Experimental and theoretical characterization of the Zn - Zn bond in [Zn2(η5-C5Me5)2]

research papers 862 doi:10.1107/S0108768107045880 Acta Cryst. (2007). B63, 862–868 Acta Crystallographica Section B Structural Science ISSN 0108-7681 Experimental and theoretical characterization of the Zn—Zn bond in [Zn 2 (g 5 -C 5 Me 5 ) 2 ] Juan F. Van der Maelen, a * Enrique Gutie ´rrez-Puebla, b A ´ngeles Monge, b Santiago Garcı ´a-Granda, a Irene Resa, c Ernesto Carmona, c Marı ´a Teresa Ferna ´ndez-Dı ´az, d Garry J. McIntyre, d Philip Pattison e and Hans-Peter Weber f a Departamento Quı ´mica Fı ´sica y Analı ´tica, Facultad de Quı ´mica, Avda. Julia ´n Claverı ´a8, University of Oviedo, E-33006 Oviedo, Spain, b Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Cientı ´ficas, Sor Juana Ine ´s de la Cruz 3, E-28049 Madrid, Spain, c Instituto de Investigaciones Quı ´micas, Consejo Superior de Investigaciones Cientı ´ficas, Ame ´rico Vespucio 49, E-41092 Sevilla, Spain, d Institut Laue–Langevin, Av. des Martyrs BP 156, F38042 Grenoble CEDEX, France, e SwissNorwegian Beam Lines, European Synchrotron Radiation Facility, Jules Horowitz 6, BP 220, F-38043 Grenoble CEDEX, France, and f Laboratory of Crystallography, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland Correspondence e-mail: [email protected] #2007 International Union of Crystallography Printed in Singapore – all rights reserved The existence and characterization of a bond between the Zn atoms in the recently synthesized complex [Zn 2 ( 5 -C 5 Me 5 ) 2 ], as well as between Zn and ligand C atoms is firmly based on neutron diffraction and low-temperature X-ray synchrotron diffraction experiments. The multipolar analysis of the experimental electron density and its topological analysis by means of the ‘Atoms in Molecules’ (AIM) approach reveals details of the Zn—Zn bond, such as its open-shell intermediate character (the results are consistent with a typical metal–metal single bond), as well as many other topological properties of the compound. Experimental results are also compared with theoretical ab initio calculations of the DFT (density functional theory) and MP2 (Møller-Plesset perturbation theory) electron densities, giving a coherent view of the bonding in the complex. For instance, charges calculated from the AIM approach applied to the atomic basin of each Zn atom are, on average, +0.72 e from both the experimental and the theoretical electron density, showing a moderate charge transfer from the metal, confirmed by the calculated topological indexes. Received 23 May 2007 Accepted 18 September 2007 1. Introduction Recently, we reported (Resa et al., 2004) the first stable molecular compound of zinc with a metal–metal bond, bis[1,2( 5 )-pentamethylcyclopentadienyl]dizinc(II)(Zn—Zn), [Zn 2 ( 5 -C 5 Me 5 ) 2 ] (1), which attracted great interest in the scientific community, and consequently three new species have been recently studied (Wang et al., 2005; Zhu et al., 2006; Grirrane et al., 2007). These compounds have been characterized by a number of techniques (including NMR, IR and Raman spectroscopies, and conventional X-ray single-crystal diffraction) in order to demonstrate, among other things, the absence of any bridging H atom between the Zn atoms. The appearance of such an elusive metal–metal bond, in spite of the fact that organozinc compounds have been well known since the early days of organometallic chemistry, moved us to study synchrotron X-ray diffraction data, and also the theoretical topological properties of the Zn—Zn bond. Several theoretical calculations dedicated to (1) and related compounds have been published to date (Del Rı ´oet al., 2005; Xie, Schaefer III & Jemmis, 2005; Xie, Schaefer III & King, 2005; Timoshkin & Schaefer III, 2005; Xie & Fang, 2005; Kress, 2005; Kang, 2005; Philpott & Kawazoe, 2006a,b; Pathak et al., 2006). These studies, based on the molecular orbital (MO) approach, have found the minima in the potential energy surface of (1), with geometries that closely resemble the previously published experimental geometry. They have also shown that the Zn—Zn bond is comparable in stability to other metal–metal bonds, with dissociation energies calculated between 259.58 and 309.82 kJ mol 1 depending on the theoretical model used (Xie & Fang, 2005; Grirrane et al., 2007). As far as we know, no studies related to the topological properties of the Zn—Zn bond, either from a theoretical or an experimental point of view, have been published so far, although some authors have mentioned the urgent need for such studies (Philpott & Kawazoe, 2006a). Our theoretical approach to this problem is based on the Quantum Theory of Atoms in Molecules (QTAM or AIM; Bader, 1990) and centred not only on the Zn—Zn bond, but also covering the Zn–ligand bonds. This treatment is complementary to the above-mentioned studies giving a fully coherent and more complete view of the bonding in (1) when combined with the MO calculations while, on the other hand, having the additional advantage of being equally applicable to both experimental and theoretical electron densities. 2. Experimental and computational details 2.1. Neutron diffraction experiment A plate-like single crystal with maximum dimensions 2 1 0.3 mm 3 was plucked from a pool of polyflorinether oil using a standard 1 mm diameter vanadium pin, and placed quickly in the pre-cooled helium-flow cryostat of the new VeryIntense Vertical-Axis Laue Diffractometer (VIVALDI) at the Institut Laue Langevin (ILL) in Grenoble (France) for the neutron diffraction experiment. VIVALDI uses the Laue diffraction technique on an unmonochromated thermal-neutron beam and with a large solid-angle (8 sterad) cylindrical image-plate detector (Wilkinson et al., 2002) to increase the detected diffracted intensity by oneto-two orders of magnitude compared with a conventional monochromatic experiment. There were 17 Laue diffraction patterns, each accumulated over 2.5 h, collected at 170 K typically in 10intervals during the rotation of the crystal perpendicular to the incident neutron beam. The patterns were indexed using the program LAUEGEN of the Daresbury Laboratory Laue Suite (Campbell, 1995; Campbell et al., 1998) and the reflections integrated using the local program ARGONNE_BOXES, which uses a two-dimensional version of the (I)/Ialgorithm (Wilkinson et al., 1988). No correction for absorption was deemed necessary in view of the small crystal dimensions. The integrated reflections were normalized to a common incident wavelength, using a curve derived by comparing equivalent reflections and multiple observations, via the program LAUENORM (Campbell et al., 1986). Reflections were observed with wavelengths between 0.85 and 3.56 A ˚, but only reflections with wavelengths less than 3.0 A ˚were accepted for scaling, as reflections at longer wavelength had too few equivalents to be able to determine the normalization curve with confidence. In all, 12 265 reflections were observed, of which 8553 were single wellresolved reflections with wavelengths between 0.85 and 3.0 A ˚, which yielded 1665 unique reflections, corresponding to 73.7% of the possible unique reflections for dspacings > 0.96 A ˚, the minimum dspacing observed. The conventional X-ray singlecrystal parameters for non-H atoms (Resa et al., 2004) were used as the initial model. The H atoms were all located from difference-Fourier maps. Refinements were carried out using research papers Acta Cryst. (2007). B63, 862–868 Juan F. Van der Maelen et al. Characterization of the Zn—Zn bond 863 Table 1 Experimental details. X-ray Neutron Crystal data Chemical formula C 20 H 30 Zn 2 C 20 H 30 Zn 2 M r 401.18 401.18 Cell setting, space group Triclinic, P 11 Triclinic, P 11 Temperature (K) 100 (1) 170 (2) a,b,c(A ˚) 6.9115 (6), 10.889 (1), 13.893 (1) 6.9329 (3), 10.8831 (5), 13.8384 (7) ,,() 109.91 (1), 101.551 (8), 93.905 (9) 109.777 (1), 101.603 (1), 94.201 (1) V(A ˚ 3 ) 952.6 (2) 951.09 (8) Z22 D x (Mg m 3 ) 1.399 1.452 Radiation type Synchrotron White beam (mm 1 )2.51 – Crystal form, color Plate, colorless Prismatic, colorless Crystal size (mm) 0.70 0.70 0.05 2.0 1.0 0.3 Data collection Diffractometer CCD area detector VIVALDI Data collection method ’and !scans Laue Absorption correction Multi-scan (based on symmetryrelated measurements) None T min 0.272 – T max 0.881 – No. of measured, independent and observed reflections 57 003, 13 873, 12 354 8553, 1665, 985 Criterion for observed reflections