Bond Characterization on a CrâCr Quintuple Bond: A Combined

ARTICLE pubs.acs.org/JPCA

Bond Characterization on a CrCr Quintuple Bond: A Combined Experimental and Theoretical Study Lai-Chin Wu,† Chia-Wei Hsu,‡ Yu-Chun Chuang,† Gene-Hsiang Lee,† Yi-Chou Tsai,‡ and Yu Wang*,† † ‡

Department of Chemistry, National Taiwan University, Taipei, Taiwan Department of Chemistry, National Tsing Hua University, Hsinchu, Taiwan

bS Supporting Information ABSTRACT: A combined experimental and theoretical charge density study on a quintuply bonded dichromium complex, Cr2 (dipp)2 (dipp = (Ar)NC(H)N(Ar) and Ar = 2,6-i-Pr2C6H3), is performed. Two dipp ligands are bridged between two Cr ions; each Cr atom is coordinated to two N atoms of the ligands in a linear fashion. The Cr atom is in a low oxidation state, Cr(I), and in low coordination number condition, which stabilizes a metalmetal multiple bond, in this case, a quintuple bond. Indeed, it gives an ultrashort CrCr bond distance of 1.7492(1) Å in the complex. The bond characterization of such a quintuple bond is undertaken both experimentally by high-resolution single-crystal X-ray diffraction and theoretically by density functional calculation (DFT). Electron densities are depicted via deformation density and Laplacian distributions. Bond characterizations of the complex are presented in terms of topological properties, Fermi hole function, source function (SF), and natural bonding orbital (NBO) analysis. The electron density at the CrCr bond critical point (BCP) is 1.70 e/Å 3 , quite a high value for metalmetal bonding and mainly contributed from the metal ion itself. The quintuple bond is confirmed with one σ, two π, and two δ interactions by NBO analysis and Fermi hole function. The molecular orbitals (MOs) illustrate that five bonding orbitals are predominantly contributed from the 3d orbitals of the Cr(I) ion. The effective bond order from NBO analysis is 4.60. The detail comparison between experiment and theory will be given. Additionally, three closely related complexes are calculated for systematic comparison.

’ INTRODUCTION The concept of chemical bond is a very basic but interesting issue for chemists. The bond characters are known to be quite different between main group and transition-metal elements. The highest bond order or the maximum bond multiplicity was known to be three between main group atoms, such as NtN and HCtCH in the sp hybrid. However, the bond order does exceed three in transition-metal complexes, for example, the quadruple bonded complex [Re2(Cl)8]2, which was synthesized in 1964.1 The ReRe bond distance, 2.24 Å, was much shorter than the sum of the covalent radii, 1.51 Å, of Re.2 This bond was qualitatively described as a quadruple bond having σ2π4δ2 configuration, that is, one σ, two π, and one δ bond; four pairs of electrons were shared between two Re atoms. This compound was an important milestone in studying metalmetal bonds; it led to a new era for studies in chemical multiple bonds. Hundreds of complexes with metalmetal (MM) multiple bonds were also synthesized after 1964; several dichromium complexes were reported with a short CrCr bond of around 1.85 Å in late 1970s as having a CrCr quadruple bond.3 The shortest MM bond distance was found to be 1.68 Å in a diatomic molecule, Cr2, which was produced from pulsed YAG laser vaporization of r 2011 American Chemical Society

chromium metal.4 The CrCr bond in this case was proposed to be a sextuple bond (formal bond order, fBO, of 6).57 However, in 2005, the first stable complex with a proposed “CrCr quintuple” bond was synthesized,8 though the distance was relatively long (1.835 Å). In recent years, a series of the dichromium complexes were reported913 with a CrCr bond distance of around 1.75 Å; the shortest one was reported by Wagner et al.14 with a bond distance of 1.729 Å. The actual bond order of these ultrashort metalmetal multiple bonds are still in debate. The complete active space (CAS) calculations were applied to a series of M2 molecules,15 in which Cr2, Mo2, and W2 diatomic species were proposed to have sextuple bond. However, the effective BO (eBO) was 3.5, 5.2, and 5.2, respectively; thus, only Mo2 and W2 could be considered to be close to a sextuple bond. The CI calculations were also performed on a few quadruply bonded bimetal complexes,1618 Special Issue: Richard F. W. Bader Festschrift Received: April 2, 2011 Revised: May 26, 2011 Published: June 21, 2011 12602

dx.doi.org/10.1021/jp203080j | J. Phys. Chem. A 2011, 115, 12602–12615

The Journal of Physical Chemistry A Cr2(O2CH)4 (CrCr = 2.20 Å) and Mo2(O2CH)4 (MoMo = 2.09 Å). The ground-state configuration of the MoMo bond was determined to be 66% σ2π4δ2 (quadruple bond); the eBO is 3.2, but there is only 18% σ2π4δ2 in the case of Cr2(O2CH)4; the eBO is only 1.5, which is much less than the expected value of 4. A CI calculation was performed19 on a complex of [H2P(CH2)2]4Cr2 (simplified from [(CH3)2P(CH2)2]4Cr220) with much shorter CrCr distance of 1.88 Å; there is 55% groundstate configuration and an eBO of 2.9. It is apparently crucial to take into account the contribution from the excited-state configurations for such transition-metal complexes before the eBO can be determined. The CrCr bond in the dinuclear chromium complex,9 Cr2(HLiPr)2, where HLiPr = N,N0 -bis(2,6diisopropylphenyl)1,4-diazadiene), was claimed to have a CrCr quintuple bond with bond distance of 1.8028(9) Å. According to their DFT calculations, five CrCr bonding orbitals were found, and an eBO of 4.28 resulted based on the NRT (Natural Resonance Theory) analysis. Furthermore, an eBO of 3.43 was obtained using the multiconfigurational quantum chemical approach21 (CASSCF/CASPT2); the lower eBO is due to the fact that one of the δ bonds is highly delocalized among Cr N bonds. A pELI-D (positive electron localizability indicator) analysis on a dichromium complex,12 with a bond distance of 1.749(2) Å, demonstrates that the local maxima are related to 1σ, 2π, and 1δ MOs along the CrCr bonding region; an additional maximum is located around each Cr atom, which represents the remaining nonbonding electron. A domain-averaged fermi holes (DAFH) approach22 indicated that this complex is plausibly described as quadruply bonded between two Cr atoms, with one nonbonding electron on each Cr having an antiferromagnetic interaction between the two. Bond characterization of MM multiple bonds is intriguing due to its large variation in bond distances and its extensive possibilities in bond types; for example, the bond distance of the CrCr quadruple bond can be varied from 1.830 to 2.541 Å for dichromium(II) complexes.23,24 Electron density studies25,26 have been used extensively for providing the bond characterization; some results on the MM bond appeared in the literature on metal carbonyl complexes.27 Detailed discussions on the nature of the MnMn bond in Mn2(CO)10 were presented in a series of publications in terms of topological properties analysis,2831 the source function (SF),32 electron localization function (ELF),33,34 and DAFH.35 In early years, charge density studies on the MM multiple bond, both experimentally and theoretically, were applied to a few cases, such as dichromium tetraacetate,36 Cr2(mhp)419 (CrCr = 1.89 Å, mhp = μ-2hydroxy-6-methyl-pyridine) and Mo2(CH3CO2)417 (Mo Mo = 2.09 Å), where a rather diffused deformation electron density of 0.4 e/Å3 was located at the midpoint of the MoMo bond; nevertheless, no other tools for the bond characterization were then available. Taking advantage of all of the available analyses nowadays, especially the Atoms in Molecule (AIM) approach,37 the nature of such short a MM bond could be clearly clarified. A combined study of experimental and theoretical charge density analysis on Cr2(dipp)211 (1, dipp = (Ar)NC(H)N(Ar) and Ar = 2,6-i-Pr2C6H3) with an expected CrCr quintuple bond is undertaken. In order to correlate the bond properties, additional theoretical charge density studies are carried out on a series of closely related complexes, [Cr2(dmp)3] (2), [Cr2(dmp)3] (3) (dmp = Ar0 NC(H)NAr0 , Ar0 = 2,6-C6H3(CH3)2)),10 and Cr2(mhp)4, (4)38 with various

