenes and osmabenzenes was about half as strong as for benzene.12 The smaller impact of aromaticity in these systems is illustrated by the fact that the most stable isomer is not the most aromatic according to NICS(1)zz and MCI descriptors of aromaticity. The same trends are observed for the rest of the complexes analyzed (see Table 1), with the metallaphosphinines being in general somewhat less aromatic than the analogous metallapyridines. To better understand the origin of the higher stability of meta isomers in some systems (IrN and RhN), ortho isomers (IrP, RhP, RuP, and OsP) in other complexes, and the almost isoenergetic situation for the RuN and OsN complexes, we made an EDA of the bonding energy for the formation of structural isomers (o-MX, m-MX with M = Ir, Rh, Ru, Os; X = N, P) from triplet aza(phospha)ethenediyl (A(o-MX)X or A(mMX)X) and triplet metal (B(o-MX)M or B(m-MX)M fragments; see Scheme 1). The o-MX and m-MX can be made from two identical aza(phospha)ethenediyl and metal fragments by just turning upside down the aza(phospha)ethenediyl red fragment in Scheme 1. Then the different components of the bonding energy for the formation of the o-MX and m-MX complexes from the same fragments can be compared, and the differences give a hint of the physical reasons for the relative stability differences. This method of analysis, for which we proposed the name turn-upside-down approach,36 was used some years ago 4895


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Table 2. Analysis of the Bonding (in kcal/mol) between Triplet Azaethenediyl, A(x-IrN)N, and Triplet IrCl2(PH3)2(C3H3), B(xIrN)Ir, Fragments in o-IrN, m-IrN, and Deformed m-IrN (m-IrNa and m-IrNb)a

ΔEPauli ΔVelstat ΔEoi ΔEoi(σ) ΔEoi(π) ΔEint ΔEdef ΔEtotc ΔEbondexactc Correct.fc

o-IrN

m-IrN

m-IrNa

m-IrNb

A(o-IrN)N + B(o-IrN)Ir

A(m-IrN)N + B(m-IrN)Ir



538.84 −326.50 −429.96 −b −b −217.61 47.98 −169.63 −162.53 0.96

692.41 (153.57) −402.69 (−76.19) −521.49 (−91.53) −459.83 −61.65 −231.76 (−14.15) 53.17 (5.19) −178.59 (−8.96) −172.74 (−10.20) 0.97

584.49 (45.65) −350.66 (−24.16) −452.91 (−22.95) −b −b −219.08 (−1.47) 47.98 (0.00) −171.10 (−1.47) −163.94 (−1.41) 0.96

698.28 (159.44) −400.97 (−74.47) −520.71 (−90.75) −b −b −223.40 (−5.79) 47.98 (0.00) −175.42 (−5.79) −166.75 (−4.22) 0.95

a

In parentheses the differences with respect to the values for the o-IrN system. Computed at the BP86/TZ2P level. See Scheme 1 for structures. AN/ BIr(o-IrN) and AN/BIr(m-IrN) refer to AN/BIr in the geometry it adopts in o-IrN and m-IrN, respectively; m-IrNa is m-IrN with frozen AN/BIr(oIrN) fragments but with connecting C−N and Ir−C bond distances as the corresponding C−C and Ir−N bond lengths in o-IrN (1.435 and 1.973 Å); m-IrNb is m-IrN with frozen AN/BIr(o-IrN) fragments but with connecting C−N and Ir−C bond distances as the optimized bond lengths in mIrN (1.348 and 1.971 Å). bNonplanar species. The exact σ/π separation is not possible. cΔEbondexact is the exact bonding energy, while ΔEtot is the sum of ΔEint and ΔEdef, and it is the bonding energy without taking into account the spin polarization effects in the fragment (see Theoretical Methods section). Correct.f gives the ΔEbondexact/ΔEtot ratio, and it is a measure of the error in the different energy components because of the lack of spin polarization effects in the fragments.

exchanged (the fragment turned upside-down). m-IrNb is mIrN constructed from the frozen o-IrN fragments with C−N and C−Ir bond lengths equal to those optimized in the m-IrN complex. As can be seen in Table 2, 162.5 and 172.7 kcal/mol are released in the formation of o-IrN and m-IrN from triplet optimized azaethendiyl and IrCl2(C3H3)(PH3)2 fragments, respectively, thus giving m-IrN as the most stable isomer by 10.2 kcal/mol. This result is somewhat surprising since, as said in the Introduction, experimentally in most azametallacycles the N atom is directly bonded to the metal atom, although it agrees with the observed relative stabilities of pyrimidine and pyridazine.36 The higher stability of m-IrN cannot be ascribed to the deformation energy of the fragments (ΔEdef), which is in fact somewhat more destabilizing for m-IrN by 5.2 kcal/mol. The main difference comes from the interaction energy (ΔEint), which is 14.2 kcal/mol more stabilizing in m-IrN. EDA results of the two ΔEint energies show that the difference is not due to Pauli repulsions (ΔEPauli), which destabilize m-IrN with respect to o-IrN by as much as 153.6 kcal/mol, but to a combination of better electrostatic (ΔVelstat) and orbital interaction (ΔEoi) components. The higher ΔEPauli and the more stabilizing ΔVelstat term in the m-IrN form are partly the result of the shorter distance (1.348 Å) of the new C−N bond formed, as compared to that of the new C−C bond (1.435 Å) generated in o-IrN. C−N bond lengths are usually shorter than C−C bond lengths because the 2p orbitals are more contracted in N, and the most effective overlap between N and C 2p orbitals takes place at shorter distances.65 ΔEoi can be further decomposed into σ and π components (ΔEσ and ΔEπ), but only for the mIrN because the o-IrN system is not planar. ΔEπ, which measures the contribution of π-delocalization to the bonding energy (it may be considered an approximation to the Hückel resonance energy)66, is significant in m-IrN (−61.7 kcal/mol) and not far from that of a classical organic analogous heteroaromatic species such as pyrimidine (−79.0 kcal/ mol).36 The percentage of ΔEoi stabilization due to the πsystem (11.8%) is similar to, but somewhat smaller than, that found by Fernández and Frenking in a series of metal-

