Building a Bridge between Coordination Compounds and Clusters

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Building a Bridge between Coordination Compounds and Clusters: Bonding Analysis of the Icosahedral Molecules [M(ER)12] (M = Cr, Mo, W; E = Zn, Cd, Hg) Moritz von Hopffgarten and Gernot Frenking* Fachbereich Chemie, Philipps-Universit€at Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany

bS Supporting Information ABSTRACT: The bonding situation of the icosahedral compounds [M(EH)12] (M = Cr, Mo, W; E = Zn, Cd, Hg), which are model systems for the isolated species [Mo(ZnCp*)3(ZnMe)9] possessing the coordination number 12 at the central atom M, have been analyzed with a variety of charge and energy decomposition methods (AIM, EDA-NOCV, WBI, MO). The results give a coherent picture of the electronic structure and the nature of the interatomic interactions. The compounds [M(EH)12] are transition metal complexes that possess 12 M-EH radial bond paths (AIM) that can be described as 6 three-center two-electron bonds (MO). The radial M-EH bonds come from the electron sharing interactions mainly between the singly occupied valence s and d AOs of the central atom M and the singly occupied EH valence orbitals (MO, EDA-NOCV). The orbital interactions provide ∼42% of the total attraction, while the electrostatic attraction contributes ∼58% to the metal
ligand bonding (EDA-NOCV). There is a weak peripheral E
E bonding in [M(EH)12] that explains the unusually high coordination number (MO). The peripheral bonding leads for some compounds [M(EH)12] to the emergence of E
E bond paths, while in others it does not (AIM). The relative strength of the radial and peripheral bonding in [Al13]
and [Pt@Pb12]2
is clearly different from the situation in [M(EH)12], which supports the assignments of the former species as cluster compounds or inclusion compounds (MO, WBI). The bonding situation in [WAu12] is similar to that in [M(EH)12].

1. INTRODUCTION Molecular compounds with coordination numbers larger than 8 to monodentate ligands are rare even for heavy transition metal atoms. The maximum coordination number 15 for monodentate ligands has been proposed for the system [PbHe15]2+ by Schwerdtfeger et al. in a computational study.1 The recent synthesis of the thorium complex [Th(H3BNMe2BH3)4] with four aminodiboronates acting as 4- and 3-dentate chelating borohydrate ligands exhibiting a coordination number of 15 clearly represents a highlight in the search for the largest possible coordination number in molecular compounds.2 Large numbers of nearest neighbor atoms can also be obtained in cluster compounds like [Pt@Pb12]2
.3 In contrast to coordination compounds, they are stabilized by strong peripheral interactions. Consequently a description of the compound with the coordination number concept of Werner4 becomes inadequate. In [Pt@Pb12]2
, the empty [Pb12]2
cage provides 26 valence electrons. Its existence and geometry is predicted by the Wade
Mingos rules5 and the cage is further stabilized by the insertion of the Pt atom.3b The tungsten compounds [WH12]6 and [WAu12]7 were first theoretically predicted and afterward observed in the gas phase and matrix experiments. A computational analysis of [WH12] revealed that tungsten binds to four hydrogen atoms and to four r 2011 American Chemical Society

H2 molecules in a side-on fashion. Thus, it should be written as [WH4(H2)4], implying a coordination number of eight.6a On the other hand, [WAu12] forms a perfect icosahedron, where all W
Au interactions are identical. The cases of [WH4(H2)4] and [WAu12] indicate that the formation of an icosahedral molecule is influenced by the strength of the radial and tangential interactions. Strong radial stabilization and the ability to form delocalized bonds over the peripheral atoms support the formation of the icosahedron. The stability of [WAu12] was explained by efficient radial W
Au bonding and by stabilizing peripheral aurophilic interactions both being substantially strengthened by relativistic effects.7a In this context, the synthesis and X-ray structure analysis of [Mo(ZnCp*)3(ZnMe)9] (4, Me = CH3, Cp* = C5Me5)8 from [Mo(GaCp*)6] and ZnMe2 was of great interest. With 12 ZnR moieties, each providing one valence electron for bonding, the molecule fulfills, like WAu12, the 18 valence electron rule. Aurophilic interactions are absent and relativity should not play Special Issue: Richard F. W. Bader Festschrift Received: April 26, 2011 Revised: July 28, 2011 Published: August 09, 2011 12758

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an important role for the stability of 4. The synthesis of 4 was the starting point of extensive experimental and computational studies on the unprecedented class of Zinc-rich transition metal compounds with coordination numbers g8 at the central atoms. So far, syntheses and preliminary bonding analyses of 4, [Ru(ZnCp*)4(ZnMe)6], [Rh(ZnCp*)3(ZnMe)6], and [TM(ZnCp*)4(ZnMe)4] (TM = Ni, Pd, Pt) have been reported.9 All molecules fulfill the 18 valence electron rule, which may thus be used as a heuristic guideline for the prediction of new members of this class of compounds. For example, the formal partial substitution of Zinc by Cadmium has been reported

recently, resulting in the isolated compounds [Mo(CdMe)9(ZnCp*)3], [Pd(CdMe)4(ZnCp*)4], and [Pt(CdCp*)4(CdMe)4].10 In this work we explore the bonding situation of the hydrogensubstituted model compounds [M(EH)12] (1H
9H), where M = Cr, Mo, W and E = Zn, Cd, Hg. We compare the electronic structures of 1H
9H with the cluster compounds [Al13]
and [Pt@Pb12]2
and with the hexacarbonyls [M(CO)6]. The performance of various DFT methods, which are based on the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, as well as hybrid and metahybrid variants, are compared in their performances on geometries, energies, and bonding analyses of 1H
9H.