I>2(I)I>2(I) R int 0.054 0.364  max () 43.5 21.8 Refinement Refinement on FF 2 R[F 2 >2(F 2 )], wR(F 2 ), S0.036, 0.040, 1.09 0.105, 0.264, 1.08 No. of reflections 11 249 1665 No. of parameters 782 469 H-atom treatment Mixture of independent and constrained refinement Mixture of independent and constrained refinement Weighting scheme w= 1/[ 2 (F o )] w= 1/[ 2 (F2 o) + (0.1322P) 2 ], where P=(F2 o+2F2 c)/3 (/) max 0.047 0.032  max , min (e A ˚ –3 ) 0.59, 0.48 0.67, 0.60 Computer programs used: CrysAlis CCD and CrysAlis RED (Oxford Diffraction, 2004), SORTAV (Blessing, 1989), SHELXL97 (Sheldrick, 1997), XD2006 (Volkov et al., 2006). SHELXL97 (Sheldrick, 1997) by full-matrix least-squares analysis with anisotropic displacement parameters for all atoms, including H atoms, with the latter considered as riding on their methyl groups. No disorder treatment was applied here to the methyl groups. Further details are given in Table 1 and the molecular geometry obtained is shown in Fig. 1. As may be clearly seen in Fig. 1, no bridging H atoms were found between the Zn atoms. This result was the main purpose of the neutron diffraction experiment, i.e. to eliminate the remote possibility of having missed bridging hydride ligands in the prior experimental studies, as certainly happened in the well known proposed cobalt compound [Co 2 ( 5 - C 5 Me 5 ) 2 ], firstly reported as having a Co—Co bond but which, in fact, is a hydride (Kersten et al., 1992). For the experimental chargedensity study the results were obtained from the synchrotron X-ray experiment without the use of neutron data. 2.2. Synchrotron X-ray diffraction experiment In order to obtain better data for the multipolar refinement than the data collected previously from conventional X-ray diffraction, a synchrotron diffraction experiment was performed. A laminar colorless single crystal of 0.70 0.70 0.05 mm 3 was selected. Measurements were carried out at the BM01A (Swiss–Norwegian Beam Line) of the European Synchrotron Radiation Facility (ESRF) in Grenoble (France). Data collection was via a KUMA KM6CH (equipped with a CCD detector) six-circle single-crystal diffractometer, utilized as a standard four-circle instrument. The data collection temperature, controlled by an Oxford cryostream cooling system, was 100 (1) K, and the wavelength of the radiation used was 0.71 A ˚. 1 The experimental strategy was as follows: (i) a good diffracting crystal was selected (the crystal was mounted on the diffractometer and a couple of frames were observed prior to starting the complete data collection); (ii) around 20 frames were then collected for indexing purposes; (iii) a run of ca 2 h of data collection was then used to try and solve the structure; (iv) finally the full dataset was collected. In fact, three different datasets were collected at this stage: a high-angle dataset, using no filter, was collected first; then a low-angle dataset was collected using a 50 mm Cu filter; finally a very low-angle data collection was performed with a 100 mm Cu filter. A total of 57 003 reflections were measured [(sin /) max =1.08A ˚ 1 ], covering 90.3% of all possible reflections from = 2.01to  max . Data reduction was then applied using the SORTAV program (Blessing, 1989), giving a total of 13 873 unique reflections (R int = 0.054), and an absorption correction was also applied using SADABS (Sheldrick, 2003; Blessing, 1995). Solution and standard (spherical atoms) refinement were made using the WinGX program package (Farrugia, 2005). Some disorder in the methyl groups was observed during the refinement and therefore some were split into two components in order to prevent them from being non-positive definite using the usual constraints (Van der Maelen Urı ´a & Sheldrick, 1996; Van der Maelen Urı ´a, 1999). Further details for this experiment are given in Table 1. 