to analyze the higher stability of phenanthrene with respect to anthracene.39 More recently, it has been applied to discuss the relative stabilities of the 1,2- and 1,3-diazacyclobutadiene, pyrazole and imidazole, and pyridazine and pyrimidine.36 Comparison between the 1,2- (C2v) and 1,3- (D2h) isomers of the M2N22− (M, N = B, Al, and Ga) clusters has been also carried out with the turn-upside-down method.40 In spite of the fact that the para-metallapyridine(phosphinine) is not the most stable in any case, we have also compared the m-MX and p-MX heterometallabenzenes following the same approach, i.e., making an EDA of the bonding energy for the formation of the m-MX and p-MX structural isomers from triplet aza(phospha)ethenediyl (A1(m-MX)X or A(p-MX)X) and triplet metal (B1(m-MX)M or B(p-MX))M fragments; see Scheme 1). We start by analyzing the differences between the o-IrN and m-IrN isomers from the EDA of the bonding energy of o-IrN and m-IrN obtained from the same two fragments, namely, the azaethendiyl A(x-IrN)N and the metal B(x-IrN)Ir fragments in their triplet states. The azaethendiyl fragments that can be obtained from o-IrN and m-IrN isomers are slightly different (C−N bonds are 1.302 and 1.327 Å and ∠HCN angles are 116.5° and 112.8° for o-IrN and m-IrN complexes, respectively), and therefore, one can build o-IrN and m-IrN using triplet-state azaethendiyl and metal fragments derived from o-IrN (A(o-IrN)N and B(o-IrN)Ir fragments) or from mIrN (A(m-IrN)N and B(m-IrN)Ir fragments; see Scheme 1). The construction of o-IrN or m-IrN complexes from these two fragments involves the formation of two σ-electron pairs (new C−C/C−N and N−Ir/C−Ir bonds for the o-IrN/m-IrN complex) plus the rearrangement of the π-system enforced by the aromatic character of the compounds. Table 2 contains the results of the analysis of the bonding for o-IrN from A(o-IrN)N and B(o-IrN)Ir fragments, m-IrN from A(m-IrN)N and B(mIrN)Ir fragments, and two deformed m-IrN structures (m-IrNa and m-IrN b) obtained using A(o-IrN) N and B(o-IrN) Ir fragments. m-IrNa is m-IrN constructed from the frozen oIrN fragments with C−N and C−Ir bond lengths equal to the C−C and N−Ir bond distances of o-IrN. Therefore, m-IrNa is o-IrN with the N and C positions of the azaethendiyl fragment 4896


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labenzenes.12 The main contribution to ΔEoi in m-IrN comes from the σ term. Indeed, the Ir−C σ-bond in m-IrN is stronger than the Ir−N σ-bond in o-IrN, and the difference is not compensated by the larger σ-bond strength of C−C than C−N bonds.67 This is the situation at the optimized geometries of oIrN and m-IrN. When we move from m-IrN to m-IrNa (the mIrN having the same geometry as the o-IrN species with the N and C atoms of the azaethendiyl fragment exchanged), we find that the bonding energy of the m-IrNa species almost matches that of the o-IrN complex. The somewhat higher ΔEPauli repulsion is compensated by slightly more stabilizing ΔVelstat and ΔEoi terms. The higher ΔEPauli in m-IrNa as compared to o-IrN is likely the result of larger Pauli repulsion for the C−N bond in comparison with the C−C bond.36,65 Partial relaxation of the m-IrNa to m-IrNb leads to a situation practically identical to that of m-IrN. When going from m-IrNa to m-IrNb, there is an important increase of the Pauli repulsion term and a stabilization of the ΔVelstat and ΔEoi terms, as expected from the substantial C−N bond length reduction by ca. 0.1 Å. Following the same procedure, we can compare the m-IrN and p-IrN isomers from the EDA of the bonding energy to form m-IrN and p-IrN from the two identical azaethendiyl A(1)(x-IrN)N and the metal B(1)(x-IrN)Ir fragments in their triplet states (see Scheme 1). The results are collected in Table 3, which contains, in addition, the analysis of the bonding of two deformed p-IrN structures (p-IrNa and p-IrNb). Results in Table 3 show that 240.2 and 231.3 kcal/mol are released in the formation of m-IrN and p-IrN from triplet azaethendiyl and IrCl2(C3H3)(PH3)2 fragments. Thus, m-IrN is more stable than p-IrN by 8.9 kcal/mol. The bond lengths in the two fragments obtained from m-IrN and p-IrN complexes are quite similar, and consequently, the deformation energy of the fragments is almost the same for the two isomers. Hence, the stabilization of m-IrN with respect to p-IrN originates from a lower overall value of ΔEint of the former. When comparing the geometries of the m-IrN and p-IrN complexes, one can see that the formed C−C and C−N bond distances differ by less than a hundredth of an angstrom. These similar bond lengths lead to comparable Pauli repulsion and orbital interaction terms. The main difference comes from the electrostatic interaction energy, which is 11.1 kcal/mol more stabilizing in m-IrN. The similar C−C and C−N bond distances in m-IrN and p-IrN species allows using the charges on the atoms of the fragments to discuss the origin of the different electrostatic interactions. The radical C atom in β position in the IrCl2(C3H3)(PH3)2 fragment bears a negative Voronoi charge of about 0.13 e, and the C atom in the α position has a charge of −0.04 e (see Table S12 in the Supporting Information). Therefore, electrostatically speaking, the azaethendiyl fragment has a more stabilizing interaction when its C atom, which is positively charged, faces the C atom in β position in the IrCl2(C3H3)(PH3)2 fragment and its N atom, which is negatively charged, connects with the C atom in α position, i.e., in the m-IrN complex. This type of reasoning cannot be used to justify the different electrostatic contributions in o-IrN and m-IrN species because the newly formed C−C and C−N bond lengths are too different in these systems. The ΔEoi term can be further decomposed into σ- and π-components (ΔEσ and ΔEπ). Although the two components of ΔEoi favor the m-IrN isomer, differences between the σ- and the π-components of the two complexes are less than 1 kcal/mol. ΔEπ in m-IrN and p-IrN complexes represents about 14.5% of the ΔE oi term. Interestingly, the values of ΔEπ are significantly larger in m-