2. THEORETICAL METHODS Geometry optimizations using density functional theory (DFT) at various levels were performed with different combinations of exchange and correlation functionals: Local DFT was employed using the functional SVWN.11,12 We also used the GGAs (generalized gradient approximations) BP8613,14 and PBE.15 At the meta-GGA level, we applied the functional TPSS.16 At the hybrid-DFT level, we used B3LYP17,18 and PBE0.19 We also employed the meta-hybrid functional TPSSh.20 The RIapproximation21 was applied in all DFT calculations. Ahlrich’s def2-TZVPP22 and the corresponding auxiliary basis sets23 for the RI approximation were used together with the Stuttgart/ K€oln effective core potentials (ECP).24 The combination of TZVPP basis sets and ECPs is abbreviated as TZVPP. The stationary points were characterized by calculating the Hessian matrices.25 The latter calculations could not be

Figure 1. Graphical representations of the energy minimum geometries of (a) [Mo(ZnCp)3(ZnMe)9] (4Cp): hydrogen atoms are omitted for clarity; and (b) [Mo(ZnH)12] (4H): Mo, red; Zn, green; C, black; and H, gray.

Table 1. Intermetallic Distances in the Dodeca-Coordinated Compoundsa method

compound

bond

BP86/ TZVPP

B3LYP/ TZVPP

PBE/ TZVPP

PBE0/ TZVPP

SVWN/ TZVPP

TPSS/ TZVPP

TPSSh/ TZVPP

2.636
2.677b 2.724
2.853b

[Mo(ZnCp*)9(ZnMe)9] (4)

Mo
Zn Zn
Zn [Mo(ZnCp)9(ZnMe)9] (4Cp) Mo
Zn Zn
Zn Cr
Zn [Cr(ZnH)12] (1H) Zn
Zn Cr
Cd [Cr(CdH)12] (2H) Cd
Cd Cr
Hg [Cr(HgH)12] (3H) Hg
Hg Mo
Zn [Mo(ZnH)12] (4H) Zn
Zn Mo
Cd [Mo(CdH)12] (5H) Cd
Cd Mo
Hg [Mo(HgH)12] (6H) Hg
Hg W
Zn [W(ZnH)12] (7H) Zn
Zn W
Cd [W(CdH)12] (8H) Cd
Cd W
Hg [W(HgH)12] (9H) Hg
Hg

X-ray

2.667
2.679 2.800
2.839 2.610 2.744 2.883 3.032 2.903 3.052 2.684 2.822 2.931 3.082 2.949 3.100 2.695 2.834 2.937 3.088 2.954 3.106

2.704
2.710 2.836
2.865 2.643 2.779 2.915 3.065 2.931 3.082 2.717 2.857 2.963 3.115 2.977 3.130 2.727 2.868 2.968 3.120 2.982 3.136

2.663
2.680 2.802
2.834 2.613 2.747 2.886 3.035 2.902 3.051 2.686 2.824 2.933 3.084 2.947 3.099 2.696 2.835 2.939 3.090 2.952 3.104

2.664
2.674 2.803
2.812 2.612 2.746 2.869 3.016 2.871 3.019 2.686 2.825 2.918 3.068 2.920 3.070 2.698 2.837 2.925 3.075 2.927 3.077

2.571
2.593 2.704
2.739 2.519 2.649 2.779 2.922 2.799 2.943 2.602 2.736 2.835 2.981 2.852 2.999 2.616 2.751 2.844 2.991 2.861 3.008

2.638
2.658 2.774
2.804 2.582 2.715 2.850 2.997 2.869 3.016 2.660 2.797 2.901 3.051 2.917 3.067 2.672 2.809 2.908 3.058 2.923 3.074

2.643
2.656 2.782
2.796 2.586 2.720 2.848 2.995 2.861 3.008 2.664 2.801 2.900 3.049 2.910 3.059 2.676 2.814 2.907 3.057 2.917 3.067

a Comparison of experimental molecular structure data from crystal structure analysis and different DFT calculations. Distances in Å. b Taken from ref 8.

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Table 2. Energies ΔEe of the Reaction [M(GaH)6] + 12 EH2 f [M(EH)12] + 6 GaH3 and Zero Point Corrected Energies ΔEo for BP86/TZVPPa BP86/TZVPP

a

ΔEe

ΔEo

B3LYP/TZVPP

PBE/TZVPP

PBE0/TZVPP

SVWN/TZVPP

TPSS/TZVPP

TPSSh/TVPP

ΔEe

ΔEe

ΔEe

ΔEe

ΔEe

ΔEe

[Cr(ZnH)12] (1H)


74.5


69.6


35.2


92.7


83.7


160.3


106.8


100.1

[Cr(CdH)12] (2H)


42.4


34.5


11.7


56.9


52.1


119.5


76.6


71.6

[Cr(HgH)12] (3H) [Mo(ZnH)12] (4H)

+38.2
96.0

+39.0
89.9

+67.2
65.1

+25.3
114.7

+29.2
116.7


49.9
180.4


1.8
129.8

+3.2
127.6
108.2

[Mo(CdH)12] (5H)