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formal bond multiplicities of 5, 4.5, and 4. The structures of these four compounds are given below.

’ EXPERIMENTAL SECTION Data Collection and Refinement. The high-resolution single-crystal X-ray diffraction data of compound 1 was measured on a Kappa CCD diffractometer at 110 K using Mo KR radiation (wavelength of 0.71073 Å) with a working power of 50 kV and 40 mA. A single crystal with a size of 0.32 0.31 0.27 mm was mounted on a goniometer under the liquid nitrogen stream and placed 4 cm away from the detector. Low- and a high-angle data sets were collected with a scan angle of 0.5°/frame and exposure times of 20 and 100 s, respectively. Diffraction intensities were integrated using the Eval-14 Program39 with 21 21 (pixels) and depths of 5 and 7 frames (39 and 54 pixels), respectively for the lowand high-angle data sets. The maximum sin θ/λ value measured was 1.08 Å1. Two data sets were merged and scaled according to the intensities of the overlapping region after the absorption correction was applied based on the face measurements using SADABS.40 All hydrogen atoms of the dipp ligand were generated according to the ideal geometry (sp2 or sp3) of the connected atoms. Full-matrix least-squares refinement41 on F2 was applied using observed reflections (I > 2σ(I)). All processes were performed using the program SHELXL.42 The crystal data of 1 are deposited in the Cambridge data bank (CCDC: 816528). 12603

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The Journal of Physical Chemistry A

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Table 1. Selected Bond Distances (Å) and Angles (°) of 1, 2, 3, and 4 210

1

438

Qb: Cr(Q)

1

1

1.5

2

fBO CrCr

5 1.7492(1)

4 1.7397(9)

4.5 1.8169(7)

4 1.8794(6)

CrN

2.0183(4), 2.0108(4)

2.092a

2.044a

2.069a

1.3266(6), 1.3250(6)

a

a

1.358a

NC

NCrCr 97.30(1), 98.08(1) a

310

1.327 97.70

a

1.324 96.64

a

91.79a

b

Average values. Q: formal charge of the Cr atom.

Table 2. Agreement Indices of Spherical and Multipole Model Refinements Based on 32521 Reflectionsa

spherical

Figure 2. Crystal structure of 1; molecule 1a and 1b are in the ac plane and oriented differently to each other in the lattice.

Multipole Model Refinement. A multipole model (MM) refinement is applied according to the Hansen and Coppens model43,44 in which the atomic electron density is described as

Fatom ðrÞ ¼ Pc Fcore ðrÞ + Pval k3 Fval ðkrÞ lmax

+ Rl ðrÞ ¼

l

k03 Rl ðk0rÞ ∑ Plm( dlm( ðθ, ϕÞ ∑ m¼0 l¼0

Rlnl + 3 nl Rl r r e ðnl + 2Þ!

The first two terms are the spherical part of atomic electron density; the third term describes the nonspherical part of the electron density, which is expressed as the sum of multipole terms using the real part of spherical harmonic functions (Ylmp); Rl(r) is the radial function; k,k0 serves as the expansioncontraction factor of the radial distribution. Pc and Pval are the populations of the core and valence electrons, respectively; Plm is the coefficient of multipole term; all Plm parameters and Pval, k,k0 are

R1

wR1

R2

wR2 0.0636

504

0.0329

0.0318

0.0446

hexadecapole

1771

0.0251

0.0128

0.0258

0.0255

+k0 3 ξ

1816

0.0251

0.0128

0.0258

0.0255

)

a Nv: number of variables; Rint = ∑[n/(n1)]1/2 |F2o F2o|/∑F2o; R1 = ∑ Fo| |Fc /∑|Fo|; wR1 = (∑|Fo Fc|2/∑w|Fo|2)1/2; R2 = ∑|F2o F2c |/∑F2o; wR2 = {∑[w(F2o F2c )2]/∑[w(F2o)2]}1/2.

)

Figure 1. Molecular structure of 1a (Ci symmetry) with 50% probability in atomic thermal ellipsoids at 110K; the local coordinates of Cr are indicated.

Nv

obtained through the MM refinements using the XD200645 program. The electron configuration of the Cr atom was taken as [Ar]4s13d5 with a K core and 3d5 at the valence shell. Single-ξ Slater-type functions used for Cr, C, N, and H were taken from Clementi and Raimondi;46,47 spherical atomic scattering amplitudes were taken from International Tables for X-ray Crystallography.48 The atomic structural parameters including position and thermal displacements were first refined using high-angle data (sin θ/λ = 0.51); then, the multipole term parameters were refined with full data. The multipole terms were chosen up to the hexadecapole for Cr, up to the octopole for C, N, and O atoms, and up to the dipole for hydrogen atoms. The values of nl are (4 4 4 4) for Cr atom and (2 2 3) for C and N atoms. The final cycle including the refinement of k0 parameter of all atom types was performed in order to obtain suitable ξ values for each atom type. Topological analyses were applied based on Bader’s Atoms in Molecules — A Quantum Theory (QTAIM).37 The experimental total electron density was calculated according to the MM. Topological properties associated with the bond critical point (BCP) and Laplacian distributions were obtained by using the XD2006 program.45 The corresponding DFT calculated ones and Fermi hole distributions were derived from DenProp49 and the XAIM program.50 The SF analyses5153 were applied both in experimental and in theoretical charge density using XD2006 and a modified version54 of the PROMEGA55,56 and PROAIMV,57 respectively.