Table 3. Analysis of the Bonding (in kcal/mol) between Triplet Azaethenediyl A(1)(x-IrN)N and Triplet IrCl2(PH3)2(C3H3) B(1)(x-IrN)Ir Fragments in m-IrN and pIrN and Deformed p-IrN (p-IrNa and p-IrNb)a m-IrN

p-IrN

p-IrNa

p-IrNb

A1(m-IrN)N + B1(mIrN)Ir

A(p-IrN)N + B(pIrN)Ir



789.37 (−3.16) −409.04 (11.09) −644.17 (1.21) −551.25 (0.66) −92.92 (0.55) −263.83 (9.15) 24.96 (−0.36) −238.87 (8.79) −231.32 (8.87) 0.97

816.07 (23.54) −416.51 (3.62) −655.57 (−10.19) −557.64 (−5.73) −97.92 (−4.45) −256.01 (16.97) 25.32 (0.00) −230.69 (16.97) −223.23 (16.96) 0.97

ΔEPauli

792.53

ΔVelstat

−420.13

ΔEoi

−645.38

ΔEoi(σ)

−551.91

ΔEoi(π)

−93.47

ΔEint

−272.98

ΔEdef

25.32

ΔEtotb

−247.66

ΔEbondexactb Correct.f

b

−240.19 0.97

801.23 (8.70) −409.52 (10.61) −652.68 (−7.30) −559.05 (−7.14) −93.62 (−0.15) −260.97 (12.01) 25.32 (0.00) −235.65 (12.01) −229.01 (11.18) 0.97

a

In parentheses the differences with respect to the values for the mIrN system Computed at BP86/TZ2P. See Scheme 1 for structures. A1N/B1Ir(m-IrN) and AN/BIr(p-IrN) refer to AN/BIr in the geometry it adopts in m-IrN and p-IrN, respectively; p-IrNa is p-IrN with frozen A1N/B1Ir(m-IrN) fragments but with connecting C−N and C−C bond distances as the corresponding C−C and C−N bond lengths in m-IrN (1.400 and 1.327 Å); p-IrNb is p-IrN with frozen A1N/B1Ir(mIrN) fragments but with connecting C−N and C−C bond distances as the optimized bond lengths in p-IrN (1.342 and 1.395 Å). bΔEbondexact is the exact bonding energy, while ΔEtot is the sum of ΔEint and ΔEdef, and it is the bonding energy without taking into account the spin polarization effects in the fragment (see Theoretical Methods section). Correct.f gives the ΔEbondexact/ΔEtot ratio, which is a measure of the error in the different energy components because of the lack of spin polarization effects in the fragments.

IrN constructed from A1(m-IrN)N and B1(m-IrN)Ir) fragments than in the same complex generated from A(m-IrN)N and B(mIrN)Ir fragments (see Tables 2 and 3 and Scheme 1). This ΔEπ value is quite dependent on how the molecule is cut into fragments, and consequently, ΔEπ values provide only a rough estimation of aromaticity in these compounds. The difference in the ΔEπ values (31.82 kcal/mol) is mainly due to the different stabilization of the π-system in the initial fragments. Indeed, the π-systems of the two fragments (A(m-IrN)N and B(m-IrN)Ir) used to form m-IrN are 32.3 kcal/mol more stable than those of the fragments (A1(m-IrN)N and B1(m-IrN)Ir) used to construct the same m-IrN species (the energy of the πsystem of each fragment is obtained in ADF in relation to the atomic fragments). Not unexpectedly, the more favorable ΔVelstat in m-IrN as compared to p-IrN is still present in the deformed p-IrNa and p-IrNb complexes. To our knowledge only a phosphametallabenzene (an osmaphosphinine) having a P atom in its six-membered ring structure has been reported to date.32 Still, we think it is interesting to discuss the effect in the relative stabilities of changing the N heteroatom to a P atom. As can be seen in Table 4, 163.7 and 142.4 kcal/mol are released in the formation of o-IrP and m-IrP from triplet phosphaethenyl and 4897


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Table 4. Analysis of the Bonding (in kcal/mol) between Triplet Phosphaethenyl A(x-IrP)P and Triplet Ir(Cl)2(PH3)2(C3H3) B(x-IrP)Ir Fragments in o-IrP, m-IrP, and deformed m-IrP (m-IrPa and m-IrPb)a

Table 5. Analysis of the Bonding (in kcal/mol) between Triplet Phosphaethenyl A(1)(x-IrP)P and Triplet Ir(Cl)2(PH3)2(C3H3) B(1)(x-IrP)Ir Fragments in m-IrP, pIrP, and Deformed p-IrP (p-IrPa and p-IrPb)a

o-IrP

m-IrP

m-IrPa

m-IrPb

m-IrP

p-IrP

p-IrPa

p-IrPb

A(o-IrP)P + B(o-IrP)Ir

A(m-IrP)P + B(m-IrP)Ir



A1(m-IrP)P + B1(m-IrP)Ir

A(p-IrP)P + B(p-IrP)Ir



523.91 (−81.07) −347.54 (36.91) −380.00 (65.80) −328.61 −51.39 −203.63 (21.64) 55.54 (0.33) −148.09 (21.97) −142.36 (21.37) 0.96

