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Organometallics 2004, 23, 1790-1796
Chemical Structures from the Analysis of Domain-Averaged Fermi Holes. The Nature of Ga-Ga Bonding in PhGaGaPh2- and (PhGaGaPh)Na2 Robert Ponec,*,† Gleb Yuzhakov,† Xavier Girone´s,‡ and Gernot Frenking*,§ Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Prague 6, Suchdol 165 02, Czech Republic, Computational Chemistry Group, Medicinal Chemistry Department, AstraZeneca R&D, Mo¨ lndal, Sweden, and Fachbereich Chemie, Philipps-Universita¨ t Marburg, D-35023 Marburg, Germany Received December 30, 2003
The nature of the Ga-Ga bond in the naked dianion PhGaGaPh2- and its Na+-coordinated counterpart is discussed using the recently proposed formalism based on the analysis of domain-averaged Fermi holes. The analysis shows clearly that three electron pairs, i.e., two σ and one π, contribute to the Ga-Ga bonding interactions in the free dianion PhGaGaPh2and in the sodium-complexed species (PhGaGaPh)Na2. The eigenvalues and the eigenvectors of the Fermi hole indicate, however, that the Ga-Ga bonding situation does not correspond to classical triple bonds and should not be interpreted using classical bonding models. The reason is that only one of the three electron pairs involved in Ga-Ga bonding, namely that contributing to the Ga-Ga π bond, corresponds to an “ordinary” shared electron pair bond in the sense of Lewis. The bonding interactions of the other two pairs are much more complex and have no classical counterparts. The eigenvalues and the eigenvectors of the latter Fermi holes cannot be considered as fully bonding, but they have partial lone-pair character. This is why the calculated bond orders yield values which are close to a weak double bond. Essentially the same bonding picture holds also for the Na+-coordinated species, but the coordination of sodium causes further weakening of the contributions of all three electron pairs to the Ga-Ga bonding. This weakening yields an effective reduction of the multiplicity of the Ga-Ga bond. The calculated bond order therefore has a value which is otherwise typical for single bonds. Introduction The chemistry of compounds containing multiple bonds between heavier main-group elements has undergone vigorous development in recent years.1-8 Numerous molecules which contain formal double or triple bonds that were previously thought unable to exist have been synthesized, and their structure and properties were characterized by X-ray structure analyses and spectroscopic measurements. However, the assignment of a compound to contain a multiple bond between heavier main-group elements has not always been undisputed, because the geometries of the molecules prevented in many cases a straightforward interpretation of the bonding situation. In particular, there are two controversies concerning the bonding situation of * To whom correspondence should be addressed. E-mail: ponec@ icpf.cas.cz (R.P.);
[email protected] (G.F.). † Czech Academy of Sciences. ‡ AstraZeneca. § Philipps-Universita ¨ t Marburg. (1) Power, P. P. J. Chem. Soc., Dalton Trans. 1998, 2939. (2) Power, P. P. Chem. Rev. 1999, 99, 3463. (3) Weidenbruch, M. J. Organomet. Chem. 2002, 646, 39. (4) Uhl, W. Coord. Chem. Rev. 1997, 163, 1. (5) Uhl, W. Rev. Inorg. Chem. 1998, 18, 239. (6) (a) Linti, G.; Schno¨ckel, H. Coord. Chem. Rev. 2000, 206-207, 285. (b) Schno¨ckel, H.; Schnepf, A. Adv. Organomet. Chem. 2001, 47, 235. (7) Robinson, G. H. Acc. Chem. Rev. 1999, 32, 773. (8) Weidenbruch, M. Angew. Chem. 2003, 115, 2322; Angew. Chem., Int. Ed. 2003, 42, 2222.