’ COMPUTATIONAL DETAILS The DFT computations were carried out for 14 using the Gaussian0358 program based on the single-point calculations. The respective geometry was taken from XRD for 1 and 4;38 the optimized geometries from the literature10 were taken for 2 and 3. The hybrid XC functional B3LYP was used with the basis sets of 6-311+G* and 6-31G*, respectively for Cr and for C, N, and H 12604



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Figure 3. Residual density maps at the phenyl ring (a,b) and at the molecular plane of 1a (c). The contour interval is 0.1 e/Å3, and solid line is positive and the dotted line negative; (a) after the spherical model; (b,c) after the MM.

atoms. Natural bond orbital (NBO) analysis was performed by NBO 3.0,59 and eBOs were calculated accordingly. NBO Analysis. The application of the NBO analysis has been described by Weinhold et al.60 The input basis set χi is transformed into various localized basis sets, such as natural atomic orbitals (NAOs), natural hybrid orbitals (NHOs), and NBOs, in which NBOs provide the most probable Lewis structure picture partitioned from the MO coefficients. The NBO analysis provides useful information about the interactions of filled and virtual orbital spaces that could be used to further analyze the chemical bonding. The donoracceptor interactions can be evaluated by carrying out a second-order perturbation theory analysis. The stabilization energy, E(2), is associated with delocalization from the Lewis donor NBO(i) to the empty acceptor NBO(j).60 These noncovalent delocalization effects can be described as donoracceptor, charge transfer, or Lewis baseacid type.60d The NBO analyses of CrCr and CrN bond will be discussed in detail.

’ RESULT AND DISCUSSION Structure Description of 1. The molecular structure of compound 1 is shown in Figure 1. Two independent molecules, one in Ci symmetry (1a) and the other in C2 symmetry (1b), are

found in the crystal lattice. The center of inversion is at the midpoint of the CrCr bond of molecule 1a, where the C2 axis passes through the midpoint of CrCr and is perpendicular to the molecular plane (Cr2N4C2) in molecule 1b. The structures of the two molecules are essentially the same. The results presented here are just from 1a, and those of 1b are given in the Supporting Information (SI). Each Cr atom is three-coordinated in a T-shape geometry with two N atoms in a linear fashion and the other Cr atom in the perpendicular direction. The amidinate ligand, dipp, is a monoanion with the negative charge delocalized on the NC(H)N part. The valence shell electronic configuration of Cr(I) is 3d5, with five d electrons presumably equally distributed among five d orbitals. Such low oxidation and a low coordination number of Cr are key factors to form the MM quintuple bond.8 This complex contains one of the shortest Cr Cr bond distances, 1.7492(1)Å, in the solid state;1012 the average CrN distance is 2.013 Å. The angle of NCrN is 164.7°. Two molecules, 1a and 1b, are orientated alternately on the ac plane and are perpendicular to each other in the crystal depicted in Figure 2. No strong intermolecular interactions or short contacts are found between the molecules. The Cr atoms of [Cr2(dmp)3] (2)10 are bridged by three amidinate ligands with the CrCr bond distance of 1.7397(9) Å; 12605



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Figure 4. Deformation density map of 1a (a) at the molecular plane, xz, (b) perpendicular to the molecular plane, yz, and (c) the cross section view of the CrCr bond, xy. (df) Corresponding maps from the DFT calculations The contour interval is 0.05 e/Å3, and the others are as those given in Figure 3.

here, each Cr is four-coordinated with three N atoms and one Cr atom in a pyramidal shape. The compound 3,10 [Cr2(dmp)3], is one-electron oxidation from 2, with a CrCr bond distance of 1.8169 (7) Å. The compound 4,38 Cr2(mhp)4, contains four bridging ligands and a CrCr bond distance of 1.889(1) Å. The CrCr bond distances of these four compounds follow the order 1 = 2 < 3 < 4 as the fBO decreases from 5 (1,2) to 4.5 (3) to 4 (4). Selected bond distances and angles for these four compounds are listed in Table 1. Multipole Model of 1. The local coordinates of the Cr atom are defined such that the z axis is along the CrCr bond and the y axis is perpendicular to the molecular plane (Cr2C2N4). In order to get more accurate atomic parameters, the data with sin θ/λ greater than 0.5 are used first in the refinement; the multipole coefficients are then refined subsequently. The significant improvement in agreement indices are apparent for the MM (see Table 2); wR2 drops from 0.064 for the spherical model to 0.026 in MM using 32521 observed reflections (I > 3σ(I)). The final k and k0 3 ξ values of the chromium atom are 0.99 and 5.26 (Å1), respectively. The success of the MM is also illustrated in the featureless residual density maps shown in Figure 3b, compared with that from the spherical model in Figure 3a, where substantial residual density is found in the bond regions. The residual density including the CrCr bond given in Figure 3c is reasonable with a slight residual remaining near Cr and N atoms. Deformation Density Maps. The deformation density is the difference in electron density between MM and the independent spherical atomic model (IAM). The deformation density maps are shown in Figure 4. Significant deformation density accumulations are found along CC and CN bonds of the ligand as expected; the density accumulation is also found on the coordinated nitrogen atom at the direction toward the Cr atom, which represents the lone pair of N as a σ donor to Cr. Although the

CrCr bond is expected to be a quintuple bond, the deformation density shows double maxima along the CrCr bond (Figure 4a), unlike those of CC and CN bonds; such a feature was also observed in other SS25 and MM19,36 bonds. However, the cross-sectional view (Figure 4c) is close to a spherical shape, which is consistent with the expected two π bonds. The deformation density shows a significant covalent bond character between two bonded Cr atoms. Good agreement between experiment and theory is illustrated in Figure 4; the theoretical ones gives more regular shape along CrCr bond. Subsequent topological analyses are based on this MM density. Laplacian Distribution. The Laplacian distributions from experiment and theory are in good agreement, as depicted in Figure 5. The CN bond shows the expected feature of a normal covalent bond;37 the valence shell charge concentration (VSCC) of a carbon or nitrogen atom is clearly indicated as an sp2 valence configuration. The lone pair charge concentration of nitrogen atoms demonstrates the donor character of the lone pair toward the Cr atom; it conforms to a typical ML coordinated bond.26a,61,62 Around the Cr atom, it clearly indicates that the 3d electron valence shell is in a rather smooth spherical surface, which conforms to evenly distributed 3d orbital electrons. The Laplacian distribution in experiment (Figure 5b) does show a nearly spherical distribution on the fourth quantum shell but contains two local charge concentrations (LCC) around each Cr along the CrCr direction; that of the theoretical one agrees well with the experimental one, except that there seems to be only one LCC away from the other Cr (Figure 5d). Characterization of the CrCr Quintuple Bond. Characterization of the interatomic interactions in terms of electron density provides a fundamental and an important descriptor of chemical bonding. From the QTAIM concept,37 the existence of BCP and associated bond paths between two atoms is the criterion for any interaction between the atoms. Different types 12606



Figure 5. Laplacian distributions at the molecular plane from (a) experiment and (c) theoretical calculation; the enlarged view around the left Cr atom is shown in (b,d) for experiment and calculation. The contours are plotted at (1)l 2m 10n e/Å5, where l = 0 or 1, m = 13, and n = 33; the solid line (red) is negative, and dashed line (blue) is positive value. The green lines in (a) are the bond paths.