870.75 (265.77) −474.68 (−90.23) −497.19 (−51.39) −b −b −101.13 (124.14) 55.21 (0.00) −45.92 (124.14) −39.57 (124.17) 0.86d

520.18 (−84.80) −343.78 (40.67) −379.39 (66.41) −b −b −202.98 (22.29) 55.21 (0.00) −147.77 (22.29) −141.44 (22.30) 0.96

664.29 (29.02) −378.58 (−11.20) 528.59 (−17.56) −443.69 (−18.36) −84.90 (0.80) −242.87 (0.26) 24.06 (−2.39) −218.81 (−2.13) −211.98 (−2.16) 0.97

839.10 (203.83) −430.29 (−62.91) −527.09 (−16.06) −432.83 (−7.50) −94.26 (−8.56) −118.28 (124.85) 26.45 (0.00) −91.83 (124.85) −84.97 (124.85) 0.93

662.13 (26.86) −376.88 (−9.50) −530.13 (−19.10) −443.29 (−17.96) −86.85 (−1.15) −244.88 (−1.75) 26.45 (0.00) −218.43 (−1.75) −211.67 (−1.85) 0.97

ΔEPauli

604.98

ΔVelstat

−384.45

ΔEoi

−445.80

ΔEoi(σ) ΔEoi(π) ΔEint

−b −b −225.27

ΔEdef

55.21

ΔEtotc

−170.06

ΔEbondexactc

−163.74

Correct.fc

0.96

ΔEPauli

635.27

ΔVelstat

−367.38

ΔEoi

−511.03

ΔEoi(σ)

−425.33

ΔEoi(π)

−85.70

ΔEint

−243.13

ΔEdef

26.45

ΔEtotb

−216.68

ΔEbondexactb

a

In parentheses the differences with respect to the values for the o-IrP system. Computed at BP86/TZ2P. See Scheme 1 for structures. AP/ BIr(o-IrP) and AP/BIr(m-IrP) refer to AP/BIr in the geometry it adopts in o-IrP and m-IrP, respectively; m-IrPa is m-IrP with frozen AP/ BIr(o-IrP) fragments but with connecting C−P and Ir−C bond distances as the corresponding C−C and Ir−P bond lengths in o-IrP (1.397 and 2.266 Å); m-IrPb is m-IrP with frozen AP/BIr(o-IrP) fragments but with connecting C−P and Ir−C bond distances as the optimized bond lengths in m-IrP (1.768 and 1.973 Å). bNonplanar species. The exact σ/π separation is not possible. cΔEbondexact is the exact bonding energy, while ΔEtot is the sum of ΔEint and ΔEdef, and it is the bonding energy without taking into account the spin polarization effects in the fragment (see Theoretical Methods section). Correct.f gives the ΔEbondexact/ΔEtot ratio, which is a measure of the error in the different energy components because of the lack of spin polarization effects in the fragments. dLow Correct.f factor due to constrained geometry, which leads to low ΔEtot and ΔEbondexact values.

Correct.f

b

−209.82 0.97

a

In parentheses the differences with respect to the values for the mIrP system. Computed at BP86/TZ2P. See Scheme 1 for structures. A1P/B1Ir(m-IrP) and AP/BIr(p-IrP) refer to AP/BIr in the geometry it adopts in m-IrP and p-IrP, respectively; p-IrPa is p-IrP with frozen A1P/B1Ir(m-IrP) fragments but with connecting C−P and C−C bond distances as the corresponding C−C and C−P bond lengths in m-IrP (1.394 and 1.737 Å); p-IrPb is p-IrP with frozen A1P/B1Ir(m-IrP) fragments but with connecting C−P and C−C bond distances as the optimized bond lengths in p-IrP (1.747 and 1.386 Å). bΔEbondexact is the exact bonding energy, while ΔEtot is the sum of ΔEint and ΔEdef, and it is the bonding energy without taking into account the spin polarization effects in the fragment (see Theoretical Methods section). Correct.f gives the ΔEbondexact/ΔEtot ratio, which is a measure of the error in the different energy components because of the lack of spin polarization effects in the fragments.

fragments lead to a C−X and a M−C bond, where X = N, P. When comparing the bonding energies for the same metal atom and fragmentation pattern (for instance, compare m-IrN vs. mIrP), the difference must lie in the relative stability of the C−X bonds. In all cases the bonding energies systematically show a difference of ca. 30 kcal/mol in favor of the m-MN species, thus indicating that the C−P bond is weaker than the C−N one by ca. 30 kcal/mol. Table 5 contains the results of the analysis of the bonding for m-IrP, p-IrP, and two deformed p-IrP structures (p-IrPa and p-IrPb). The bonding energy for the formation of m-IrP from A1(m-IrP)P and B1(m-IrP)Ir fragments is −209.8 kcal/mol, whereas the interaction between A(p-IrP)P and B(p-IrP)Ir fragments to form p-IrP releases 212.0 kcal/mol, thus pointing out that p-IrP is marginally more stable than m-IrP, by 2.2 kcal/mol. EDA analysis shows that the ΔEint contributions are essentially equal, so that the slightly higher stability of the p-IrP isomer comes from the somewhat smaller ΔEdef energy associated with the para isomer. Interestingly the ΔEπ component of the orbital interaction term is, first, almost the same as that for the m-IrP and p-IrP complexes (about 85 kcal/mol) and, second, somewhat smaller than those of the mIrN and p-IrN complexes (about 93 kcal/mol). Both trends are in agreement with the calculated NICS(1)zz and MCI values