71.5


62.0


48.0


86.7


93.1


151.3


108.9

[Mo(HgH)12] (6H)

+8.1

+10.5

+30.2


5.4


11.9


82.7


34.9


33.8

[W(ZnH)12] (7H)


100.3


94.0


70.3


119.2


122.7


185.4


134.5


132.9

[W(CdH)12] (8H)


73.1


63.3


50.3


88.5


97.1


154.6


111.4


111.5

[W(HgH)12] (9H)

+5.4

+8.2

+26.6


8.3


17.2


86.9


38.4


38.2

Single point calculations on BP86/TZVPP structures were performed. Energies in kcal/mol.

performed for [Mo(ZnCp)3(ZnMe)9] (4Cp) due to the excessive computational cost. We characterized optimized structures obtained with Ahlrich’s def2-SVP basis set,22 in this case, assuming that the final TZVPP structure exhibits the same number of imaginary modes. All parent structures were confirmed to be minima on the potential energy surface (no imaginary modes). The 4Cp structures were confirmed to be true minima or to exhibit only small imaginary frequencies ( Cd > Hg. The calculations thus predict that the most stable compound of the series is [W(ZnH)12] (7H) and the least stable molecule is [Cr(HgH)12] (3H). Because [Mo(ZnCp*)3(ZnMe)9] is experimentally known; the tungsten homologue [W(ZnCp*)3(ZnMe)9] (7) should be accessible. 3.2. Bonding Analysis. To get insight into the bonding situation of the title molecules, we first examined their molecular orbitals (MOs). The icosahedral point group Ih has nondegenerated irreducible representations ag and au, triply degenerated sets t1g, t2g, t1u, and t2u, quadruply degenerated gg and gu, and quintuply degenerated hg and hu irreducible representations.

Atomic s orbitals of an atom in the center of an icosahedral molecule are in the ag irreducible representation, p orbitals in t1u, and d orbitals in hg. In 4H, the highest occupied molecular orbital (HOMO) is triply degenerated t1u, followed by a set of quintuply degenerated hg MOs (HOMO-1) and, close in energy to each other, an ag (HOMO-2) and triply degenerated t2u MOs (see Figure 2 for a plot of the energy order of the occupied valence orbitals). Visual inspection of the occupied valence MOs (Figure 3) reveals that the four highest sets of occupied orbitals can be associated with Mo
Zn-, Zn
Zn-, and Zn
H- interactions. The HOMO (t1u) is mainly constructed from p-atomic orbitals at the zinc atoms (Znp-AOs) exhibiting bonding interactions with the hydrogen atoms but also with neighboring zinc atoms. The HOMO-1 set (hg) is constructed from Znp-AOs interacting 12762

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Table 3. Wiberg Bond Indices (WBI) of Radial M
E and Peripheral E
E Bonds in [M(EH)12] (M = Cr, Mo, W; E = Zn, Cd, Hg) at BP86/TZVPP WBI M

E

M
E

E
E

[Cr(ZnH)12] (1H)

Cr

Zn

0.42

0.10

[Cr(CdH)12] (2H)

Cr

Cd

0.43

0.10

[Cr(HgH)12] (3H)

Cr

Hg

0.42

0.11

[Mo(ZnH)12] (4H)

Mo

Zn

0.46

0.11

[Mo(CdH)12] (5H) [Mo(HgH)12] (6H)

Mo Mo

Cd Hg

0.50 0.47

0.12 0.13 0.09

[W(ZnH)12] (7H)

W

Zn

0.44

[W(CdH)12] (8H)

W

Cd

0.47

0.11

[W(HgH)12] (9H)

W

Hg

0.45

0.11

Figure 5. Molecular orbital correlation diagram of the interaction Mo + (ZnH)12, as chosen for the EDA-NOCV. Orbital energies E in eV.

with hydrogen and with the d orbitals of the molybdenum atom. The HOMO-2 is the totally symmetric ag MO, which mainly represents the interaction of the Znp-AOs with the s-AO at molybdenum. The HOMO-3 (t2u) set does not contain any Mo
Zn interactions, but only Zn
H bonding. The remaining valence MOs include three more sets of orbitals describing Mo
Zn interactions: 11hg consists of Zn interactions with the Mod-AOs, 11t1u has contributions of the Mop-AOs and 7ag includes the Mos-AO. The three sets of orbitals have only small coefficients at Mo. The 11hg and 11t1u sets describe interactions with Zns-AOs. All other valence MOs consist of linear combinations of d-AOs at the zinc atoms showing none or negligible contributions of AOs at molybdenum or hydrogen. We denote these sets as Znd orbitals in the MOscheme (Figure 2). Figure 3 shows one member of each MO set of the Znd orbital block. The shapes of the orbitals in all compounds 1H
9H are similar to those in 4H. In some cases, the energy order of the MOs changes slightly (see Figures S1a
c in the Supporting Information for a plot of the energy levels of the occupied valence MOs of 1H
9H). We also analyzed the electronic structure of [M(EH)12] with the AIM method. Figure 4 shows the contour plots of the Laplacian r2F(r) and the molecular graphs of 1H
9H. All molecules exhibit M
E and E
H bond paths, but only three species ([Cr(CdH)12], [Cr(HgH)12], and [Mo(HgH)12])