gallium compounds. One example is the Fe-Ga bond in (CO)4FeGaPh, for which a multiplicity ranging from 1 to 3 was proposed.9-11 It seems that a recent energy decomposition analysis settled the question in favor of an Fe-Ga single bond.12 Similar ambiguities exist, which have not been resolved so far, concerning the nature of the Ga-Ga bond in molecules such as [(C6H3-2,6-Trip2)GaGa(C6H3-2,6Trip2)]Na2 (Trip ) C6H2-2,4,6-iPr3), for which the assignment as a triple bond13-15 was challenged in several studies.16-19 Our aim in this study is to contribute to the continuing discussion concerning the Ga-Ga bond and to reconsider the problem of the nature of this bond using a recently proposed formalism based on the analysis of domain-averaged Fermi holes.20-25 The success of the new methodology in elucidating the (9) Su, J.; Li, X. W.; Crittendon, R. C.; Campana, C. F.; Robinson, G. H. Organometallics 1997, 16, 4511. (10) Cotton, F. A.; Feng, X. Organometallics 1998, 17, 128. (11) (a) Uddin, J.; Boehme, C.; Frenking, G. Organometallics 2000, 19, 571. (b) Boehme, C.; Frenking, G. Chem. Eur. J. 1999, 7, 2184. (12) (a) Uddin, J.; Frenking, G. J. Am. Chem. Soc. 2001, 123, 1683. (b) Frenking, G.; Wichmann, K.; Fro¨hlich, N.; Loschen, C.; Lein, M.; Frunzke, J.; Rayo´n, V. M. Coord. Chem. Rev. 2003, 238-239, 5. (13) Su, J.; Li, X. W.; Crittendon, Ch.; Robinson, G. H. J. Am. Chem. Soc. 1997, 119, 5471. (14) (a) Xie, Y.; Grev, R. S.; Gu, J.; Schaefer, H. F., III; Schleyer, P. v. R.; Su, J.; Li, X. W.; Robinson, G. H. J. Am. Chem. Soc. 1998, 120, 3773. (b) Xie, Y.; Schaefer, H. F., III; Robinson, G. H. Chem. Phys. Lett. 2000, 317, 174. (15) Klinkhammer, K. W. Angew. Chem. 1997, 109, 2414; Angew. Chem., Int. Ed. 1997, 21, 36.
10.1021/om0344067 CCC: $27.50 © 2004 American Chemical Society Publication on Web 03/19/2004
Ga-Ga Bonding in PhGaGaPh2- and (PhGaGaPh)Na2
structure of several molecules with complex bonding patterns, involving systems with multiple metal-metal bonds,26 stimulated us to apply it also to the study of the conflicting case of Ga-Ga bonding. For this purpose we report the analysis of Ga-Ga bonding in the simple model dianion PhGaGaPh2-. Moreover, to apply this model to the real system [(C6H3-2,6-Trip2)GaGa(C6H32,6-Trip2)]Na2, for which the existence of triple Ga-Ga bonding was proposed, the effect of coordinating the model dianion with Na+ ions on the nature of the bond will also be briefly addressed. We think that the results of this work may help to resolve the controversy13-19 which developed in the past about whether the Ga-Ga bond in, for example, [(C6H3-2,6-Trip2)GaGa(C6H3-2,6Trip2)]Na2 should be considered as a triple bond or not. Theoretical Details The domain-averaged Fermi hole gΩ(r1) is defined by eq 1, where F(r1) and F(r1, r2) are electron and pair densities,
gΩ(r1) ) NΩF(r1) - 2
∫ F(r ,r ) dr Ω
1
2
2
(1)
respectively, and the averaging (integration) is performed over the finite domain Ω. The importance of the holes for the structural elucidation is due to the fact that their actual form depends on how the domain Ω is chosen. Although one can imagine various possibilities of choosing the domain Ω, there is one particular choice which is especially interesting and important for chemistry. Such a choice is represented by a situation where the domain Ω is identified with the atomic domains resulting from the virial partitioning of the electron density function F(r1).27 As we have shown in previous studies, the analysis of the hole (1), averaged in a given molecule over the atomic domain of the atom A, yields information about the valence state of that atom in the molecule.20-24 Similarly, it is also possible to analyze the holes averaged over more complex domains which are formed by several atomic subdomains that correspond, for example, to a functional group. In such a case the hole (1) yields information about the chemical bonds and electron pairs within the fragment as well as about the bonding interactions of the fragment with the rest of the molecule. The required structural information can be retrieved from the hole (1) by the diagonalization of the matrix that represents the hole in the