2 A selection of the molecular geometry data, compared with the results from neutron diffraction, is shown research papers 864 Juan F. Van der Maelen et al. Characterization of the Zn—Zn bond Acta Cryst. (2007). B63, 862–868 Table 2 Selected molecular geometry data (A ˚,) for (1). Bond distance or angle Conventional X-ray† Neutron diffraction‡ Multipole X-ray‡ Zn—Zn 2.305 (3) 2.292 (1) 2.3186 (3) Zn—C§ 2.268 (2)–2.306 (2) 2.272 (4)–2.326 (3) 2.2756 (12)–2.3132 (9) Zn—Zn—C§ 145.72 (6)–150.52 (6) 145.2 (4)–150.2 (4) 145.12 (6)–150.65 (4) † Data from Resa et al. (2004). ‡ This work. § Lowest and highest values; individual values may be found in the supplementary material (Tables S1 and S2). Figure 1 Displacement ellipsoid plot of (1) from the neutron diffraction experiment, drawn at the 80% probability level, showing the atomic labelling scheme (labels for H atoms are omitted for clarity). 1 In our proposal for the experiment, different experimental conditions were asked for: a wavelength of 0.5 A ˚and a temperature of 10 K, but only a more standard set-up was made available. 2 Supplementary data for this paper are available from the IUCr electronic archives (Reference: BS5050). Services for accessing these data are described at the back of the journal. in Table 2. All in all, due mainly to a greater redundancy of the data collected, a better precision than in the conventional Xray diffraction experiment was achieved, as reflected in the lower standard deviations (see x3 for more detailed comments). 2.3. Multipole refinement The multipole refinement was carried out by means of the program XD2006 (Volkov et al., 2006), which uses the Hansen–Coppens formalism for the aspherical atomic density expansion (Hansen & Coppens, 1978). Several models were tried, but the best results were obtained with a treatment that proceeded as follows. Hexadecapole representation was used for the Zn and C atoms, while the H atoms were treated as oriented dipoles, with their coordinates fixed, during the early stages of the multipole refinement process, at the positions found in the spherical-atom refinement. An average distance of 1.0495 A ˚, obtained from the neutron diffraction experiment, was used later as a constraint for all the C—H bond distances. Radial parts for core, spherical-valence and deformation-valence densities were all constructed using relativistic Dirac–Fock atomic wavefunctions expanded over Slater-type basis sets for the Zn atoms (Su & Coppens, 1998), while for C and H atoms the radial parts of the deformation valence densities were single-Slater-type functions. Further constraints were used to keep the refined parameters of all the H atoms within each methyl group equal. Radial scaling parameters for the spherical and deformation parts of the valence density (and 0 l;l= 0–4) were independently refined for both Zn atoms, while for the C atoms only and 0 0were independently refined, using the constraint 0 l=0 0(l= 1–4) for the other scaling parameters. For the H atoms all these parameters were left fixed to their default values. In addition, occupation factors for the two components of the disordered methyl groups that were split during the spherical atom refinement were left fixed at their earlier values (P val parameters). A total of 782 parameters were refined against the 11 249 ‘observed’ reflections [F>3(F)] included in the refinement (N ref /N par = 14.4). The final conventional Rfactor over Fwas 0.036 for the ‘observed’ reflections and 0.043 for the whole set of unique reflections. Refinement values given in Table 1 are for what we consider to be the ‘best’ experimental model (BE model), in the sense that it has the best final statistical indexes (R,S, max,min , difference Fourier map, convergence criteria etc.), but we also used other multipole models in the topological calculations in order to further check their accuracy against topological indexes (see below). 2.4. Experimental and theoretical topological calculations The XDPROP module of the program XD2006 (Volkov et al., 2006) was used to study the topological properties of the experimental electron density by means of the AIM approach (Bader, 1990; Coppens, 1997). Both local (location of critical points and bond-path analyses, among others) and integral properties (atomic charges, volumes, dipole moments etc.) were calculated. Usually the calculations were carried out using the default values given by the program for the different control parameters; however, for the integral properties several integration parameters had to be tested and modified in order to increase the accuracy of the results. The betasphere