Figure 6. Graphical representation of NOCV deformation densities of Mo + (ZnH)12. Blue surfaces indicate regions of charge accumulation, red surfaces indicate regions of charge depletion. Energy values ΔE of the corresponding orbital interactions in kcal/mol. Isosurfaces at +0.001 au (blue) and
0.001 au (red).

possess E
E bond paths. It seems that E
E bond paths in [M(EH)12] are more likely to show up for heavier elements E and for lighter central atoms M. This does not mean that there is a qualitative difference between the bonding situation in compounds [M(EH)12] with and without E
E bond paths. The calculation of [M(EH)12] species with slightly distorted geometries exhibit E
E bond paths that are absent in the Ih equilibrium geometry. The calculated Wiberg bond indices (WBI) of 1H
9H (Table 3) for the radial M
E bonds are between 0.4
0.5, while the bond orders for the peripheral interactions are substantially smaller (0.09
0.13). The WBI values agree with the visual inspection of the shape of the molecular orbitals and with the results of the AIM analysis, which reveal bond paths for the strong M
E interactions, while the much weaker peripheral E
E bonding in[M(EH)12] is a borderline case for exhibiting bond paths. The charge partitioning analysis of the bonding situation in [M(EH)12] was complemented by an energy partitioning analysis. To this end, we calculated the interaction of the central atoms M with the (EH)12 fragment with the EDA-NOCV. Electronic states of the fragments were chosen in a way which resembles the degeneracy of the molecular orbitals: Interactions of the d-AOs of the central atom M with (EH)12 are always quintuply degenerated so each should be treated equally. The valence d-AOs of the central atoms are singly occupied resulting in an s1d5 valence orbital occupation, which correlates with the 12763

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The Journal of Physical Chemistry A corresponding 7Ag state of the (EH)12 fragment. Unpaired electrons at the central atoms have R spin, while those at the (EH)12 fragments have β spin. Figure 5 shows the resulting MO correlation diagram of 4H. While in the standard EDA scheme the orbital interaction is decomposed into contributions from the different irreducible representations, in EDA-NOCV it is decomposed into contributions from different NOCV pairs that are combined to NOCV deformation densities Fdef (see the original literature35a for details). Each individual contribution represents the energy change due to the deformation of the associated electron density F upon bond formation. In general, only few Fdef have significant contributions to ΔEorb.35a We present and discuss the results for [Mo(ZnH)12] in more detail in order to elucidate the EDANOCV approach. Figure 6 shows deformation densities of 4H that supply >1.0 kcal/mol to ΔEorb. The largest contribution comes from deformation density Fdef(1R). It corresponds to a donation of R electron density from the valence s-AO at molybdenum into the (ZnH)12 fragment. The β donation from (ZnH)12 into the s-AO is described by Fdef(6β). The contribution of the latter is much smaller (
2.3 kcal/mol) than that of Fdef(1R) (
94.2 kcal/mol). They sum up to
96.5 kcal/mol of s-type orbital stabilization. Deformation densities Fdef(2R)-Fdef(6R) describe R-electron donations from d-AOs of molybdenum into the cage and Fdef(1β)-Fdef(5β) are the respective donations of β-electron density into the d-AOs. The orbital energy contributions of Fdef(2R)-Fdef(6R) and Fdef(1β)-Fdef(5β) amount to
287.5 kcal/mol of total d-type orbital interactions (71.2% of ΔEorb) in 4H (Table 4). As the valence p-AOs of molybdenum are vacant and the t1u fragment orbitals at (ZnH)12 are doubly occupied, Fdef(7R)-Fdef(9R) as well as Fdef(7β)-Fdef(9β) describe electron donation from (ZnH)12 into the valence p-AOs of molybdenum contributing much less to ΔEorb (
13.8 kcal/mol; 3.4%) than the s- and d-type interactions. The very similar appearance of the p-type deformation densities of R and β electrons that exhibit very different stabilization energies arise from a technical issue of the EDA-NOCV. The EDA-NOCV can only be performed for identical R and β orbitals that may have different occupations. As the p-type orbitals of R- and β-electrons have the same occupation, the respective deformation densities are the same as well. Nevertheless, the R and β orbitals have different energies in the fragments due to the singly occupied ag and hg fragment orbitals. Hence, the resulting orbital stabilization contributions differ even for electrons from doubly occupied orbitals. The remaining part of the orbital stabilization that is not covered by the 18 deformation densities presented in Figure 6 is only 1.4%. The results are similar to those obtained from the standard EDA scheme that were discussed for 4H in our previous communication.8 The numerical results of the EDA-NOCV calculations are given in Tables 4
6. The total interaction energy ΔEint for M-(EH)12 increases for each atom E in the order Cr < Mo < W (
277.5 kcal/mol for 1H,
349.0 kcal/mol for 4H, and
391.0 kcal/mol for 7H). The same trend Cr < Mo < W is observed for the Pauli repulsion ΔEPauli, the electrostatic interactions ΔEelstat and the orbital interactions ΔEorb. Orbital interactions contribute about 40% of the total attractive interactions. Tables 4
6 gives the assignments to s-, p-, and d-type deformation densities and the corresponding contributions to the total orbital interactions ΔEorb of all species [M(EH)12]. Graphical representations of the deformation densities Fdef are given in the Supporting Information (Figures S2a
h). A striking