basis of atomic orbitals and the subsequent isopycnic transformation28 of the eigenvectors associated with nonzero eigenvalues. Using this approach, the chemical bonds and core and/or lone electron pairs within the fragment are represented by the eigenvectors of the hole associated with (16) (a) Hardman, N. J.; Wright, R. J.; Phillips, A. D.; Power, P. P. J. Am. Chem. Soc. 2003, 125, 2667. (b) Allen, T. L.; Fink, W. H.; Power, P. P. Dalton 2000, 407. (c) Olmstead, M. M.; Simons, R. S.; Power, P. P. J. Am. Chem. Soc. 1997, 119, 11705. (d) Twamley, B.; Power, P. P. Angew. Chem. 2000, 112, 3643; Angew. Chem., Int. Ed. 2000, 39, 3500. (17) (a) Grunenberg, J.; Goldberg, N. J. Am. Chem. Soc. 2000, 122, 6045. (b) Takagi, N.; Schmidt, M. W.; Nagase, S. Organometallics 2001, 20, 1646. (c) Himmel, H. J.; Schno¨ckel. H. Chem. Eur. J. 2002, 8, 2397. (18) Cotton, F. A.; Cowley, A. H.; Feng, X. J. Am. Chem. Soc. 1998, 120, 1795. (19) Molina, J. M.; Dobado, J. A.; Herald, G. L.; Bader, R. F. W.; Sundberg, M. R. Theor. Chem. Acta 2001, 105, 365. (20) Ponec, R. J. Math. Chem. 1997, 21, 323. (21) Ponec, R. J. Math. Chem. 1998, 23, 85. (22) Ponec, R.; Duben, A. J. Comput. Chem. 1999, 8, 760. (23) Ponec, R.; Roithova´, J. Theor. Chem. Acta 2001, 105, 393. (24) Ponec, R.; Girone´s X. J. Phys. Chem. A 2002, 106, 9606. (25) Ponec, R.; Roithova´, J.; Girone´s, X.; Lain, L.; Torre, A.; Bochicchio, R. J. Phys. Chem. A 2002 106, 1019. (26) Ponec, R.; Yuzhakov, G.; Carbo´-Dorca, R. J. Comput. Chem. 2003, 24, 1829. (27) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon Press: Oxford, U.K., 1994. (28) Cioslowski, J. Int. J. Quantum Chem. 1990, S24, 15.
Organometallics, Vol. 23, No. 8, 2004 1791 Table 1. Calculated Geometrical Parametersa of the Naked Dianion PhGaGaPh2-
basis param
3-21G**
6-311G**
LANL2DZ
RGa-Ga (Å) RC-Ga (Å) ∠CGaGa (deg)
2.420 (2.32) 2.089 (2.080) 127 (126)
2.430 (2.32) 2.079 (2.069) 126 (128)
2.470 (2.32) 2.058 (2.040) 126 (128)
a The values from the constrained optimizations are given in parentheses.
eigenvalue values that are close to 2. The nature of the electron pairs can easily be interpreted by visual inspection of the form of the corresponding eigenvectors. Similarly it is also possible to detect the number and the nature of eventual “free valences” formed by formal isolation of the fragment from the rest of the molecule. The choice of the fragments to be analyzed is dictated by the nature of the studied problem. In the present case of GaGa bonding, whose analysis we are interested in here, the most straightforward information about the metal-metal bonding in the conflicting case of ArGaGaAr2- can advantageously be obtained from the analysis of the Fermi holes associated with Ga-Ga and PhGa fragments, respectively.
Computational Details The analysis of the nature of Ga-Ga bonding in PhGaGaPh2and its Na+-coordinated counterpart required two types of calculations. In the first step it was necessary to generate the wave functions which serve for the construction of the Fermi holes. We first optimized the geometries of the molecules at the B3LYP level of theory29 using 3-21G**, 6-311G**, and LANL2DZ basis sets followed by calculation of the Hessian matrices. The optimized structures are energy minima on the potential energy hypersurfaces. The calculations have been performed using Gaussian 98.30 The wave functions of the optimized geometries were then used for the construction of the Fermi holes, which were analyzed in the next step using our own program WFermi,31 which is available upon request. The technical details of the calculations are the same as in previous studies.20-23,26
Results and Discussion The most important geometrical parameters of the parent dianion PhGaGaPh2- are summarized in Table 1. The same geometry parameters were also calculated (29) (a) Becke, A. D. J. Chem. Phys. 1992, 96, 2155, (b) J. Chem. Phys. 1993, 98, 5648. (c) Lee, H.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785. (30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision E.1; Gaussian, Inc.: Pittsburgh, PA, 1995. (31) Girone´s, X.; Ponec, R.; Roithova´, J. Program WFermi, v. 1.1; Prague, Czech Republic, 2000.