IrCl2(C3H3)(PH3)2 fragments, respectively, o-IrP being the most stable isomer by 21.4 kcal/mol. The ortho is the most stable isomer in all phosphametallabenzenes studied in this work. To understand the origin of the higher stability of the oIrP complex, we made an EDA of the bonding energy for the formation of structural isomers o-IrP and m-IrP from two triplet phosphaethendiyl A(x-IrP)P and IrCl2(C3H3)(PH3)2 B(x-IrP)Ir fragments. The results of this analysis are listed in Table 4. The main difference between o-IrP and m-IrP comes from the ΔEint term, which is 21.6 kcal/mol more stabilizing in o-IrP. The lower ΔEint is not due to smaller Pauli repulsion but because of more stabilizing ΔVelstat and ΔEoi terms. In particular, ΔEoi is more favorable in o-IrP by as much as 65.8 kcal/mol. From ΔEπ results of Tables 3 and 5−7, one can assume that ΔEπ is likely to be similar in the two complexes. If this assumption is correct, then the main difference stems from the ΔEσ term, which is the result of the stronger Ir−P and C−C bonds formed in o-IrP as compared to the Ir−C and C−P bonds generated in m-IrP.67 Interestingly, the situation was the opposite for o-IrN and m-IrN.67 This observation can be understood by comparing the bonding energies of m-MN and m-MP species for M = Ir, Os. The A1+B1 fragments lead to the formation of a C−X and a C−C bond, whereas the A+B 4898


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Table 6. Analysis of the Bonding (in kcal/mol) between Triplet Azaethenediyl A(x-OsN)N and Triplet OsCl(CO)(PH3)2(C3H3) B(x-OsN)Os Fragments in o-OsN, m-OsN, and Deformed m-OsN (m-OsNa and m-OsNb)a o-OsN

m-OsN

m-OsNa

m-OsNb

m-OsN

p-OsN

p-OsNa

p-OsNb

A(o-OsN)N + B(oOsN)Os

A(m-OsN)N + B(mOsN)Os



A1(m-OsN)N + B1(mOsN)Os

A(p-OsN)N + B(pOsN)Os



582.31 (107.45) −344.94 (−43.85) −466.40 (−64.05) −420.03 (−55.16) −46.37 (−8.89) −229.03 (−0.45) 46.65 (1.51) −182.38 (1.06) −174.07 (0.81) 0.95

515.52 (40.66) −319.43 (−18.34) −416.16 (−13.81) −379.94 (−15.07) −36.21 (1.27) −220.07 (8.51) 45.14 (0.00) −174.93 (8.51) −166.36 (8.52) 0.95

590.73 (115.87) −355.34 (−54.25) −461.34 (−58.99) −415.63 (−50.76) −45.71 (−8.23) −225.95 (2.63) 45.14 (0.00) −180.81 (2.63) −170.72 (4.16) 0.94

ΔEPauli

474.86

ΔVelstat

−301.09

ΔEoi

−402.35

ΔEoi(σ)

−364.87

ΔEoi(π)

−37.48

ΔEint

−228.58

ΔEdef

45.14

ΔEtotb

−183.44

ΔEbondexactb

−174.88

Correct.f

b

Table 7. Analysis of the Bonding (in kcal/mol) between triplet Azaethenediyl A(1)(x-OsN)N and Triplet OsCl(CO)(PH3)2(C3H3) B(1)(x-OsN)Os Fragments in mOsN, p-OsN, and Deformed p-OsN (p-OsNa and p-OsNb)a

0.95

ΔEPauli

795.33

ΔVelstat

−426.03

ΔEoi

−659.46

ΔEoi(σ)

−554.78

ΔEoi(π)

−104.68

ΔEint

−290.16

ΔEdef

34.13

ΔEtotb

−256.03

ΔEbondexactb Correct.f

a

b

−247.08 0.97

804.62 (9.29) −420.93 (5.10) −669.31 (−9.85) −560.13 (−5.35) −109.19 (−4.51) −285.63 (4.53) 34.68 (0.55) −250.95 (5.08) −242.00 (5.08) 0.96

814.47 (19.14) −421.77 (4.26) −669.43 (−9.97) −558.40 (−3.62) −111.03 (−6.35) −276.73 (13.43) 34.13 (0.00) −242.60 (13.43) −233.65 (13.43) 0.96

818.02 (22.69) −425.35 (0.68) −672.31 (−12.85) −563.39 (−8.61) −108.92 (−4.24) −279.64 (10.52) 34.13 (0.00) −245.51 (10.52) −236.39 (10.69) 0.96

a

In parentheses the differences with respect to the values for the oOsN system. Computed at BP86/TZ2P. See Scheme 1 for structures. AN/BOs(o-OsN) and AN/BOs(m-OsN) refer to AN/BOs in the geometry it adopts in o-OsN and m-OsN, respectively; m-OsNa is m-OsN with frozen AN/BOs(o-OsN) fragments but with connecting C−N and Os−C bond distances as the corresponding C−C and Os− N bond lengths in o-OsN (1.445 and 2.062 Å); m-OsNb is m-OsN with frozen AN/BOs(o-OsN) fragments but with connecting C−N and Os−C bond distances as the optimized bond lengths in m-OsN (1.364 and 2.095 Å). bΔEbondexact is the exact bonding energy, while ΔEtot is the sum of ΔEint and ΔEdef, and it is the bonding energy without taking into account the spin polarization effects in the fragment (see Theoretical Methods section). Correct.f gives the ΔEbondexact/ΔEtot ratio, which is a measure of the error in the different energy components because of the lack of spin polarization effects in the fragments.