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Table 4. Results of EDA-NOCV Analyses of [M(ZnH)12] Compounds (M = Cr, Mo, W) at BP86/TZ2P+a Cr + (ZnH)12

Mo + (ZnH)12

W + (ZnH)12

ΔEint


277.5


349.0

ΔEPauli

495.0

594.6


391.0

ΔEelstatb


452.6

(58.6%)
540.1

(57.2%)
581.0

(58.3%)

ΔEorbb


320.0

(41.4%)
403.5

(42.8%)
416.4

(41.8%)

606.4

R Fdef(1R) c
106.9 (s) Fdef(2R) c
46.8 (d)


94.2 (s)
39.8 (d)


81.4 (s)
43.1 (d)

Fdef(3R) c
46.8 (d)


39.8 (d)


43.1 (d)

Fdef(4R) c
46.8 (d)


39.8 (d)


43.0 (d)

Fdef(5R) c
46.8 (d)


39.8 (d)


43.1 (d)

Fdef(6R) c
46.8 (d)


39.8 (d)


43.0 (d)

Fdef(7R) c
3.1 (p)


3.1 (p)


3.5 (p)

Fdef(8R) c
3.1 (p)


3.1 (p)


3.5 (p)

Fdef(9R) c
3.1 (p)


3.1 (p)


3.5 (p)

Fdef(1β) c +7.3 (d)


17.8 (d)


18.6 (d)

Fdef(2β) c +7.3 (d)


17.8 (d)


18.6 (d)

Fdef(3β) c +7.3 (d)


17.8 (d)


18.6 (d)

Fdef(4β) c +7.3 (d)


17.8 (d)


18.6 (d)

Fdef(5β) c +7.3 (d)


17.8 (d)


18.6 (d)

Fdef(6β) c
1.3 (s)


2.3 (s)


5.7 (s)

Fdef(7β) c
1.4 (p)


1.5 (p)


1.7 (p)

Fdef(8β) c
1.4 (p) Fdef(9β) c
1.4 (p)


1.5 (p)
1.5 (p)


1.7 (p)
1.7 (p)

β

sum s d


108.2

(33.8%)
96.5

(23.9%)
87.1

(20.9%)

sum d d


197.5

(61.7%)
287.5

(71.2%)
308.3

(74.0%)

sum p d


13.5

(4.2%)

rest d


0.8

( Mo > W (
108.2 kcal/mol and 33.8% for 1H,
96.5 kcal/mol and 23.9% for 4H,
87.1 kcal/mol and 20.9% for 7H). In chromium molecules the donation of the unpaired β electrons from the (EH)12 fragments into the singly 12764

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Table 5. Results of EDA-NOCV Analyses of [M(CdH)12] Compounds (M = Cr, Mo, W) at BP86/TZ2P+a Cr + (CdH)12

Mo + (CdH)12

Table 6. Results of EDA-NOCV Analyses of [M(HgH)12] Compounds (M = Cr, Mo, W) at BP86/TZ2P+a

W + (CdH)12

Cr + (HgH)12

Mo + (HgH)12

W + (HgH)12

ΔEint


233.3


307.9


343.7

ΔEint


253.5


328.7

ΔEPauli

412.4

514.1

520.2

ΔEPauli

457.5

567.5

ΔEelstatb


406.1

(62.9%)
492.5

(59.9%)
520.5

(60.2%)

ΔEelstatb


450.0

(63.3%)
539.3

(60.2%)
564.5

(60.1%)

ΔEorbb


239.5

(37.1%)
329.6

(40.1%)
343.5

(39.8%)

ΔEorbb


261.0

(36.7%)
356.9

(39.8%)
374.7

(39.9%)

R


365.1 574.1

R

Fdef(1R) c
85.1 (s)


81.4 (s)


67.8 (s)
30.8 (d)

Fdef(1R) c
88.8 (s) Fdef(2R) c
35.0 (d)


85.5 (s)
32.8 (d)

Fdef(2R) c
31.3 (d)


28.4 (d)


70.9 (s)
36.0 (d)

Fdef(3R) c
31.3 (d)


28.4 (d)


30.8 (d)

Fdef(3R) c
35.0 (d)


32.8 (d)


36.0 (d)

Fdef(4R)
31.3 (d) Fdef(5R) c
31.3 (d)


28.4 (d)
28.4 (d)


30.8 (d)
30.8 (d)

Fdef(4R) c
35.0 (d)


32.8 (d)


36.0 (d)

Fdef(5R) c
35.0 (d)


32.8 (d)


36.0 (d)

Fdef(6R) c
31.3 (d)


28.4 (d)


30.8 (d)

Fdef(6R) c
35.0 (d)


32.8 (d)


36.0 (d)

Fdef(7R) c
3.4 (p)


3.0 (p)


3.9 (p)

Fdef(7R) c
3.6 (p)


3.2 (p)


4.0 (p)

Fdef(8R) c
3.4 (p)


3.0 (p)


3.9 (p)

Fdef(8R) c
3.6 (p)


3.2 (p)


4.0 (p)

Fdef(9R) c
3.4 (p)


3.0 (p)


3.9 (p)

Fdef(9R) c
3.6 (p)


3.2 (p)


4.0 (p)

Fdef(1β) c +4.5 (d)


16.7 (d)


18.0 (d)

Fdef(1β) c +5.3 (d)


15.8 (d)