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of chemical interaction, such as shared interaction, known as covalent bonding (e.g., carboncarbon bonding) or polar covalent bonding (e.g., metalligand coordinated bonding), and closed-shell interaction (such as ionic bonding, hydrogen bonding, and even van der Waals interactions) are categorized by their distinct topological properties associated with BCPs. The BCP of the CrCr quintuple bond is localized at the midpoint between Cr atoms; the associated bond paths are easily traced, shown as a green line in Figure 5a; the CrCr, CrN, NC, and CC bonds are all illustrated well in Figure 5a,c. Detail topological properties associated with BCPs are listed in Table 3, together with some relevant properties of MM bonds as well as the wellcharacterized CC multiple bonds. The experimental and theoretical results for 1 are in excellent agreement; the value of Fb at the CrCr bond in 1 is 1.64(1) e/Å3; to the best of our knowledge, this is so far the highest value for the MM bond from experimental charge density studies, which roughly equals that of the CC single bond, 1.62 e/Å3. The Laplacian, r2Fb, at the BCP of CrCr is a large positive number, 31.62 e/Å5, due to the unusually large value of λ3, 57.61 e/Å5, because the CrCr distance is so short that the BCP may lie within the inner core shell of the charge depletion region37,63 of Cr; such a phenomenon was realized27b,37 for the CO molecule a long time ago; this is also recognized for d-block compounds with a metalmetal bond,32 where the higher the fBO, the larger the value of r2Fb. In the case of 14, the r2Fb value is 25 e/Å5 for 1 and 2 (fBO 5), 21 e/Å5 for 3 (fBO 4.5), and 15 e/Å5 for 4 (fBO 4). Nevertheless, (λ1, λ2) of the CrCr bond are clearly large negative values, indicating the local accumulation at the cross section of the bond, similar to those of normal covalent bonds;37 in addition, the value of the total energy density at BCP (Hb) is negative, 0.58 H/Å3, which again strongly supports the covalent bond characters of such CrCr bonds. The topological properties associated with the CrCr BCP is in good agreement between experiment and DFT calculation. The value of Fb is 1.71 e/Å3 from DFT calculations, slightly larger than the experimental one, 1.64 e/Å3. The total energy density Hb of 1.36 H/Å3 from DFT is more negative than the experimental one of 0.58 H/Å3; the difference is mainly attributed to the difference in the potential energy density; the difference in the kinetic energy density is insignificant. The electron density at the BCP, Fb, does correlate with the bond strength; as the value of Fb increases, it normally indicates that the bond strength increases too. For instance, the Fb of the CC bond in C2H6, C2H4, and C2H2 molecules increases when the bond order increases; the Fb's of CC, CdC, and CtC are 1.60, 2.32, and 2.78 e/Å3 respectively,64 which is consistent with the increasing bonding energies of 85, 151, and 200 (kcal/mol),64 respectively. Similar trends are observed in compounds 14. The fBOs of the CrCr bond are 4, 4.5, 5, and 5; the corresponding bond distances are 1.889, 1.802, 1.755, and 1.749 Å, and the corresponding Fb's are 1.27, 1.53, 1.69, and 1.71 e/Å3. The bond strengths of 1 and 2 are roughly the same, and they are stronger than those of 3 and 4. To compare with compounds 14, the MnMn in Mn2(CO)1028 and the CoCo bond in Co2(CO)6(AsPh3)227a show much weaker shared interaction character with a much smaller Fb value (0.2 e/Å3) and a smaller absolute value of Hb (0.03 H/Å3). The Fb values of these two bonds are roughly the same as those of moderate hydrogen bond interactions.65,66 According to the theoretical studies32 on a series of 4d metal complexes with a MM bond in M2L4 (L = HNCHNH), with a Fb value of ∼1.0 e/Å3 for Nb, Mo , and Tc 12607



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Table 3. Topological Properties Associated with MM and CC Bondsa fBO (units)

Fb e/Å3

r2Fb e/Å5

λ1 e/Å5

λ3 e/Å5

Gb H/Å3

Hb H/Å3

Hb/Fb H/e

|Vb|/Gb

H3CCH337

DFT

1

1.530

1.62

13.64

0.42

1.37

0.85

4.26

H2CdCH237

DFT

2

1.340

2.26

23.83

0.95

2.62

1.16

3.76

HCtCH37

DFT

3

1.210

2.66

27.10

1.89

3.79

1.42

3.01

MnMn29

MM

1

2.9042(8)

0.190(4)

0.815(8)

0.20

1.21

0.09

0.03

0.16

1.33

1 1

2.906 2.6430(2)

0.192 0.20(1)

0.124 1.344(8)

0.27

0.65

CoCo27a

DFT MM

0.06 0.12

0.05 0.03

0.26 0.15

1.83 1.25

DFT

1

2.64

0.27

0.04

0.09

0.09

0.33

2.00

MM

5

1.7492(1)

1.64(1)

31.62(4)

13.61

57.61

3.08

0.58

0.35

1.19 1.43

Cr2(dipp)2 (1)

a

dist. Å

DFT

5

1.749

1.71

25.79

10.43

46.37

3.16

1.36

0.80

Cr2(Dmp)3 (2)

DFT

5

1.755

1.69

25.35

10.07

45.47

3.11

1.34

0.79

1.43

Cr2(Dmp)3 (3)

DFT

4.5

1.802

1.53

21.09

- 8.64

38.32

2.61

1.13

0.74

1.43

Cr2(mhp)4 (4)

DFT

4

1.889

1.27

15.42

- 6.39

28.20

Nb2(L)432 Mo2(L)432

DFT DFT

3 4

2.284 2.141

0.88 1.12

8.55 12.48

Tc2(L)432

DFT

3

2.122

1.11

Ru2(L)432

DFT

2

2.540

0.49

Rh2(L)432

DFT

1

2.501

Pd2(L)432

DFT

0

2.730

1.87

0.79

0.62

1.42

0.94 1.37

0.34 0.49

0.39 0.44

1.37 1.36

12.09

1.32

0.48

0.43

1.36

1.59

0.30

0.19

0.38

1.63

0.49

1.67

0.30

0.18

0.37

1.61

0.28

3.61

0.29

0.04

0.13

1.12

L = HNCHNH. MM: from experiment; DFT: from calculation.

Figure 6. Hessian eigenvalues (λ1, λ3) versus bond distance for metalmetal (f, 9), metalligand ((), and intraligand (b) interactions. Lines are given for the simulated CrCr bond.