radii of the atoms were taken, for the integrations, as the distance between the atom nucleus and its closest bondcritical point (b.c.p.). Starting from the ‘best’ experimental model obtained in the multipolar refinement, as defined above, the procedure followed was able to find all the b.c.p.s in the molecule, whereas for the other models several b.c.p.s were either missing or located at odd positions (e.g. between the H atoms of different methyl groups). Accordingly, only the BE model was used to obtain the computationally lengthy integral properties. On the other hand, both molecular geometries obtained from neutron and X-ray diffraction experiments were used for the theoretical electronic structure calculations performed using the GAUSSIAN03 program package (Frisch et al., 2004). The electronic structure calculations were performed on the experimental geometries using both DFT and ab initio perturbation theory methods. The following methods were used: the hybrids B3LYP, B3P86 and B3PW91 Becke’s threeparameter exchange functional (Becke, 1993) with the nonlocal Lee-Yang-Parr (Lee et al., 1988), Perdew (Perdew, 1986) and Perdew-Wang (Perdew et al., 1996) correlation functionals, respectively, and the Vosko–Wilk–Nusair local correlation functional (Vosko et al., 1980), together with the Møller–Plesset MP2 and MP3 methods were tried. All-electron standard basis sets 6-31G(d), 6-31G(d,p) and 6-311G(d,p) have been used for all atoms as is usual for other calculations of organometallic compounds (Van der Maelen Urı ´aet al., 2003, 2005). The ground-state electronic wavefunctions obtained were then used for further calculations on the topology of the theoretical electron density, including both local and integral properties, performed with the aid of the program AIM2000 (Biegler-Ko ¨nig & Scho ¨nbohm, 2002). The accuracy of the integrated properties was finally set at 1.0  10 4 from the Laplacian of the integrated electron density, whereas for the local properties the accuracy was much greater (1.0 10 10 from the gradient of the electron density at the b.c.p.s). Some theoretical models (a combination of molecular geometry, method and basis set) were able to find all the b.c.p.s found from the ‘best’ experimental (BE) model, but the best results, in the sense that theoretical local properties were close to the experimental ones, were obtained using the MP2/6-311G(d,p) model with the neutron diffraction geometry (BT model). In fact, some calculations made on the X-ray diffraction geometry were even unable to find the Zn— Zn b.c.p. Consequently, integral properties were then calculated using only the BT model, which we call the ‘best’ theoretical model. 3. Results and discussion Neutron diffraction experiments carried out at the ILL (see x2) provided us both with experimental evidence of the absence of bridging H atoms between the Zn atoms in (1), and research papers Acta Cryst. (2007). B63, 862–868 Juan F. Van der Maelen et al. Characterization of the Zn—Zn bond 865 with the nuclear coordinates to be used in the theoretical electronic structure calculations, as explained earlier. The molecular geometry, shown in Fig. 1, does not differ much from the previous results (Resa et al., 2004), giving the typical sandwich structure already proposed. In Table 2 some relevant bond distances and angles obtained from the neutron diffraction data and from the X-ray synchrotron diffraction data are compared with previously available values from conventional X-ray diffraction. As may be seen from the table, the Zn—Zn distance obtained from the neutron diffraction experiment is shorter than the distances found from both Xray data, whereas the Zn—C distances are only slightly longer and the main bond angles are almost the same. The neutron Zn—Zn distance in (1) is even shorter than the same distance in the bulk metal, so there could be an extra repulsion from the core electrons of the two metal atoms that would push them away from the intermetallic region, therefore giving an X-ray distance larger than the neutron value. Published theoretical calculations for the optimized geometry of (1) show Zn—Zn distances over a wide range, varying from 2.287 to 2.339 A ˚, depending on the theoretical model used (Grirrane et al., 2007; Kress, 2005; Xie & Fang, 2005). On the other hand, conventional X-ray experimental data obtained for two recently synthesized compounds, Zn 2 [{(2,6i Pr 2 C 6 H 3 )- N(Me)C} 2 CH] 2 (Wang et al., 2005) and Zn 2 {C 6 H 3 -2,6-(C 6 H 3 - 2,6i Pr 2 ) 2 } 2 (Zhu et al., 2006), gave Zn—Zn distances of 2.3586 (7) and 2.3591 (9) A ˚, respectively. In order to obtain good quality electron densities suitable for an experimental topological analysis (Coppens, 1997; Koritsanszky & Coppens, 2001; Coppens et al., 2005) we carried out a multipolar analysis of the experimental electron density obtained from the synchrotron X-ray data described in x2, followed by the application of the AIM approach (Bader, 1990). This analysis gave a consistent view of a fully connected molecule, including the complete set of one b.c.p. between the Zn atoms, 10 b.c.p.s between Zn and C atoms, 20 b.c.p.s for the C—C bonds and 30 b.c.p.s for the C—H bonds, together with the 12 ring critical points (r.c.p.) and two cage critical points (c.c.p.). In Fig. 2 a gradient trajectory map for (1) is shown, where the critical point and the bond path (b.p.) between the Zn atoms are clearly seen. Also shown are the b.c.p.s and b.p.s found between each of the Zn atoms, and the C-Me group in the ligand ring located in the plane of the plot. Owing to the (nearly) cylindrical symmetry of the molecule, the image in Fig. 2 may be rotated around the Zn—Zn axis to obtain a complete picture of the electron-density gradient field. In fact, very similar plots are found if different planes are selected. Furthermore, our theoretical calculations made at the ab initio level show results that closely resemble experimental calculations. For instance, charges calculated from the AIM approach applied to the atomic basin of each Zn atom are, on average, +0.720 e from the experimental electron density and research papers 866 Juan F. Van der Maelen et al. Characterization of the Zn—Zn bond Acta Cryst. (2007). B63, 862–868 Figure 2 Gradient trajectories mapped on a total density plot (contour levels at 0.1 e A ˚ 3 ) for the Zn2—Zn1—C1 plane of (1). B.c.p.s (red circles) and b.p.s (dashed lines) are also shown. Figure 3 Three-dimensional representation of the molecular electrostatic potential mapped on an electron density isosurface. Color codes from +0.567 (dark blue) to 0.002 e A ˚ 1 (dark red). Density contour value: 0.27 e A ˚ 3 . +0.725 e from the theoretical electron density. These values are slightly lower than the formal charge of +1 e empirically postulated for the Zn atoms in (1) and, compared with other theoretical values obtained from MO approaches (Resa et al., 2004; Kang, 2005; Kress, 2005; Grirrane et al., 2007), suggest the existence of a certain amount of charge transfer from the ligands (see below). Accordingly, average experimental and theoretical charges for the ten C atoms of the two Cp * rings are 0.39 and 0.27 e, respectively. Fig. 3 shows the experimental electrostatic potential mapped on an electron density isosurface. In Table 3 a summary of the topological properties calculated from both experimental and theoretical electron densities is shown. As clearly seen in the table, the experimental value for the Zn—Zn bond length calculated from the bond path (see Fig. 2) matches almost perfectly the X-ray synchrotron interatomic distance (Table 2), hence showing no bending in the bond path. Although the theoretical value reflects a slight bending, giving a difference of only 0.15 A ˚ between the theoretical bond-path length and the experimental interatomic distance, it is fair to conclude that this is a nearly perfect bond, a result which is confirmed by the extremely low ellipticity calculated for this bond (0.001). This result is in line with previous results, based on NBO and similar MO analyses (Kress, 2005; Grirrane et al., 2007), which show that the Zn—Zn bond is mainly formed by interaction of the 4smetal orbitals, although with small contributions from p  and d  orbitals (Philpott & Kawazoe, 2006a). Current bond classifications based on the atomic valence shell for molecules involving heavy atoms make use of both local (at the b.c.p.) and integral (over the atomic basin) properties (Macchi et