In parentheses the differences with respect to the values for the mOsN system. Computed at BP86/TZ2P. See Scheme 1 for structures. A1N/B1Os(m-OsN) and AN/BOs(p-OsN) refer to AN/BOs in the geometry it adopts in m-OsN and p-OsN, respectively; p-OsNa is pOsN with frozen A1N/B1Os(m-OsN) fragments but with connecting C−N and C−C bond distances as the corresponding C−C and C−N bond lengths in m-OsN (1.385 and 1.318 Å); p-OsNb is p-OsN with frozen A1N/B1Os(m-OsN) fragments but with connecting C−N and C−C bond distances as the optimized bond lengths in p-OsN (1.324 and 1.376 Å). bΔEbondexact is the exact bonding energy, while ΔEtot is the sum of ΔEint and ΔEdef, and it is the bonding energy without taking into account the spin polarization effects in the fragment (see Theoretical Methods section). Correct.f gives the ΔEbondexact/ΔEtot ratio, which is a measure of the error in the different energy components because of the lack of spin polarization effects in the fragments.

shown in Table 1 for m-IrN, p-IrN, m-IrP, and p-IrP complexes. ΔEπ values suggest that the m-IrN complex is the most aromatic among these four complexes, at variance with NICS(1)zz and MCI results, which consider p-IrN as the most aromatic system. In all cases, however, differences are small. The geometry deformation in m-IrPa and p-IrPa is too large when compared to m-IrP and p-IrP to use the EDA to extract meaningful conclusions. The C−C and C−P bond distances differ by roughly 0.3 Å. On the other hand, the EDA results for m-IrPb and p-IrPb are similar to those found for m-IrP and pIrP, respectively. EDA for the RhCl2(XC4H4)(PH3)2 complexes with X = N, P can be found in the Supporting Information (see Tables S2, S3, S4, and S5). Note that these two metals belong to the same group in the periodic table (group 9), and they have similar Pauling electronegativities (χ(Ir) = 2.20; χ(Rh) = 2.28).68 Thus, not surprisingly, EDA trends observed in the iridium systems do not change when we move to rhodium. In all cases, however, the bonding energy is somewhat smaller in the rhodium complexes, and this is in accordance with the fact that 5d metallabenzenes are more stable than their 4d analogues.4−6

3.2. MCl(CO)(XC4H4)(PH3)2 Complexes with M = Os, Ru; X = N, P. BP86/TZ2P (B3LYP/cc-pVDZ-PP) relative energies (Table 1) indicate that the compound o-OsN is more stable than the m-OsN isomer by only 0.8 kcal/mol (1.5 kcal/ mol) and more stable than p-OsN by 5.9 kcal/mol (6.2 kcal/ mol). The aromaticity of the singlet ground state of these three isomers is supported by the negative values of the NICS indicator of aromaticity (o-OsN: NICS(1)zz = −10.4 ppm; mOsN: NICS(1)zz = −9.5 ppm; p-OsN: NICS(1)zz = −13.4 ppm) and the positive value of the electronic delocalization multicenter index (o-OsN: MCI = 0.022; m-OsN: MCI = 0.024; p-OsN: MCI = 0.026). As for IrN complexes, NICS(1)zz and MCI values point out that the aromaticity of the different OsN isomers is similar, the least stable p-OsN being somewhat more aromatic. The ortho and meta isomers for the OsN complexes are almost isoenergetic, in contrast to the IrN complexes, for which the meta isomer was clearly the most stable. To understand the origin of this different behavior, we have made an EDA for the formation of o-OsN and m-OsN from triplet azaethendiyl (A(o-OsN)N or A(m-OsN)N) and metal (B(o-OsN)Os or B(mOsN)Os) fragments (see Scheme 1) following the same 4899


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to overcome the much lower overall value of ΔEint for o-OsP. Because of a cancellation of the different terms, the ΔEπ contribution almost fully accounts for the energy difference between the two isomers. Once more, the larger ΔEπ term (in absolute value) of o-OsP agrees with larger MCI and more negative NICS(1)zz values. On the other hand, the EDA results for the m-OsP and p-OsP isomers indicate that they are almost isoenergetic (p-OsP is more stable by only 0.6 kcal/mol). The situation resembles that found for m-IrP and p-IrP isomers, where the ΔEint slightly favors the meta isomer, but the smaller ΔEdef contribution associated with the para isomer leads to its marginally higher stability. Indeed, trends observed are equivalent to those found for m-IrP and p-IrP isomers (Table 5). The EDA results for ruthenium complexes in the Supporting Information (see Tables S8, S9, S10, and S11) show that ruthenapyridines and phosphinimines behave in the same way as their osmium analogues. This is not surprising if one takes into account that ruthenium and osmium belong to the same group in the periodic table (group 8) and have the same Pauling electronegativity (2.2).68 In all cases, however, the bonding energy is somewhat smaller in the ruthenium complexes, and this is in accordance with the fact that 5d metallabenzenes are more stable than their 4d analogues.4−6 A different type of analysis can be carried out by considering that the ortho, meta, and para isomers essentially differ by the number and type of bonds formed in the ring. In the case of meta and para isomers there are only C−X and C−C bonds, two of each type. In the ortho isomer one M−C bond is lost in favor of a C−C one, and another C−X bond is replaced by a M−X one. Thus, differences in bond energies could help us to rationalize the relative energies of the isomers, particularly between the ortho and meta ones. The meta and para isomers exhibit the same type of bonds so their relative energies are associated with more intricate nonadditive effects. The direct comparison of the m-MX energies for M = Ir, Os and X = N, P using the A+B (Tables 2, 4, and 6) and the A1+B1 fragments (Tables 3, 5, and 7) systematically shows a difference of ca. 70 kcal/mol in favor of the latter. The A1+B1 fragments lead to the formation of a C−X and a C−C bond, whereas the A+B fragments lead to a C−X and a M−C bond. Therefore, the difference stands between the C−C and the M− C bonds: the former is roughly 70 kcal/mol stronger than the latter, disregarding the nature of the metal. Similarly, the comparison of the o-MX and m-MX (using A1+B1 fragments) bonding energies inform about the relative strength of the C−X bonds with respect to the M−X ones. In the case of X = N, the C−N bond is consistently stronger than the M−N one by ca. 70 kcal/mol, whereas for X = P this difference decreases down to roughly 50 kcal/mol. Thus, in the case of X = P the ortho isomer is favored by ca. 70 kcal/mol with the formation of an extra C−C bond, whereas it is disfavored by ca. 50 kcal/mol because of the formation of a weaker M−P bond. Globally, the ortho isomer is expected to be favored by ca. 20 kcal/mol with respect to the para or meta ones, disregarding the nature of the metal atom, in good agreement with the data reported in Table 1. In the case of X = N, the gain in the formation of the new C−C bond in the ortho isomer is essentially compensated by the loss associated with the formation of a M−N bond, much weaker than the extra C−N one present in the meta isomer. Accordingly, the energy difference between the ortho and meta isomers should be small. This is clearly the case for M = Os, Ru,