compounds, which is slightly smaller than the value of the CrCr bond in 4 (1.27 e/Å3), the absolute Hb value is also slightly smaller (∼0.5 H/Å3) than that of 4 (0.79 H/Å3). On the contrary, a much smaller Fb value (∼0.5 e/Å3) and smaller absolute values of Hb (∼0.2 H/Å3) are found for those MM bonds of Ru, Rh, and Pd compounds; therefore, the MM bond is much weaker in Ru, Rh, and Pd than that in Nb, Mo, and Tc. Accordingly, r2Fb, Fb, and Hb values of 4 are basically comparable to those of Mo2L4 with the same fBO of 4; the CrCr bonds in 14 could definitely be characterized as covalent bonds. The values of r2Fb of all of these MM multiple bonds are normally large and positive; however, the sum of the Hessian eigenvalues at the bond cross section, λ1 + λ2, represents substantial local density accumulation at BCPs. The Hessian

eigenvalues of MM, ML, and intraligand bonds versus bond distances are plotted in Figure 6. The experimental and theoretical Hessian eigenvalues of Cr related bonds seem to follow the lines of the simulated CrCr bond based on the same level calculations. As the bond distance decrease, the values of λ1 and λ2 become more negative; this conforms to the increase in bond strength (Fb). The intraligand interactions of 1 (see Figure 6 and detail topological properties given in the SI) can be classified into three groups; the λ1, λ2 value of a CC single bond is 10 e/Å5, that of the CC bond in benzene is 15 e/Å5, and that of a delocalized CN double bond is 20 e/Å3; these values together with their Fb values correlate well with their known corresponding bond orders. Accordingly, the CrCr bond can also be seen into different groups, 10 e/Å5 for 1 and 2, 8 e/Å5 for 3, and 6 e/Å5 for 4, listed in Table 3. The calculated total energy density, Hb, of the CrCr bond in 1 is 1.36 H/Å3, apparently dominated by the potential energy density, like the other CrCr complexes 24 with 1.34, 1.13, and 0.79 H/Å3 respectively. The bond classification of the MM bond is by no means trivial, simply based on the values of Fb and r2Fb; Espinosa67,68 suggested more indices for the bond characterization, that is, Hb/Fb, named the bond degree (BD), which is the ratio of the total energy density and the electron density at the BCP. BDs of CrCr multiple bonds for 14 (0.8 to 0.62 from theory) as listed in Table 3 are bigger negative values than those of MnMn and CoCo (∼0.15) in metal carbonyls.27,28 Basically, the BD values of MM increase with the increase in fBO; in addition, the value of the BD of the CrCr quintuple bond is rather close to that of the CC single bond (0.85). Furthermore, the other index introduced is |Vb|/Gb, which is the ratio of the potential energy density to the kinetic energy density at the BCP; when the ratio of |Vb|/Gb is greater than 2, it is classified as a shared interaction (covalent);31,67 and when it is between 2 and 1, it is transient region, like an incipient covalent bond; when it is less than 1 (or equal to 1 as Hb = 0), it is classified as a closed-shell 12608



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Table 4. AIM Charges of 1a N (e)

atom Cr N N C

Q (e)

L (au)

V001 (Å3)

VTOT (Å3) 22.25

MM

23.52

0.48

0.0008

20.25

DFT

23.33

0.67

0.0009

18.77

23.33

MM

8.07

1.07

11.56

11.56

0.002

DFT

8.32

1.32

0.002

13.29

14.76

MM

8.09

1.09

0.002

11.69

11.69

DFT

8.32

1.32

0.002

13.29

14.76

MM

5.27

0.73

0.001

7.79

7.79

DFT

4.81

1.19

0.004

7.08

8.11

a

MM: R multipole model. VTOT: total atomic volume, VTOT(Ω) = Ω diτ; the V001 is defined as the volume of the region of the atomic basin where F(r) is greater than or equal to 0.001 au, R V001(Ω) = Ω dτ0.001.

Figure 7. (a) The gradient field of the electron density at the molecular plane; atomic basin of (b) Cr and (c) N atoms. Atoms are shown by black dots, BCPs are blue dots, and RCPs (ring critical points) are green dots; the zero flux surface, n 3 rF = 0, is shown by dark red lines; bond paths are blue lines.

interaction. Accordingly, the topological properties associated with the BCP of CrCr as well as CrN bonds of 14 are characterized as incipient covalent bonds. However, the |Vb|/Gb values of the MM bond in 14 are nearly constant, and a similar observation is also given in M2L4 compounds;32 hence, such a |Vb|/Gb value appears inadequate for the classification of the MM bond. On the basis of the further analyses (see below SF, NBO), we believe that the CrN bond is indeed an incipient covalent bond (coordinated bond), but the CrCr should be a covalent bond. As analyzed before on the Crnitrido triple bond,26a it does have quite distinct topological properties than other CrNpy coordinated bonds, such as relatively larger negative values in Hb (1.73 versus 0.03 H/Å3) and larger values in Fb (1.87 versus 0.55). Here, the Hb and Fb values of CrCr bonds in 14 are closer to the values of the CrN triple bond than those of the CrNpy coordinated bond. AIM Charge. Atomic charges can be obtained in various ways depending on how one partitions the electron density among the atoms; the partition gives rise to an atomic basin, where integration on the electron density over each atomic basin yields the number of electrons of the atom. The gradient field on the molecular plane and the atomic basin of Cr and N are given in Figure 7ac, respectively. In this work, the atomic basin is defined by a zero-flux surface (dark-red thick line); such a surface

correlates well with their bonding environment, for example, the atom domains of carbon and nitrogen atoms are in a triangular shape, which corresponds to a sp2 hybrid; that of chromium atom is in a trapezoidal shape, perhaps with sd5 hybrids. The atomic charge thus obtained is called an AIM charge; such charges in 1 are listed in Table 4, where the number of electrons (N) of an atom is obtained by integrating over its atomic basin (VTOT). The atomic charge (Q) is then calculated against the neutral atom; the AIM charge (Q) of the Cr atom is +0.5 from the MM model, which is slightly less than that (+0.67) from DFT calculations. The charges on N and C are roughly 1 and 0.73. V001 is the volume where F(r) is equal to and greater than 0.001 au. It is noticeable that there is no difference between V001 and VTOT for C or N atoms, but it is significantly different by 10% for Cr, which does indicate the rather diffused electron density distribution around Cr. Source Function. The SF was recently developed5153 to further our understanding of the bonding characters by using the topological properties at the BCP, namely, the electron density, Fb, of a certain bond can be partitioned into the sum of the contributions from the atoms. For instance, the value of Fb of the MnMn in the Mn2(CO)10 complex32 was evidence that it was mainly contributed to by carbonyl ligands, especially the oxygen atoms, instead of directly contributed to by Mn atoms. On the contrary, source contributions on Fb of MM from each M is as high as 41% in M2L432 where M = Nb, Mo, and Tc with fBOs of 3, 4, and 3, respectively, where each L contributes ∼4.7%. However, the source contribution from M is very low, ∼17%, when M = Ru, Rh, and Pd, where each L contributes roughly the same, 17%. According to the SF analysis listed in Table 5, the Fb at the Cr Cr bond in 1 is contributed to almost entirely by two Cr atoms with ∼47% each; the source contributions from the ligand are minimal. The DFT calculations give the same conclusion with 93% contribution from two Cr atoms, illustrated in Figure 8; such a feature is the same as that found in the CC bond of acetylene with 47.9% from each C atom. Hence, the SF analysis supports a highly covalent character in the CrCr bond of 1. In general, the MM bond in the d-block element is expected to be strongest in the 4d or 5d series due to the greater spatial expansion of the d orbitals, for example, the MM bond of M2(formate)416 is the strongest when M = Mo and the weakest when M = Cr. Here, we compare the CrCr bond of 4 with the MoMo bond of Mo2L4. The SF contribution to the Fb is slightly higher in the CrCr bond (82.5 versus 81.2%), and both should be covalent; perhaps 12609



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Table 5. Source Function Contributions at bcps of CrCr and CrX (X = N or O) of 1 and 4 CrCr