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Table 2. Calculated Geometrical Parametersa of the Na+-Coordinated Dianion (PhGaGaPh)Na2
Table 3. Calculated Wiberg Bond Ordersa for the Naked Dianion PhGaGaPh2- and Its Na+-Coordinated Counterpart molecule PhGaGaPh2(PhGaGaPh)Na2
basis param
3-21G**
6-311G**
LANL2DZ
RGa-Ga (Å) RC-Ga (Å) RGa-Na (Å) ∠GaGaNa (deg) ∠CGaGa (deg)
2.429 (2.32) 2.040 (2.030) 2.780 (2.760) 64 (65) 118 (125)
2.479 (2.32) 2.040 (2.030) 2.98 (3.060) 65 (67) 125 (128)
2.528 (2.32) 2.030 (2.030) 3.090 (3.060) 66 (67) 125 (128)
a The values from the constrained optimizations are given in parentheses.
for the Na+-coordinated counterpart, which represents the model of the species for which the actual geometry is known experimentally. The theoretical values are summarized in Table 2. In the first study reporting the synthesis of [(C6H32,6-Trip2)GaGa(C6H3-2,6-Trip2)]Na2, the Ga-Ga bond was classified as a triple bond and the molecule was claimed to be the first example of a gallyne.13 The main argument for such an assignment was the relatively short Ga-Ga bond distance of 2.32 Å. This classification was, however, questioned, and according to more recent reconsiderations, the Ga-Ga bond is classified by various authors as either a single16c or a double bond.18,19 One of the most serious arguments against the triplebond character of the Ga-Ga bond is that this type of bonding would require a linear arrangement of the ArGaGaAr skeleton, while the molecule is bent. As is evident from Tables 1 and 2, the same arrangement was also found in our geometry optimizations, which is in agreement with previous calculations.14,15,16b,c,18 The most important conclusion that can be deduced from the comparison of calculated geometrical parameters with available experimental data concerns the Ga-Ga bond length, which is systematically overestimated by all the methods. Because the bond length is crucially important for any interpretation of the nature of Ga-Ga bond, the reliability of the Fermi hole analysis based on overestimated bond lengths could be questioned. To evaluate the importance of this problem, not only was our method applied to the analysis of Fermi holes generated from the optimized geometries but the same methodology was also applied to structures resulting from constrainedgeometry optimizations with the Ga-Ga bond length kept fixed at the experimental value of 2.32 Å. Tables 1 and 2 show that the effect of constraining the Ga-Ga bond length on the other geometrical parameters is small. It will be interesting to see how much the electronic structure is influenced by shortening the GaGa bond to the experimental value. It is important to consider in this context the results of the theoretical study of Nagase et al.,17c who carried out the most extensive calculations of the system (ArGaGaAr)Na2 (Ar ) aryl), where the effect of the bulky Ar was studied in great detail. It was found that the nature of the alkyl groups in the aryl substituents
bond order XY
3-21G**
6-311G**
LANL2DZ
GaGa GaC GaGa GaC GaNa
1.592 (1.732) 0.872 (0.876) 1.030 (1.162) 0.880 (0.806) 0.234 (0.252)
1.956 (2.052) 0.742 (0.730) 1.020 (1.102) 0.768 (0.754) 0.366 (0.364)
2.030 (2.168) 0.770 (0.796) 1.134 (1.324) 0.712 (0.756) 0.366 (0.360)
basis set
a The values from constrained optimizations are given in parentheses.
of [(C6H3-2,6-Trip2)GaGa(C6H3-2,6-Trip2)]Na2 has a significant influence on the calculated Ga-Ga bond length. Substitution of isopropyl by methyl, yielding the compound [(C6H3-2,6-Mes2)GaGa(C6H3-2,6-Mes2)]Na2 (Mes ) C6H2-2,4,6-Me), results in a lengthening of the GaGa distance by 0.042 Å.17c The authors could show that it is a subtle interplay of the coordination of sodium by the aryl groups and the steric repulsion of the alkylsubstituted aryl ligands which enforces a particular sodium-gallium interaction, giving a rather short GaGa bond. They concluded that “the heart of the molecule is a Ga2Na2 cluster rather than a simple Ga-Ga bond”. Experimental investigations by Twamley and Power16d showed that the same reaction protocol which leads to the formation of [(C6H3-2,6-Trip2)GaGa(C6H3-2,6-Trip2)]Na2 does not give the corresponding mesityl-substituted compound but rather the trigallium species [(C6H3-2,6Mes2)3Ga3]Na2. Since we are concerned in our work with the electronic situation of the Ga-Ga bonding, it is justified to use the experimental geometry of the Ga2Na2 cluster. The first qualitative insight into the effect of Ga-Ga bond length on the nature of this bond comes from the calculated bond orders. In our study we characterized bond orders using the so-called Wiberg indices,32 generalized for nonorthogonal basis sets by Mayer.33,34 The corresponding values calculated for both the parent dianion PhGaGaPh2- and for its Na+-coordinated counterpart (PhGaGaPh)Na2 at optimized and experimental Ga-Ga distances are summarized in Table 3. Before discussing the conclusions that can be deduced from this table, it is necessary to note, however, that although the values of Wiberg bond orders, at least for “ordinary” organic molecules, often coincide with classical bond multiplicities,35-37 their application to inorganic systems can be more complex. This is due to the fact that bonding interactions in these molecules can be often much more intricate and the bonding schemes associated with the traditional concepts of single, double, and triple bonds as known from organic chemistry need not always be straightforwardly transferable. As will be shown below, the Ga-Ga bonding situation is an example of this. To reveal the nature of the Ga-Ga bond, we will first discuss the qualitative trends in the calculated bond orders of the parent naked dianion and its Na +coordinated counterpart for both optimized and experi(32) Wiberg, K. B. Tetrahedron 1968, 24, 1083. (33) Mayer, I. Chem. Phys. Lett. 1983, 97, 270. (34) Mayer, I. Int. J. Quantum Chem. 1986, 29, 73, 477. (35) Ponec, R. Strnad, M. Int. J. Quantum Chem. 1994, 50, 43. (36) Ponec, R. Croat. Chem. Acta 1994, 67, 55. (37) Ponec, R.; Uhlik, F. THEOCHEM 1997, 391, 159.