procedure as that used to analyze the IrN systems. The results of the analysis of the bonding for o-OsN, m-OsN, and two deformed m-OsN structures (m-OsNa and m-OsNb) are collected in Table 6. Formation of o-OsN and m-OsN from triplet azaethendiyl and OsCl(CO)(C3H3)(PH3)2 fragments releases 174.9 and 174.1 kcal/mol, respectively. The trends in the different components of the bonding energy are the same as those found for the analogous IrN species. However, unlike IrN systems, the ΔEint term is now only marginally smaller in mOsN (by less than 0.5 kcal/mol), so that the smaller ΔEdef contribution in o-OsN (by more than 1.5 kcal/mol) accounts for its minor stability with respect to the meta isomer. It is interesting to note that the formation of Os−C and N−C σbonds in the m-OsN isomer is 55.2 kcal/mol more stabilizing than formation of Os−N and C−C σ-bonds in o-OsN. Also closing the metallacycle leads to significant better π-interactions in m-OsN than in o-OsN. The more negative ΔEπ term in mOsN may be an indication of somewhat higher aromaticity for this system, and this is reflected by the MCI values, but not by the NICS(1)zz results. When we move from m-OsN to mOsNa (the m-OsN having the same geometry as the o-OsN species with the N and C atoms of the azaethendiyl fragment exchanged), we find that the ΔEPauli term decreases significantly as compared to m-OsN, but also the stabilizing ΔVelstat and ΔEoi terms decrease in comparison to m-OsN. As a whole, mOsNa is 8.5 kcal/mol less stable than o-OsN. Partial relaxation of the m-OsNa to m-OsNb, the latter being a deformed m-OsN generated from A(o-OsN)N and B(o-OsN)Os fragments but with connecting C−N and C−Os bond distances equal to the corresponding bond lengths in m-OsN, leads to a situation similar to that of m-OsN. Results in Table 7 show that 247.1 and 242.0 kcal/mol are released in the formation of m-OsN and p-OsN from triplet azaethendiyl and OsCl(CO)(C3H3)(PH3)2 fragments, respectively. Thus, as in IrN species, the meta isomer is slightly more stable than the para by 5.1 kcal/mol. The lengths of the two new formed bonds in m-OsN and p-OsN complexes are quite similar (the formed C−C and C−N bond distances differ by less than a hundredth of an angstrom), and consequently, differences between the components of the EDA are small. These similar bond lengths result in comparable Pauli repulsion, electrostatic repulsion, and orbital interaction terms. The ΔEσ and ΔEπ components of ΔEoi favor the pOsN isomer by about 5 kcal/mol. The larger ΔEπ term in pOsN concurs with its larger MCI and more negative NICS(1)zz values (Table 1). As stated for m-IrN, the values of ΔEπ are significantly larger in m-OsN constructed from A1(m-OsN)N and B1(m-OsN)Ir fragments than in the same complex generated from A(m-OsN)N and B(m-OsN)Ir fragments (see Scheme 1). The ΔEPauli and ΔEoi terms compensate each other, and consequently, the larger stability of the m-OsN form can be attributed to slightly more stabilizing ΔVelstat. Because the geometry of the deformed p-OsNa and p-OsNb complexes does not differ substantially from that of optimized p-OsN, EDA values for these deformed species are similar to those found for p-OsN. As found in all phosphametallabenzenes studied here, the ortho isomer is the most stable among the OsP isomers (see Tables S2 and S3 in the Supporting Information). The EDA results comparing o-OsP and m-OsP indicate that the reasons for the larger stability of o-OsP (16.8 kcal/mol) are the same as those described for o-IrP. The only difference is that in OsP the ΔEdef contribution favors the meta isomer, but not enough 4900


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where the two isomers are almost degenerate. The energy difference in favor of the meta isomer in the case of M = Ir, Rh can be understood by comparing the bonding energies between the o-IrX and o-OsX species. For X = P both Ir−P and Os−P bonding energies are essentially equal, whereas for X = N one can infer that the Ir−N bond is ca. 12 kcal/mol weaker than the Os−N one. This value is again very close to the 10.20 and 9.67 kcal/mol energy differences in favor of the meta isomers for M = Ir and Rh, respectively.