1 FMM, DFT

1.641, 1.712 3

S (e/Å )

atom Cr Cr N N C ∑S% of CrX, X = Cr, N

CrN 0.619, 0.616 3

S%

S (e/Å )

S%

MM

0.787

48.0

0.223

36.1

DFT

0.794

46.4

0.218

35.4

MM

0.789

48.1

0.042

6.7

DFT

0.794

46.4

0.058

9.4

MM DFT

0.004 0.002

0.2 0.1

0.171 0.190

27.7 30.8

MM

0.005

0.3

0.008

1.3

DFT

0.002

0.1

0.003

0.5 5.1

MM

0.012

0.7

0.031

DFT

0.017

1.0

0.035

5.7

MM

1.575

96.0

0.395

63.8

DFT

1.588

92.8

0.408

66.2

4 FDFT

CrCr

CrN

CrO

1.267

0.543

0.626

S (e/Å3)

atom

S%

S (e/Å3)

S%

S (e/Å3)

S%

Cr

DFT

0.523

41.3

0.149

27.5

0.193

30.8

Cr

DFT

0.522

41.2

0.030

5.6

0.030

4.7

N

DFT

0.005

0.4

0.140

25.7

0.005

0.8

O

DFT

0.014

1.1

0.009

1.6

0.232

37.1

C ∑S% of CrX, X = Cr, N, O

DFT DFT

0.009 1.040

0.7 82.1

0.021 0.319

3.9 58.8

0.022 0.213

3.6 67.9

Fermi Hole Analysis. The Fermi hole (FH) distribution37 is

Figure 8. Source function contribution in percentage (S%) at BCPs of CrCr and CrX (X = N or O) bonds in compounds 1 and 4. Blue and red dots indicate source and sink contributions, respectively.

in this case, the CrCr bond is slightly stronger, though Cr is a 3d metal ion but in a low oxidation state. As for the character of the CrN bond of 1, the major contribution comes from the bonded Cr and N atoms with high contributions of 36.4 and 26.5%, respectively; the neighboring Cr and C atoms contribute 7.5 and 5.4% to this bond. The corresponding DFT values are in good agreement with the experimental ones, except one of nitrogen atom gives an opposite contribution in sign to CrN. To compare the CrN bond of 4 with that of M2L4,32 shown in Figure 8, it is clear that the source contribution from the bonded atoms is ∼60%, which is similar to those of M2L4; however, the other Cr contributes ∼5%, similar to that when M = Mo but much higher than that when M = Pd. This also explains the difference in the MM bond between Mo and Pd.

based on the Pauli exclusion principle, which represents the probability of finding an electron with the same spin of the reference electron in space; in other words, the distribution correlates exactly with the paired electron spin in space, that is, the indication of electron localization and delocalization from the reference point. It has been used to clarify the ML σ and dp π bond.26c,d,61,69 In order to characterize the CrCr quintuple bond, the FH distributions are undertaken for 1, depicted in Figure 9; the reference electron (f) is sequentially placed at 1.0 and 1.5 au away from the Cr atoms in the directions of the σ and π orbitals in the yz and xz planes (Figure 9ac). The FH distributions apparently spread out from the target Cr atom to the bonded Cr atom with expected σ and π bond features. Interestingly, as the reference electron is placed at 2 au away from Cr atom in the direction perpendicular to the CrCr bond, which is the maximum of the dx2y2 or dxy orbital, to illustrate the FH distribution on account of the δ bond, it is not so easy to present such a distribution in one diagram; therefore, it is displayed in two planes, that is the yz or [110] plane and two xy planes containing each Cr atom (Figure 9dg). As the reference electron is placed close to one Cr atom, the δ bond feature is clearly demonstrated on the other Cr atom 1.75 Å away. According to the Fermi hole density distribution, it only spreads out to two Cr atoms, which strongly supports a dd interaction, dx2y2 dx2y2, δ bond. However, the Fermi hole density of the dxydxy δ bond spreads out not only over the CrCr bond but also over the CrN bond (Figure 9g), though it is still majorly on two Cr atoms. Overall, such Fermi hole distributions do provide 12610



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Figure 9. Fermi hole distribution of the CrCr bond of 1 with the reference electron (f) placed (a) at 1 au away from Cr atom along CrCr bond and at 1.5 au away from Cr for π interactions at the (b) xz and (c) yz planes, and (d,e and f,g) at 2 au away from Cr for dx2y2δ and dxyδ interactions, respectively; (e) and (g) are plotted in the xy plane including the Cr1 atom at z = 0 and the Cr2 atom at 1.75 Å. The contours are in atomic units with 2i 10j (i = 13; j = 30). The CrN bond with the reference electron (f) placed at 0.5 au away from N atom along the (h) σ direction and (i) π interaction.

Figure 10. Bonding MOs of the CrCr bond of 1 (ae) and of 4 (fi).

important features of MM σ, π, and δ bonds as well as those of CrN σ and π bonding characters (Figure 9h,i). Further illustration on the bond characterization is given by the following molecular orbital (MO) and natural orbital analysis. MO Analysis. The MOs of the CrCr quintuple bond have recently been studied10,11,21,70 a great deal. The quintuple bond is confirmed with five bonding orbitals, namely, one σ, two π, and two δ bonds in which two π bonds are purely from d orbitals; on the contrary, the σ and the two δ bonds are in sd hybrid orbitals.10,11,70 The MOs of 2 (fBO = 5) are also found to have five bonding orbitals (1σ, 2π, 2δ); those of 3 (fBO = 4.5) are found10 to have four bonding orbitals (1σ, 2π, 1δ) plus a singly occupied bond orbital (δdx2y2). Again, four bonding MOs are

found in 4, namely, 1σ, 2π, and 1δ. Here, we present the CrCr bonding MOs of 1 and 4 in Figure 10. The MOs of 1 and 210 are similar, where five bonding orbitals are indeed clearly identified, two degenerate δ MOs, which are hybrids of dxydxy and dx2y2dx2y2 interactions (Figure 10a,b), two degenerate π MOs formed by dxzdxz and dyzdyz interactions (Figure 10d,e), and one σ MO formed by a dz2dz2 interaction (Figure 10c). The relative orbital energies of these five MOs are in the order of dδ = dδ > dσ > dπ > dπ. The energy difference between dσ and dπ MOs is about 0.3 eV, and it is about 0.2 eV between two dπ MOs. In 4, four bonding MOs (1σ, 2π, 1δ) are illustrated in Figure 10fi, in which the energy of the dδ bond is the highest one; the other three (dσ, dπ) are roughly degenerate. The energy 12611



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Table 6. Natural Bonding Orbital (NBO) Analysis of the CrCr Bond of 1, 2, 3, and 4 σ 3d%a

(fBO)

occ.

1

1.99

96

(5)

d z2

dx2y2, s

2

1.98

100

(5)

d z2

3

a

π 4s%a 4

occ. 1.97

π 3d%a

3d%a

occ.

100

2.00

dxz 1.98

δ

100

dyz 100

1.98

dxz

100

dyz

δ

occ.