Ga-Ga Bonding in PhGaGaPh2- and (PhGaGaPh)Na2
Organometallics, Vol. 23, No. 8, 2004 1793
Figure 1. Eigenvectors of the Fermi holes associated with the GaGa fragment in the naked dianion PhGaGaPh2-.
mental bond lengths. The comparison (Table 3) shows that shortening the Ga-Ga interatomic distance yields only slightly larger bond orders for the Ga-Ga bond, while the values for the Ga-C bond become a bit smaller. The small changes suggest that the bonding situation does not alter very much when the Ga-Ga bond is stretched. Much larger changes are found, however, between the bond order values of the parent dianion PhGaGaPh2- and (PhGaGaPh)Na2. The calculated Ga-Ga bond order of the neutral complex is smaller by nearly a factor of 2 compared with that of the dianion, while the Ga-C bond orders change very little. This means that it is dangerous to use the calculated bonding situation of the Ga-Ga bond in PhGaGaPh2- as representative of the bonding situation in (PhGaGaPh)Na2. This is in agreement with the findings of Power et al.,16d who reported that a change of the counterion from sodium to potassium yields a completely different structure which has four gallium atoms in the center rather than two. It was concluded that the stability of (ArGaGaAr)Na2 depends on the matching size of the sodium ion and the presence of NaGa and Na-Ar interactions that stabilize their Na2Ga2 core structures.16a To get a deeper insight into the nature of the Ga-Ga bond in the free dianion and in the neutral complex, we report next the results of the analysis of domainaveraged Fermi holes associated with GaGa and PhGa fragments. The analysis was performed at the B3LYP/ LANL2DZ level of theory using wave functions generated from both completely optimized geometries and from the calculations with fixed Ga-Ga bond length. The results of the analyses were very similar, and the observed differences are only of marginal importance with no qualitative effect on the nature of the Ga-Ga bond. For this reason, we confine the discussion to the results based on the Fermi holes generated from completely optimized geometries. We will first analyze the bonding in the isolated dianion PhGaGaPh2- by scrutinizing the hole associated with the GaGa fragment. In this case the analysis of the hole provides information about the electron pairs
Table 4. Eigenvalues of the Fermi Hole Associated with the GaGa Fragment in the Naked Dianion PhGaGaPh2- and Its Na+-Coordinated Counterparta eigenvalue
degeneracy
interpretation
1.916 (1.593) 1.555 (1.222) 0.549 (0.598)
2 1 2
polarized lone pairs on Ga atoms delocalized Ga-Ga π bond broken valence of σGaC bond
a Values for the Na+-coordinated counterpart are given in parentheses. The holes were calculated at the B3LYP/LANL2DZ level.