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Corresponding Author

*Fax: +34-972-41 83 56. E-mail: [email protected]; miquel. [email protected]. Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS Calculated relative stabilities of the ortho, meta, and para MClY(XC4H4)(PH3)2 heterometallabenzenes (M = Ir, Rh; X = N, P; Y = Cl and M = Os, Ru; X = N, P; Y = CO) indicate that the meta isomer is the most stable for the IrN and RhN complexes, the ortho is the most stable in all studied metallaphosphinines, and the ortho and meta are almost isoenergetic for RuN and OsN species. When comparing meta and para isomers, in all metallaphosphinines the two isomers have almost the same energy, while for metallapyridines the meta isomer is always more stable than the para. The electronic structure and bonding has been investigated with energy decomposition analyses of the interaction energy between various fragments using the turn-upside-down approach. Our results indicate that for all metallaphosphinines the ortho isomer is always more stable, disregarding the nature of the metal atom, because it exhibits the smaller number of C−P bonds, which are found to be about 30 kcal/mol weaker than the C−N ones. In the case of metallapyridines, the formation of an extra C−C bond in the ortho isomer is energetically compensated by the loss of a relatively strong C−N bond, so the energetic differences between the isomers are much smaller than for the metallaphosphinines. For the OsN and RuN families the ortho and meta isomers are almost isoenergetic, whereas in the case of IrN and RhN species the lower stability of the ortho isomer with respect to the meta one is associated with the formation of relatively weak Ir(Rh)−N bonds. The higher stability of the m-MN species with respect to the p-MN ones for any metal atom M is associated with better electrostatic interactions in the former. The bonding energy in the analyzed heterometallabenzenes is found to be somewhat smaller in the 4d complexes, in agreement with the fact that 5d metallabenzenes are more stable than their 4d analogues. Although the formal number of π-electrons in the heterometallabenzenes studied is controversial, the molecular orbitals indicate that they are best described as 10π-electron species. The values of the multicenter index of aromaticity and nucleus-independent chemical shifts point out that the complexes studied should be classified as aromatic or slightly aromatic. Remarkably, we obtain that the aromaticity is not correlated with the stability of the isomer.

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AUTHOR INFORMATION

ACKNOWLEDGMENTS We thank the following organizations for financial support: the Ministerio de Ciencia e Innovación (MICINN, project numbers CTQ2011-23156/BQU, CTQ2011-23441/BQU, and CTQ2011-25086, Ramón y Cajal contract to J.P., and FPI fellowship to M.E.H.), the DIUE of the Generalitat de Catalunya (project numbers 2009SGR637, 2009SGR528, and XRQTC), and the FEDER fund (European Fund for Regional Development) for the grant UNGI08-4E-003. Excellent service by the Centre de Supercomputació de Catalunya (CESCA) is gratefully acknowledged. Support for the research of M.S. was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates (in Å) for all optimized complexes. EDA results for the osmaphosphinines and rhodium and ruthenium heterometallabenzenes. Voronoi charges for all fragments in studied complexes, singlet−triplet energy gaps, and metal contribution to the π molecular orbitals of all heterometallabenzenes analyzed. Figures with the optimized molecular geometry of all heterometallabenzenes analyzed. Plot of the valence π orbitals of the ring of the meta-osmapyridine species. 4901


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Organometallics

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Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Chem. Rev. 2005, 105, 3842. (60) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. J. Chem. Phys. 1996, 104, 5497. Wolinski, K.; Hilton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (61) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon: Oxford, 1990. (62) Cossío, F. P.; Morao, I.; Jiao, H. J.; Schleyer, P. v. R. J. Am. Chem. Soc. 1999, 121, 6737. (63) Schleyer, P. v. R.; Manoharan, M.; Jiao, H. J.; Stahl, F. Org. Lett. 2001, 3, 3643. (64) Corminboeuf, C.; Heine, T.; Seifert, G.; Schleyer, P. v. R.; Weber, J. Phys. Chem. Chem. Phys. 2004, 6, 273. (65) Bickelhaupt, F. M.; Nibbering, N. M. M.; Van Wezenbeek, E. M.; Baerends, E. J. J. Phys. Chem. 1992, 96, 4864. (66) Schaad, L. J.; Hess, B. A. Chem. Rev. 2001, 101, 1465. (67) Estimates of Ir−C (75.2 kcal/mol) and Ir−N (57.3 kcal/mol) bonding energies are obtained from the singlet IrCl2(C2H3)(NCH2) (PH3)2 complex by dissociating it to doublet C2H3 and IrCl2(NCH2) (PH3)2 and doublet NCH2 and IrCl2(C2H3)(PH3)2, respectively. Estimates of Ir−C (71.1 kcal/mol) and Ir−P (55.5 kcal/mol) bonding energies are obtained from the singlet IrCl2(C2H3)(PCH2)(PH3)2 complex by dissociating it to doublet C2H3 and IrCl2(PCH2)(PH3)2 and doublet PCH2 and IrCl2(C2H3)(PH3)2, respectively. Estimates of C−C (111.1 kcal/mol), C−N (98.3 kcal/mol), and C−P (79.8 kcal/ mol) are obtained from homolytic dissociation of ethane, methylamine, and methyphosphine. Estimates of Os−C (74.7 kcal/mol) and Os−N (61.3 kcal/mol) bonding energies are obtained from the singlet OsCl(CO)(C2H3)(NCH2)(PH3)2 complex by dissociating it to doublet C2H3 and OsCl(CO)(NCH2)(PH3)2 and doublet NCH2 and OsCl(CO)(C2H3)(PH3)2, respectively. Estimates of Os−C (73.4 kcal/mol) and Os−P (48.1 kcal/mol) bonding energies are obtained from the singlet OsCl(CO)(C2H3)(PCH2)(PH3)2 complex by dissociating it to doublet C2H3 and OsCl2(PCH2)(PH3)2 and doublet PCH2 and OsCl(CO)(C2H3)(PH3)2, respectively. (68) Pauling, L. J. Am. Chem. Soc. 1932, 54, 3570.

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