al., 2002; Macchi & Sironi, 2003; Gervasio et al., 2004, 2005; Gatti, 2005). Among the former, the electron density ( b ), the Laplacian of the electron density (r 2  b ), the total energy density ratio (H b / b ) and the kinetic-energy density ratio (G b /  b ), with H(r)=G(r)+V(r)and1 4r 2 (r)=2G(r)+V(r)[V(r)is the potential energy density], are by far the most common. From the values in Table 3 it is clear that the Zn—Zn bond in (1) is a typical open-shell metal–metal bond (e.g. Co—Co, Macchi et al., 2002; Macchi & Sironi, 2003; or Ru—Ru, Stash et al., 2005), which differs from a pure covalent bond (such as C—C in ethane). This result is confirmed by the integral properties listed in Table 3, i.e. the delocalization index,  (Zn—Zn), and the electron density integrated over the whole Zn—Zn interatomic surface, HZn\Zn ðrÞ. The former is indeed nearly equal to the formal bond order of 1.0, showing that there is just one electron pair shared by the two atoms, while the latter has a value comparable in magnitude to that of pure covalent bonds (2.16 for the C—C bond in ethane; Gatti, 2005, and references therein), despite the fact that  b is one order of magnitude lower for (1). Some topological properties for the Zn—Cp * interactions are also listed in Table 3. There is more literature on the topological properties of metal–ligand bonds than for metal– metal bonds, but they are mainly centred on metal–CO interactions (Pillet et al., 2003; Stash et al., 2005; Farrugia et al., 2006). It is not unusual to find just one bond path between a metal and a -bound ligand similar to Cp * (e.g. the Zr–indenyl interactions; Stash et al., 2005). As mentioned above, a most remarkable feature of the topological analysis for the Zn—C interactions in (1) is that some, although not all, of the models tried, both experimental and theoretical, provided the ten b.c.p.s and bond paths between the Zn and C atoms, a pair of which is shown in Fig. 2. Therefore, in this case it is fair to conclude that we are concerned here with real bonds, not just ‘interactions’, in the sense that real bond paths have been found between Zn and C atoms. The topological parameters also reflect this fact; for instance, the value of the delocalization index listed in Table 3 for each of the five Zn—C bonds is large enough to confirm the above assertion and, in addition, suggests than just one electron pair is shared between a Zn atom and its bonded Cp * ring. The values for the other topological magnitudes shown in the table are very similar to those found in other metal—C bonds, notably some Zr— C(indenyl) (Stash et al., 2005) and Zr—C(imine) (Pillet et al., 2003) bonds. According to the classification of Macchi and Sironi (Macchi & Sironi, 2003), they are not purely ionic bonds but they may be labelled as donor–acceptor bonds, with a moderate charge transfer revealed by the relatively modest value of HZn\CðrÞ. Moreover, since the average experimental bond path length for the Zn—C bond in (1) differs only slightly from the average experimental interatomic distance (0.03 A ˚), it can be said that these are nearly straight bonds and therefore there is a nearly pure transfer of approximately one electron from each metal atom to its ligand. Finally, from the clearly large values found for the experimental (3.21) and theoretical (4.20) ellipticities, it must be concluded that the Zn—C bonds in (1) have a definite character, in agreement with previous theoretical studies based on MO theory (Xie & Fang, 2005; Philpott & Kawazoe, 2006a,b). research papers Acta Cryst. (2007). B63, 862–868 Juan F. Van der Maelen et al. Characterization of the Zn—Zn bond 867 Table 3 Selected experimental (first row) and theoretical [second row, MP2/6-3111G(d,p) level] topological parameters for (1). d A–B : bond path length;  b : electron density at the b.c.p.; r 2  b : Laplacian of the electron density at the b.c.p.; H b / b : total energy density ratio at the b.c.p. (see text); G b / b : kinetic energy density ratio at the b.c.p.; (A–B): delocalization index (see text); HA\B: integrated electron density (see text). Bond distance d A–B (A ˚) b (e A ˚ 3 )r 2  b (e A ˚ 5 )H b / b (h e 1 )G b / b (h e 1 )(A–B)HA\B(e A ˚ 1 ) Zn—Zn 2.3206 (3) 0.348 (3) 1.824 (17) 2.1657 0.426 1.622 0.361 0.627 0.919 1.252 Zn—C† 2.2642 (12) 0.398 (8) 1.952 (20) 2.1699 0.332 3.922 0.160 1.118 0.225 0.254 † Average values. 