directly involved in Ga-Ga bonding as well as about bonding interactions of this fragment with the rest of the molecule. The results of this analysis are summarized in Table 4. There are five nonzero eigenvalues associated with the GaGa fragment. Two of them have the eigenvalue 1.916: i.e., they are close to 2. Inspection of the corresponding eigenvectors shows (one of them is displayed in Figure 1a) that they are reminiscent of electron lone pairs at individual Ga atoms. However, these “lone pairs” are clearly polarized toward the neighboring Ga atom. This polarization, as well as a slight decrease of the corresponding eigenvalue compared to what is otherwise typical for lone electron pairs, indicates that they should not simply be considered as lone electron pairs but they are also involved in GaGa σ bonding. More details about the Ga-Ga bonding character of the “pseudo lone-pair electrons” will be revealed by the analysis of the PhGa fragments below. In addition to the interaction of the “polarized” lone pairs, significant contribution to Ga-Ga bonding comes from the eigenvector associated with the eigenvalue 1.555 (Table 4). The inspection of this eigenvector (Figure 1b) shows that it corresponds to the Ga-Ga π bond. The slight decrease of the corresponding eigenvalue compared again to what is usual for “ordinary” two-center-two-electron chemical bonds suggests that the Ga-Ga bond is partially delocalized toward adjacent phenyl rings, which is clearly visible in Figure 1b. In addition to the above three eigenvectors associated with Ga-Ga bonding, the analysis of the Fermi hole associated with the GaGa fragment yields yet another
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Table 5. Eigenvalues of the Fermi Hole Associated with the PhGa Fragment in the Naked Dianion PhGaGaPh2- and Its Na+-Coordinated Counterparta eigenvalue
degeneracy
interpretation
∼2 (∼2) ∼2 (∼2) ∼2 (∼ 2) 1.982 (∼2) 1.050 (0.643) 1.416 (1.218)
11 6 3 1 1 1
0.594 (0.446)
1
σCH and σCC bonds of the phenyl ring 1s2 core on carbons of the phenyl ring π bonds in Ph ring σGaC bond Ga-Ga π bond polarized lone pair on Ga belonging to the PhGa fragment polarized lone pair on Ga not belonging to the PhGa fragment
a Values for the Na+-coordinated counterpart are given in parentheses. The holes were calculated at the B3LYP/LANL2DZ level.
two degenerate nonzero eigenvalues whose values are 0.549. One of the corresponding eigenvectors is depicted in Figure 1c. The shape of the eigenvector shows clearly that it corresponds to the localized orbital of the σGaC bond which can be interpreted as “broken” or “free” valence of the Ga-C bond. The corresponding eigenvalues can thus be regarded as the contribution of gallium to the shared electron pair of the Ga-C bond. The rather small eigenvalue ∼0.5 suggests that the electron pair of this bond is significantly polarized in the direction Gaδ+-Cδ-. The remaining ∼1.5 electrons required to “complete” the electron pair of the Ga-C bond comes from the contribution of the “free” valence of the phenyl group. The eigenvector corresponding to this “free” valence can indeed be found among the eigenvectors of the Fermi hole associated with this fragment. The shape of this eigenvector, which is depicted in Figure 1d, is very similar to the eigenvector shown in Figure 1c. The similar shapes and nearcomplementary values of the corresponding eigenvalues (1.460 + 0.549 ≈ 2) clearly suggest their interpretation as contributions of Ga and the phenyl group to the 2c2e Ph-Ga single bond. After having reported the bonding situation resulting from the analysis of the GaGa fragment, we now discuss the Fermi hole associated with the PhGa fragment. As the isolation of this fragment from the rest of the molecule requires the formal splitting of Ga-Ga bond(s), the analysis of this fragment gives pertinent information about the bonds and electron pairs whose splitting is required to isolate the PhGa fragment from the rest of the molecule. The results of the analysis of this hole are summarized in Table 5. The analysis of the hole associated with the PhGa fragment yields 24 nonzero eigenvalues, of which 21 are ∼2. Inspection of the corresponding eigenvectors suggests that 15 of them correspond to electron pairs of σ and π bonds within the PhGa fragment (Table 5). The remaining 6 eigenvalues are the 1s2 core electron pairs at carbon atoms of the phenyl group. None of these 21 electron pairs are directly relevant to Ga-Ga bonding. Consequently, the nature of this bond is thus primarily determined only by the character of the interactions of eigenvectors associated with the remaining 3 nonzero eigenvalues. One of them, associated with the eigenvalue 1.050, is depicted in Figure 2a. It clearly corresponds to the “broken” or “free” valence of the Ga-Ga π bond. The “missing” additional electron required to
Figure 2. Eigenvectors of the Fermi hole associated with the PhGa fragment in the naked dianion PhGaGaPh2-.