17.3 (d)

Fdef(2β) c +4.5 (d)


16.7 (d)


18.0 (d)

Fdef(2β) c +5.3 (d)


15.8 (d)


17.3 (d)

Fdef(3β) c +4.5 (d) Fdef(4β) c +4.5 (d)


16.7 (d)
16.7 (d)


18.0 (d)
18.0 (d)

Fdef(3β) c +5.3 (d)


15.8 (d)


17.3 (d)

Fdef(4β) c +5.3 (d)


15.8 (d)


17.3 (d)

Fdef(5β) c +4.5 (d)


16.7 (d)


18.0 (d)

Fdef(5β) c +5.3 (d)


15.8 (d)


17.3 (d)

Fdef(6β) c
2.4 (s)


3.1 (s)


7.3 (s)

Fdef(6β) c
2.7 (s)


3.2 (s)


7.4 (s)

Fdef(7β) c
1.6 (p)


1.4 (p)


1.9 (p)

Fdef(7β) c
1.7 (p)


1.5 (p)


2.0 (p)

Fdef(8β) c
1.6 (p)


1.4 (p)


1.9 (p)

Fdef(9β) c
1.6 (p)


1.4 (p)


1.9 (p)

Fdef(8β) c
1.7 (p) Fdef(9β) c
1.7 (p)


1.5 (p)
1.5 (p)


2.0 (p)
2.0 (p)

c

β

sum sd d

sum d sum pd d

remain

β


87.5

(36.5%)
84.5

(25.6%)
75.1

(21.9%)

sum sd


91.5

(35.1%)
88.7

(24.9%)
78.3

(20.9%)


134.0
15.0

(55.9%)
225.5 (6.3%)
13.2

(68.4%)
244.0 (4.0%)
17.4

(71.0%) (5.1%)

sum dd


148.5

(56.9%)
243.0

(68.1%)
266.5

(71.1%)

sum pd


15.9

(6.1%)


14.1

(4.0%)


18.0

(4.8%)


3.0

(1.2%)

(2.0%)

remaind


5.1

(2.0%)


11.1

(3.1%)


11.9

(3.2%)


6.4

(1.9%)


7.0

a

a

Fragments were chosen as M s1Rd5R and (CdH)12 ag1βhg5β. Energies in kcal/mol. b Values in parentheses give the percentage contributions to the total attractive interactions ΔEelstat + ΔEorb. c Values in parentheses give the eigenvalues |v(| of the corresponding NOCV pairs. d Values in parentheses give the percentage contributions to the total orbital interactions ΔEorb.

Fragments were chosen as M s1Rd5R and (HgH)12 ag1βhg5β. Energies in kcal/mol. b Values in parentheses give the percentage contributions to the total attractive interactions ΔEelstat + ΔEorb. c Values in parentheses give the eigenvalues |v(| of the corresponding NOCV pairs. d Values in parentheses give the percentage contributions to the total orbital interactions ΔEorb.

occupied d-AOs at Cr yields small destabilizing contributions to ΔEorb. This destabilization is overcompensated by the backdonation of the unpaired d-electrons at Cr into the hg fragment orbitals at (EH)12, which yields attractive d-type interactions. This shows that in an electron-sharing bond it is not necessary to stabilize both electrons as long as net stabilization is obtained. The donation of electrons into the d-AOs at Cr is necessary for electron pairing but orbital stabilization is only obtained from the synchronous back-donation of the d-electrons at Cr. The donation of unpaired electrons into singly occupied d-AOs of Cr is less favorable than donation into d-AOs at Mo and W. The EDA-NOCV analysis thus provides evidence that the main orbital bonding interactions come from electron-sharing bonds with valence s and d electrons of the central atom. The energetically highest lying hg and ag orbitals (HOMO-1 and HOMO-2 in 4H, Figure 3) are the MOs that describe these interactions. Donation into vacant p-AOs at the central atom is small. Hence, 12 valence electrons (VE) are substantially involved in chemical bonding of the central atom M with the ligand

cage (EH)12. The t1u MOs (HOMO in 4H, Figure 3) exhibit only small contributions from the p-AOs of M and are the most important orbitals for E
E bonding. Counting 12 VE for 12 M
E interactions, only six VE remain for 30 equal peripheral E
E interactions. These 6 electrons occupy the 12t1u MOs. Thus, the s1d5 occupation of the valence AOs of M yield sd5 hybridized orbitals. The six sd5 hybrid orbitals form an icosahedron,43 the two lobes per hybrid orbital pointing toward opposite corners (Figure 7). In this model, each of the six sd5 hybrid orbitals forms a linear 2-electron-3-center E
M
E bond using 12 VE in total. The calculated Wiberg bond indices of ∼0.4 for radial M
E bonds are in good agreement with the expected bond order of 0.5. Six VE for 30 equal E
E interactions are 1/10 electron pair per interaction, which is also in good agreement with the small Wiberg bond indices for E
E bonds (∼0.1, Table 3). Hence, E
E bonding interactions are present in all title compounds but they are weak. Sometimes they result in bond critical points in the electron density and sometimes not; the overall picture of the 12765