3d%a

1.96

78

dx2y2

dz2, s

1.63

100

0.99

99

1

0.99

100

0.99

100

0.87

100

0.99

99

1

0.99

100

0.99

100

0.87

100

97

2

d z 2, s 1.97 d z 2, s

dxz 1.97 dxz

dyz 99

22

1.84

100

1.81 dx2y2

eBOb

100

4.6

100

4.1

99

3.8

dxy 1.63 0.88

dx2y2

1.97 dyz

3d%a

dxy

β 4 (4)

occ.

dx2y2

R

(4.5)

4s%a

dxy 100

3.4

The percentage of s or d orbitals in hybrid orbitals. b eBO = effective bond order = (no. of bonding electrons no. of antibonding electrons)/2.

Table 7. Selected DonorAcceptor Interactions of 1 Based on the Second-Order Perturbationa donor NBO (i) LP(1) LP(1)

a

N3 N6

E(2) kcal/mol

E(j) E(i) eV

F(i,j) eV

Cr1 Cr2

84.64 85.62

8.30 8.30

4.35 4.63

CrN σ CrN σ N σ + CrCr π*

acceptor NBO (j) LP*(1) LP*(1)

LP(1)

N3

BD*(3)

Cr1Cr2

10.35

9.51

1.63

LP(1)

N6

BD*(3)

Cr1Cr2

9.85

9.51

1.63

LP(1)

N3

BD*(4)

Cr1Cr2

16.09

9.08

1.90

LP(1)

N6

BD*(4)

Cr1Cr2

15.75

9.08

1.90

LP(2)

N6

BD*(5)

Cr1Cr2

9.17

4.39

1.09

DA interaction

N σ + CrCr δ* L π + CrCr δ*

LP for a one-center valence lone pair, and * represents unoccupied; BD* is the two-centered antibonding. L is the ligand.

gaps between the HOMO and LUMO are 3.11 eV for 1 and 3.43 eV for 4. It is worth noticing that one of the dπ MOs of 1, a dxzdxz interaction (Figure 10d), does not only contribute to the CrCr π bond but also slightly interacts with the p orbital of N atoms, indicating π delocalization among CrCr and the NCN ligand, similar to what was found in Cr2(HLiPr)2;9 however, the occupancy of the CrCr dπ bonding orbital of 1 is as high as 1.97. On the contrary, the MCI quantum chemical approach on the simplified quintuple Cr2(HLiPr)2 compound21 illustrated that one dδ MO is in very low occupancy, 0.09, whereas the CrN π bonding orbital is found to be in high occupancy of 1.83. Therefore, the five bonding orbitals in 1 are all with high occupancies, which justifies the quintuple CrCr bond character. NBO Analysis. Furthermore, NBO analyses on the CrCr bonds of 14 listed in Table 6 are also quite consistent with those of MOs illustrated in Figure 10. There are a total of five bonding NBOs for 1, 2, and 3 and a total of four bonding NBOs for 4. In 1, two π and one δ bonds are 100% contributed to by dxz, dyz, and dxy orbitals. The other δ bond is a hybrid of 4s, 3dz2, and 3dx2y2, which can be recognized as side-on sdπδ hybrid orbitals;70 the contributions of 4s and 3d orbitals are 22 and 78%, respectively. Furthermore, the σ bond is also a combination of 4s, dx2y2, and dz2, with the d orbital as the highest contribution (96%) and only 4% from 4s. The bonding orbitals of 24 are almost 100% contributed to by 3d orbitals. The eBO of the CrCr bond thus calculated is 4.6, 4.1 3.8 and 3.4 for 1, 2, 3, and 4, respectively. Nevertheless, such an eBO is purely calculated from the ground-state configuration; it would be somewhat smaller if the limited or full CI were taken into account.1618 In summary, the outcome of NBO analyses confirms that the CrCr multiple bonds are essentially formed from 3d orbitals

Table 8. Occupancies and Compositions of NHOs for the Selected Lewis Donor and Acceptor NBOsa (%) orb. energy NBO

bond

eV

occ s%

p%

d%

BD (1) Cr1Cr2

π, dyz

6.37

2.00

BD (2) Cr1Cr2

σ, dz2

6.28

1.99

BD (3) Cr1Cr2

π, dxz

6.12

1.97

BD (4) Cr1Cr2

δ, dx2y2

6.41

1.96 22

78

4.01 10.09

1.84 1.72 27

100

BD (5) Cr1Cr2 δ, dxy LP (1) N3, N4, N5, N6 px LP (2)

N5, N6

py

LP*(1) Cr1, Cr2

5.34

100 4

1.49

1.79

0.34 75

π*, dyz

0.09

0.05

BD*(2) Cr1Cr2

σ*, dz2

0.12

0.03

BD*(3) Cr1Cr2

π*, dxz

0.58

0.12

BD*(4) Cr1Cr2

δ*, dx2y2

BD*(5) Cr1Cr2

δ*, dxy

a

1.01

25 100

4

0.18 22 0.23

73 100

BD*(1) Cr1Cr2

0.95

96 100

96 100 78 100

LP and BD are as those in Table 7.

of two Cr atoms; the same conclusion is drawn from the SF analyses. In the former section, the Fermi hole density indicates that the d electron might be delocalized between Cr and N atoms. In order to understand this observation, the second-order perturbation theory analyses are performed. The selected donoracceptor 12612



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are in good agreement and also give substantial insight concerning MM bonding. Typically, large negative values of Hb and high Fb values found in ML multiple bond are also observed here with the CrCr bond of 14. The quintuple bond of 13, composed of one σ, two π, and two δ bonds, is well verified with SF, Fermi hole density, MOs, and NBOs. The SF analysis does provide a clear picture of the major contributions on the MM bond. The σ bond of CrN is recognized as a pure donation of lone pair electrons from N to Cr; the π bond is represented through pπ of NCN and the CrCr δ*(dxy) orbitals. Significant electron delocalization is demonstrated between ligand dipp orbitals and MM π* and δ* orbitals, which slightly weaken the MM bonding to make the eBO less than five. This may provide clues on the future design of proper ligands particularly for MM multiple bonds. The eBO thus derived is 4.6, 4.1, 3.8, and 3.4, respectively, for 1, 2, 3, and 4. In summary, the characteristics on the CrCr bond of these four complexes are depicted as follows in its geometry, distance, eBO, and Fb values. Figure 11. Relative energy levels of selected frontier NBOs; (a) all orbitals concerned; lone pair (LP) of N with antibonding orbitals (BD*) of the CrCr bond at the (b) molecular plane and (c) perpendicular plane.