complete the electron pair of the Ga-Ga π bond comes from the hole associated with the complementary PhGa fragment. The remaining two nonzero eigenvalues of the PhGa Fermi hole come from eigenvectors which are depicted in Figure 2b,c. A comparison with Figure 1a shows that they are reminiscent of the “polarized” lone pairs on Ga detected in the previous analysis of the Fermi hole associated with the GaGa fragment. However, the analysis of the eigenvectors of the PhGa Fermi hole yields further information about the nature of the associated electron pairs. The two eigenvectors complement each other; i.e., one of them is localized at one Ga atom with an eigenvalue of 1.416, while the other eigenvector having an eigenvalue of 0.594 is localized at the other Ga atom. The eigenvectors thus have a substantial Ga-Ga σ-bonding character as well as lonepair character. Note that the eigenvectors which are associated with the Ga-C bond have eigenvalues of 0.549 and 1.460. A similar polarization is found for the Ga-Ga σ bond. This feature of the eigenvectors can be explained in the following way. The Ga-Ga bond of linear PhGaGaPh2- has a σ and a degenerate π component. Upon bending, the in-plane π bond and the σ bond mix. The mixing is enhanced when the bending becomes larger. The π component becomes eventually a lone electron pair, while the σ component remains bonding. When the bonding angle becomes 90°, the σ component would be the only bonding component left. An example for such a bonding situation is the valence isoelectronic compound ArPbPbAr (Ar ) aryl group), which was recently synthesized.38,39 In the present case, the nonzero eigenvalues 1.416 and 0.594 of the PhGa Fermi hole suggest a mixed electron lone pair/σ bonding
Ga-Ga Bonding in PhGaGaPh2- and (PhGaGaPh)Na2
Organometallics, Vol. 23, No. 8, 2004 1795
Figure 3. Eigenvectors of the Fermi hole associated with the GaGa fragment in the Na+-coordinated dianion (PhGaGaPh)Na2.
character. There are two such eigenvalues because the other PhGa fragment has the same properties. In summary, the analysis of the Fermi holes indicates that the equilibrium structure of PhGaGaPh2- has two polarized lone pair/σ bonding electron pairs and one π bond. Thus, there are three electron pairs which have Ga-Ga bonding character, but due to the specific nature of the bonding interactions of the lone pair/σ electron pairs, their contributions to bonding are weaker than for shared electron pairs of the classical Lewis model. It is thus a matter of definition if such a bonding situation is considered as a triple bond or if one prefers to emphasize the weakness of specific polarized lone pairs/σ bonding interactions and classify this bond as “effective” double bond, which is consistent with the calculated bond order. Nevertheless, irrespective of which of the alternative classifications is preferred, the above conclusions are valid for the naked PhGaGaPh2dianion. The calculated bond orders suggest that coordination leads to further decrease of the multiplicity of the Ga-Ga bond by a factor of 2 to a value which is characteristic for single bonds, which means that the bonding situation in PhGaGaPhNa2 might be substantially different from that of the free dianion. To address this problem, we have also performed the analysis of the effect of Na+ coordination on the nature of Ga-Ga bond. The main issue of this analysis is the explanation of the dramatic decrease of the Ga-Ga bond order and its eventual impact on the nature of the bond. For this purpose a Fermi hole analysis similar to that used in the case of the parent dianion was performed for its Na+-coordinated counterpart. The results of this analysis are summarized in Tables 4-6 and in Figures 3-5. The inspection of Tables 4 and 5 shows that the results of the Fermi hole analyses of the holes associated with the fragments GaGa and PhGa in the presence of the Na+ counterions give qualitatively the same results as for the naked dianion PhGaGaPh2-. However, the eigenvalues of the corresponding Fermi holes in the coordinated species are always smaller, except for the (38) Chen, Y.; Hartmann, M.; Diedenhofen, D.; Frenking, G. Angew. Chem. 2001, 113, 2107; Angew. Chem., Int. Ed. 2001, 40, 2051. (39) Pu, L.; Twamley, B.; Power. P. P. J. Am. Chem. Soc. 2000, 122, 3524.
Table 6. Eigenvalues of the Fermi Hole Associated with the NaGaGaNa Fragmenta eigenvalue
degeneracy
interpretation
1.937 1.938 0.598
2 1 2
polarized lone pairs on Ga atoms delocalized Ga-Ga π bond broken valence of σGaC bond
a
The holes were calculated at the B3LYP/LANL2DZ level.
Figure 4. Eigenvectors of the Fermi hole associated with the PhGa fragment in the Na+-coordinated dianion (PhGaGaPh)Na2.
broken valence of the σGaC bond which is calculated for the GaGa fragment (Table 4). The shapes of the corresponding eigenvalues which are given in Figures 3 and 4 reveal important information about the differences in the bonding situations between the naked dianions and the Na+-coordinated species. A comparison of the eigenvectors for the holes associated with the GaGa fragment of the free dianion (Figure
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Organometallics, Vol. 23, No. 8, 2004
Figure 5. Eigenvectors of the Fermi hole associated with the NaGaGaNa fragment in the Na+-coordinated dianion (PhGaGaPh)Na2.