dx.doi.org/10.1021/jp2038762 |J. Phys. Chem. A 2011, 115, 12758–12768

The Journal of Physical Chemistry A AIM results can be explained by the small bond orders of the E
E interactions. Note that the model of sd5 hybridization has been successfully applied earlier for the explanation of the equilibrium structures of [MH6] and [M(CH3)6] compounds (M = Mo, W), which exhibit C3v symmetry instead of Oh.43b,44 Their energy minimum geometries can be derived from an icosahedron spanned by the six sd5 hybrid orbitals. A total of 6 of the 12 corners are occupied by ligands; the corners opposite to the ligands are vacant. 3.3. Comparison with Other Icosahedral Compounds and with Transition Metal Complexes. It is helpful to compare the bonding properties of [M(EH)12] with structurally related systems such as the typical cluster compound [Al13]
(10), the inclusion compound [Pt@Pb12]2
(11), the gold compound [WAu12] (12), and the hexacarbonyls [M(CO)6] (M = Cr, Mo, W; 13
15). Figure 8 shows contour plots of the Laplacian r2F(r) of the electron densities and the molecular graphs of 10
12. All compounds show peripheral bond paths.

ARTICLE

Table 7 gives the Wiberg bond indices (WBI) of 10
15, which may be compared with the values for [M(EH)12] (Table 3). There is a striking difference between the latter systems and the values for 10 and 11, where the bond indices for peripheral bonding (0.42 and 0.44) are much higher than in [M(EH)12] (0.09
0.13). The WBI values for peripheral bonding in 10 and 11 are even larger than the data for the radial bonding (0.34, 0.35). The calculated bond indices support the classification of 10 and 11 as cluster compounds, where the bonding within the cage is stronger than between the central atom and the peripheral atoms. The WBI values for the radial bonds (0.66) but also for the peripheral bonds (0.17) in 12 are both larger than for [M(EH)12], which explains why there are Au
Au bond paths in the former compound. The WBI values suggest that the bonding situation in [WAu12] is related to the bonding situation in [M(EH)12]. The data in Table 7 reveal a significant difference between the inclusion compound [Pt@Pb12]2
and [WAu12]. The WBI results support the assignment of the latter compound by Pyykk€o7a who suggested that [WAu12] should not be considered as an inclusion compound. The bond indices for the carbonyls [M(CO)6] serve as reference values for a standard transition metal complex that has only radial bonds but no peripheral bonds. Graphical representations of the molecular graphs of [M(CO)6] are given in Figure S3 in the Supporting Information. Figure 9 shows the energetically highest lying occupied MOs of [Al13]
(10) and [Pt@Pb12]2
(11), which may be compared with the related MOs of [Mo(ZnH)12] (Figure 3). It becomes obvious that the orbitals that are most strongly associated with radial bonding (7t1u, 7ag in 10, 9hg, 8hg, 6ag in 11) have significantly smaller overlap between the valence AOs of the Table 7. Internuclear Distances d in Å and Wiberg Bond Indices WBI of BP86/TZVPP for Compounds 10
15 M


Figure 7. Graphical representation of six sd5 hybrid orbitals.

E d(M
E) d(E
E) WBI(M
E) WBI(E
E)

[Al13] (10)

Alc Alp

2.666

2.803

0.34

[Pt@Pb12] (11)

Pt

Pb

3.106

3.266

0.35

0.44

[WAu12] (12)

W

Au

2.742

2.883

0.66

0.17

[Cr(CO)6] (13) Cr C

1.907

2.697

1.10

0.04

[Mo(CO)6] (14) Mo C

2.060

2.913

1.10

0.03

[W(CO)6] (15)

2.071

2.928

1.11

0.03

W

C

0.42

Figure 8. Contour plots of the Laplacian r2F(r) of the electron density and molecular graphs of the icosahedral molecules [Al13]
(10), [Pt@Pb12]2
(11), and [WAu12] (12). Solid lines connecting the atom critical points represent the bond paths. Solid lines separating the atomic basins which cross the bond paths at the bond critical points indicate the zero-flux surfaces crossing the molecular plane. 12766

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The Journal of Physical Chemistry A

ARTICLE

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

Figure 9. Graphical representation of relevant Kohn
Sham MOs of [Al13]
(10; top) and [Pt@Pb12]2- (11; bottom). One orbital of each set of the five highest occupied molecular orbitals is presented. Isosurfaces are at 0.033 au.

central atom and the peripheral atoms than in [Mo(ZnH)12]. Thus, the summing-up of the results which come from different methods for analyzing the electronic structure of a molecule (AIM, EDA-NOCV, WBI, MO) gives a coherent picture of the bonding situation in the novel icosahedral complexes [M(EH)12] and in the systems [Al13]
[Pt@Pb12]2
and [WAu12].

4. SUMMARY The bonding situation in [M(EH)12], which are model compounds for the isolated species [Mo(ZnCp*)3(ZnMe)9], has been analyzed with a variety of charge and energy decomposition methods (AIM, EDA-NOCV, WBI, MO), which give a coherent picture of the electronic structure and nature of the interatomic interactions. The compounds [M(EH)12] are transition metal complexes that possess 12 M-EH radial bond paths (AIM) that can be described as 6 three-center two-electron bonds (MO). The radial M
EH bonds come from the electron sharing interactions mainly between the singly occupied valence s- and d-AOs of the central atom M and the singly occupied EH valence orbitals (MO, EDA-NOCV). The orbital interactions provide ∼42% of the total attraction, while the electrostatic attraction contributes ∼58% to the metal
ligand bonding (EDA-NOCV). There is weak peripheral E
E bonding in [M(EH)12], which explains the unusually high coordination number (MO). The peripheral bonding leads for some compounds [M(EH)12] to the emergence of E
E bond paths, while in others it does not (AIM). The relative strength of the radial and peripheral bonding in [Al13]
and [Pt@Pb12]2
is clearly different from the situation in [M(EH)12], which supports the assignments of the former species as cluster compounds or inclusion compounds (MO, WBI). The bonding situation in [WAu12] is similar to that in [M(EH)12]. ’ ASSOCIATED CONTENT