results of 1 are listed in Table 7, and the related NHO characters of NBO are analyzed in Table 8. Each one is described in terms of filled (donor) Lewis-type NBOs and empty (acceptor) NBOs as well as the orbital occupancy. Such analyses have been applied on the understanding of metalligand71 and hydrogen bonds.72 The donoracceptor interactions of CrN are represented mainly between the lone pair, LP(1) (px), of the nitrogen atoms with the unoccupied lone pair orbital, LP*(4s), of the Cr atom, which contributes a significant stabilization energy of 85 kcal/ mol. This interaction represents CrN σ interactions. The CrN π interactions are observed as py of N coupled with the δ*dxy antibonding orbital of the CrCr bond, giving a stabilization energy, E(2), of around 5 kcal/mol. It is worth noticing that the sum of the occupancies of five bonding orbitals of the CrCr bond is 9.76, very close to being fully occupied (Table 8), whereas the total occupancies of the CrCr antibonding orbitals is around 0.6, which is not negligible and which comes from the ligand donor on the CrCr π* and two δ* orbitals. This observation supports the idea of the presence of electron delocalization between the NCN ligand and two Cr atoms. This also provides a good explanation for the eBO of 4.6 for the Cr Cr bond. The relative orbital energies of relevant donor and acceptor orbitals derived from NBO are plotted in Figure 11, where the interactions on the molecular plane (xz) and those in the π (y) direction are separated on different columns for clarity. Here, it is clear that the py lone pairs of nitrogen atoms are delocalized among CrCr δ* orbitals; such analyses are quite consistent with what was shown in the Fermi hole density depicted in Figure 9hi. In short, the MO analyses, NBO, Fermi hole density, and SF all provide clear evidence of CrCr quintuple bond character.

’ CONCLUSION The MM bond character of 3d-block elements exhibits a wide variety; on the basis of the electron density at the BCPs, it can be indicative of a very weak bond such as the MnMn bond in Mn2(CO)10 or a characteristic covalent bond in Cr2(dipp)2. The topological properties between experiment and theory for 1

’ ASSOCIATED CONTENT

bS

Supporting Information. (a) Electron density maps of molecule 1b; (b) the energy diagram of MM orbitals of compounds 1 and 4; (c) plot of BD versus |Vb|/Gb classifying interatomic interactions; (d) table of crystal data and structure refinement of 1; (e) AIM charges of 1b; (f) complete topological properties of 1; and (g) donoracceptor interactions of 1a. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. 12613



’ ACKNOWLEDGMENT This work is supported by the National Science Council of Taiwan. We thank the National Center for High-Performance Computing (NCHC) for part of the computing and are grateful to Prof. Gatti for providing the SF_ESI programs. Thanks are also due to Prof. Wang and Prof. Lu at the Department of Chemistry, Soochow University, Taipei, for helpful discussions. ’ REFERENCES (1) Cotton, F. A.; Curtis, N. F.; Johnson, B. F. G.; Mague, J. T.; Wood, J. S.; Harris, C. B.; Robinson, W. R.; Lippard, S. J. Science 1964, 145, 1305–1307. (2) Cordero, B.; Gomez, V.; Platero-Prats, A. E.; Reves, M.; Echeverria, J.; Cremades, E.; Barragan, F.; Alvarez, S. Dalton Trans. 2008, 21, 2832–2838. (3) Bino, A.; Cotton, F. A.; Kaim, W. J. Am. Chem. Soc. 1979, 101, 2506–2507. (4) Bondybey, V. E.; English, J. H. Chem. Phys. Lett. 1983, 94, 443–447. (5) Weltner, W.; Vanzee, R. J. Annu. Rev. Phys. Chem. 1984, 35, 291–327. (6) Frenking, G.; Tonner, R. Nature 2007, 446, 276–277. (7) Merino, G.; Donald, K. J.; D’Acchioli, J. S.; Hoffmann, R. J. Am. Chem. Soc. 2007, 129, 15295–15302. (8) Nguyen, T.; Sutton, A. D.; Brynda, M.; Fettinger, J. C.; Long, G. J.; Power, P. P. Science 2005, 310, 844–847. (9) Kreisel, K. A.; Yap, G. P. A.; Dmitrenko, O.; Landis, C. R.; Theopold, K. H. J. Am. Chem. Soc. 2007, 129, 14162–16163. (10) Tsai, Y. C.; Hsu, C. W.; Yu, J. S. K.; Lee, G. H.; Wang, Y.; Kuo, T. S. Angew. Chem., Int. Ed. 2008, 47, 7250–7253. (11) Hsu, C. W.; Yu, J. S. K.; Yen, C. H.; Lee, G. H.; Wang, Y.; Tsai, Y. C. Angew. Chem., Int. Ed. 2008, 47, 9933–9936. (12) Noor, A.; Wagner, F. R.; Kempe, R. Angew. Chem., Int. Ed. 2008, 47, 7246–7249. (13) Noor, A.; Glatz, G.; Muller, R.; Kaupp, M.; Demeshko, S.; Kempe Z. Anorg. Allg. Chem. 2009, 635, 1149–1152. (14) Wagner, F. R.; Noor, A.; Kempe, R. Nat. Chem. 2009, 1, 529–536. (15) Roos, B. O.; Borin, A. C.; Gagliardi, L. Angew. Chem., Int. Ed. 2007, 46, 1469–1472. (16) Atha, P. M.; Hillier, I. H.; Guest, M. F. Mol. Phys. 1982, 46, 437–448. (17) Hino, K.; Saito, Y.; Benard, M. Acta Crystallogr., Sect. B 1981, 37, 2164–2170. (18) Cotton, F. A.; Murillo, L. A.; Walton, R. A. Multiple Bonds Between Metal Atoms, 3rd ed.; Springer: Berlin, Germany, 2005. (19) Mitschler, A.; Rees, B.; Wiest, R.; Benard, M. J. Am. Chem. Soc. 1982, 104, 7501–7509. (20) Cotton, F. A.; Hanson, B. E.; Ilsley, W. H.; Rice, G. W. Inorg. Chem. 1979, 18, 2713–2717. (21) La Macchia, G.; Aquilante, F.; Veryazov, V.; Roos, B. O.; Gagliardi, L. Inorg. Chem. 2008, 47, 11455–11457. (22) Ponec, R.; Feixas, F. J. Phys. Chem. A 2009, 113, 8394–8400. (23) Cotton, F. A.; Koch, S. Inorg. Chem. 1978, 17, 2021–2024. (24) Cotton, F. A.; Extine, M. W.; Rice, G. W. Inorg. Chem. 1978, 17, 176–186. (25) (a) Wang, C. C.; Hong, Y. Y.; Ueng, C. H.; Wang, Y. J. Chem. Soc. Dalton 1992, 3331–3336. (b) Lin, K. J.; Wang, Y. J. Phys. Chem. 1993, 97, 3176–3182. (c) McCormack, K. L.; Mallinson, P. R.; Webster, B. C.; Yufit, D. S. J. Chem. Soc., Faraday Trans. 1996, 92, 1709–1716. (26) (a) Wang, C. C.; Tang, T. H.; Wang, Y. J. Phys. Chem. A 2000, 104, 9566–9572. (b) Lee, J. J.; Lee, G. H.; Wang, Y. Chem.—Eur. J. 2002, 8, 1821–1832. (c) Lee, C. R.; Tang, T. H.; Chen, L.; Wang, Y. Chem.— Eur. J. 2003, 9, 3112–3121. (d) Wang, C. C.; Tang, T. H.; Wu, L. C.; Wang, Y. Acta Crystallogr., Sect. A 2004, 60, 488–493. (e) Farrugia, L. J.;

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