1) with the corresponding eigenvectors of the Na+coordinated species (Figure 3) shows that the shapes of the polarized lone pairs on the Ga atoms are very similar, although the eigenvalue of the latter eigenvector (1.593) is significantly smaller than the former (1.916). The former eigenvector is more diffuse and has a larger extension toward the carbon atom of the phenyl group. The eigenvalue of the Fermi hole of the Ga-Ga π bond in (PhGaGaPh)Na2 is also clearly smaller (1.222) than in the free dianion (1.555). Figure 3b shows that the corresponding eigenvector of (PhGaGaPh)Na2 extends over the sodium atoms, which means that the Ga-Ga π bond becomes strongly deformed through the influence of Na+. The shape of the eigenvector indicates that the π bond has some four-center-two-electron bonding character. However, the calculated eigenvalue 1.222 indicates that the major contribution of the electron pair is the Ga-Ga π bond. Note that the latter eigenvector of the Na+-coordinated species does not extend over the R-carbon atom of the phenyl group (Figure 3b), while the corresponding eigenvector of the free dianion does (Figure 1b). The shapes and the eigenvalues of the “broken” valence of the Ga-C σ bond of the free dianion (Figure 1c,d) and the sodiumcomplexed species (Figures 3c,d) are very similar. The rather strong influence of Na+ on the Ga-Ga bonding situation which is revealed by the analysis of the domain-averaged Fermi holes explains the experimental finding of Power et al.16d that replacement of sodium by potassium in the synthesis yields a completely different structure. A comparison of the Fermi holes associated with the PhGa fragments between the naked dianion (Figure 2) and the Na+-coordinated species (Figure 4) shows similar analogies. The eigenvector of the Ga-Ga π bond in the latter species extends over the Na atoms (Figure
Ponec et al.
4a), which explains why the eigenvalue is much smaller (0.643) than in the former species (1.050). The eigenvector of the polarized lone pair on Ga of the free dianion which belongs to the PhGa fragment (Figure 2b) is not very different from the corresponding eigenvector in the sodium-complexed species (Figure 4b), which is in agreement with the similar eigenvalues of the former (1.416) and the latter (1.218) molecules. The same holds true for the eigenvectors and eigenvalues of the corresponding polarized lone pair on Ga of the free dianion which do not belong to the PhGa fragment (Figures 2c and 4c). The decrease of the eigenvalues reflects the partial transfer of electrons originally contributing to electron pairs involved in Ga-Ga bonding into empty orbitals of coordinated Na+ ions. We also analyzed the Fermi holes associated with the fragment NaGaGaNa. The caculated eigenvalues are given in Table 6, and the eigenvectors are shown in Figure 5. The results of the latter analysis are very similar to the previous findings. There are five nonzero eigenvalues which are now easy to interpret. Three eigenvalues are ∼2. The degenerate eigenvalue 1.937 belongs to the polarized lone pairs at the Ga atoms (Figure 5a), while the eigenvalue 1.938 belongs to the Ga-Ga π-bond which extends over the sodium atoms (Figure 5b). The eigenvalue 0.623 belongs to the broken valence of the Ga-C σ bond (Figure 5c). Summary The results of the bonding analysis shows that three electron pairs, i.e., two σ and one π, contribute to the Ga-Ga bonding interactions in the free dianion PhGaGaPh2- and in the sodium-complexed species (PhGaGaPh)Na2. The eigenvalues and the eigenvectors of the Fermi hole indicate, however, that the Ga-Ga bonding situation does not correspond to classical triple bonds and should not be interpreted using classical bonding models. The reason is that only one of the three electron pairs involved in Ga-Ga bonding, namely the one contributing to the Ga-Ga π bond, corresponds to an “ordinary” shared electron pair bond in the sense of Lewis. The bonding interactions of the other two pairs are much more complex and have no classical counterparts. The eigenvalues and the eigenvectors of the latter Fermi holes show that the corresponding electron pairs cannot be considered as fully bonding but that they have partial lone-pair character. This is why the calculated bond orders yield values which are close to a weak double bond. Essentially the same bonding picture holds also for the Na+-coordinated species, but the coordination of sodium causes further weakening of the contributions of all three electron pairs to the Ga-Ga bonding. This weakening yields an effective reduction of the multiplicity of the Ga-Ga bond. The calculated bond order has therefore a value which is otherwise typical for single bonds. Acknowledgment. This study was supported by a grant from the grant agency of the Czech Academy of Sciences (No. IA4072006) and by the European Community project “Access to Research Infrastructure Action” of the Improving Human Potential Program. The use of the advanced computational facilities of CEPBA is gratefully acknowledged. OM0344067