bS

Supporting Information. Cartesian coordinates of all calculated molecules, BP86/TZ2P+ geometry parameters, WBI from different functionals and basis sets, energy levels of orbitals, and graphical representations of deformation densities and molecular graphs. This material is available free of charge via the Internet at http://pubs.acs.org.

’ ACKNOWLEDGMENT Excellent service of the Hochschulrechenzentrum of the Philipps-Universit€at Marburg is gratefully acknowledged. Further computer time was provided from the Centre for Scientific Computing of the Goethe-Universit€at Frankfurt/Main. This work was supported by the Deutsche Forschungsgemeinschaft (Project No. FR641/23-1). ’ REFERENCES (1) (a) Hermann, A.; Lein, M.; Schwerdtfeger, P. Angew. Chem. 2007, 119, 2496–2499. Angew. Chem., Int. Ed. 2007, 46, 2444–2447. (2) (a) Daly, S. R; Piccoli, P. M. B.; Schultz, A. J.; Todorova, T. K.; Gagliardi, L.; Girolami, G. S. Angew. Chem. 2010, 122, 3451–3453. Angew. Chem., Int. Ed. 2010, 49, 3379–3381. (3) (a) Esenturk, E. N.; Fettinger, J.; Lam, Y.-F.; Eichhorn, B. Angew. Chem. 2004, 116, 2184–2186. Angew. Chem., Int. Ed. 2004, 43, 2132– 2134. (b) Esenturk, E. N.; Fettinger, J.; Eichhorn, B. J. Am. Chem. Soc. 2006, 128, 9178–9186. (4) Werner, A. Z. Anorg. Chem. 1893, 3, 267–330. (5) (a) Wade, K. Adv. Inorg. Chem. Radiochem. 1976, 18, 1–66. (b) Mingos, D. M. P. Acc. Chem. Res. 1984, 17, 311–319. (6) (a) Gagliardi, L.; Pyykk€o, P. J. Am. Chem. Soc. 2004, 126, 15014–15015. (b) Wang, L.; Andrews, X.; Infante, I.; Gagliardi, L. J. Am. Chem. Soc. 2008, 130, 1972–1978. (c) Infante, I.; Gagliardi, L.; Wang, X.; Andrews, L. J. Phys. Chem. A 2009, 113, 2446–2455. (7) (a) Pyykk€o, P.; Runeberg, N. Angew. Chem. 2002, 114, 2278– 2280. Angew. Chem., Int. Ed. 2002, 41, 2174–2176. (b) Autschbach, J.; Hess, B. A.; Johansson, M. P.; Neugebauer, J.; Patzschke, M.; Pyykk€o, P.; Reiher, M.; Sundholm, D. Phys. Chem. Chem. Phys. 2004, 6, 11–22. (c) Li, X.; Kiran, B.; Li, J.; Zhai, H.-J.; Wang, L.-S. Angew. Chem. 2002, 114, 4980–4983. Angew. Chem., Int. Ed. 2002, 41, 4786– 4789. (8) (a) Cadenbach, T.; Bollermann, T.; Gemel, C.; Fernandez, I.; v. Hopffgarten, M.; Frenking, G.; Fischer, R. A. Angew. Chem. 2008, 120, 9290–9295. Angew. Chem., Int. Ed. 2008, 47, 9150–9154. (9) Cadenbach, T.; Bollermann, T.; Gemel, C.; Tombul, M.; I.; v.; Hopffgarten, M.; Frenking, G.; Fischer, R. A. J. Am. Chem. Soc. 2009, 101, 16063–16077. (10) Bollermann, T.; Cadenbach, T.; Gemel, C.; v. Hopffgarten, M.; Frenking, G.; Fischer, R. A Chem.—Eur. J. 2010, 16, 13372–13384. (11) Slater, J. C. Phys. Rev. 1951, 81, 385–390. (12) Vosko, S.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200– 1211. (13) Becke, A. D. Phys. Rev. A 1988, 38, 3098–3100. (14) Perdew, J. P. Phys. Rev. B 1986, 33, 8822–8824. (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (16) Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Phys. Rev. Lett. 2003, 92, 146401. (17) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (18) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789. (19) Perdew, J. P.; Ernzerhof, M.; Burke, K. J. Chem. Phys. 1996, 105, 9982–9985. (20) Staroverov, V. N.; Scuseria, G. E.; Tao, J.; Perdew, J. P. J. Chem. Phys. 2003, 119, 12129–12137. (21) Ahlrichs, R. Phys. Chem. Chem. Phys. 2004, 6, 5119–5121. (22) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. € (23) (a) Eichkorn, K.; Treutler, O.; Ohm, H.; H€aser, M.; Ahlrichs, R. Chem. Phys. Lett. 1995, 242, 652–660. (b) Eichkorn, K.; Weigend, F.; 12767

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