4. Conclusions In summary, the existence and characterization of a bond between the Zn atoms in the complex [Zn 2 ( 5 -C 5 Me 5 ) 2 ], as well as between the Zn and the Cp * C atoms, have been firmly based on neutron diffraction and low-temperature X-ray synchrotron diffraction experiments, together with the multipolar analysis of the experimental electron density and the topological analysis via the AIM approach of both the experimental and the theoretical electron density. Further studies on this complex based on maps of the Laplacian of the electron density, as well as other properties, including the topological analysis of the ligands themselves, are in progress in our laboratory. Financial support from the Spanish Ministerio de Educacio ´n y Ciencia (MAT2006-01997 and ‘Factorı ´a de Cristalizacio ´n’ Consolider-Ingenio 2010) is gratefully acknowledged. We also like to thank the Co-editor and the referees, whose helpful comments and suggestions much improved the original manuscript. References Bader, R. F. W. (1990). Atoms in Molecules: A Quantum Theory. Oxford: Clarendon Press. Becke, A. D. (1993). J. Chem. Phys. 98, 5648–5652. Biegler-Ko ¨nig, F. & Scho ¨nbohm, J. (2002). J. Comput. Chem. 23, 1489–1494. Blessing, R. H. (1989). J. Appl. Cryst. 22, 396–397. Blessing, R. H. (1995). Acta Cryst. A51, 33–38. Campbell, J. W. (1995). J. Appl. Cryst. 28, 228–236. Campbell, J. W., Habash, J., Helliwell, J. R. & Moffat, K. (1986). Inf. Q. Protein Crystallogr. 18, 23–31. Campbell, J. W., Hao, Q., Harding, M. M., Nguti, N. D. & Wilkinson, C. (1998). J. Appl. Cryst. 31, 23–31. Coppens, P. (1997). X-ray Densities and Chemical Bonding. Oxford Science Publications. Coppens, P., Iversen, B. & Larsen, F. K. (2005). Coord. Chem. Rev. 249, 179–195. Del Rı ´o, D., Galindo, A., Resa, I. & Carmona, E. (2005). Angew. Chem. Int. Ed. 44, 1244–1247. Farrugia, L. J. (2005). WinGX Program System, Version 1.70.01. University of Glasgow, Scotland. Farrugia, L. J., Frampton, C. S., Howard, J. A. K., Mallinson, P. R., Peacock, R. D., Smith, G. T. & Stewart, B. (2006). Acta Cryst. B62, 236–244. Frisch, M. J. et al. (2004). GAUSSIAN03, Revision C.02. Gaussian Inc., Pittsburgh, PA, USA. Gatti, C. (2005). Z. Kristallogr. 220, 399–457. Gervasio, G., Bianchi, R. & Marabello, D. (2004). Chem. Phys. Lett. 387, 481–484. Gervasio, G., Bianchi, R. & Marabello, D. (2005). Chem. Phys. Lett. 407, 18–22. Grirrane, A., Resa, I., Rodrı ´guez, A., Carmona, E., A ´lvarez, E., Gutie ´rrez-Puebla, E., Monge, A., Galindo, A., del Rı ´o, D. & Andersen, R. (2007). J. Am. Chem. Soc. 129, 693–703. Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909–921. Kang, H. S. (2005). J. Phys. Chem. A,109, 4342–4351. Kersten, J. L., Rheingold, A. L., Theopold, K. H., Casey, Ch. P., Widenhoefer, R. A. & Hop, C. E. C. A. (1992). Angew. Chem. Int. Ed. 31, 1341–1343. Koritsanszky, T. S. & Coppens, P. (2001). Chem. Rev. 101, 1583– 1627. Kress, J. W. (2005). J. Phys. Chem. A,109, 7757–7763. Lee, C., Yang, W. & Parr, R. G. (1988). Phys. Rev. B,37, 785–789. Macchi, P., Garlaschelli, L. & Sironi, A. (2002). J. Am. Chem. Soc. 124, 14173–14184. Macchi, P. & Sironi, A. (2003). Coord. Chem. Rev. 238, 383–412. Oxford Diffraction (2004). CrysAlis. Oxford Diffraction, Abingdon, Oxfordshire, UK. Pathak, B., Pandian, S., Hosemane, N. & Jemmis, E. D. (2006). J. Am. Chem. Soc. 128, 10915–10922. Perdew, J. P. (1986). Phys. Rev. B,33, 8822–8824. Perdew, J. P., Burke, K. & Wang, Y. (1996). Phys. Rev. B,54, 16533– 16539. Philpott, M. R. & Kawazoe, Y. (2006a). Theochem. 773, 43–52. Philpott, M. R. & Kawazoe, Y. (2006b). Chem. Phys. 327, 283–290. Pillet, S., Wu, G., Kulsomphob, V., Harvey, B. G., Ernst, R. D. & Coppens, P. (2003). J. Am. Chem. Soc. 125, 1937–1949. Resa, I., Carmona, E., Gutie ´rrez-Puebla, E. & Monge, A. (2004). Science,305, 1136–1138. Sheldrick, G. M. (1997). SHELXL97. University of Go ¨ttingen, Germany. Sheldrick, G. M. (2003). SADABS. University of Go ¨ttingen, Germany. Stash, A. I., Tanaka, K., Shiozawa, K., Makino, H. & Tsirelson, V. G. (2005). Acta Cryst. B61, 418–428. Su, Z. & Coppens, P. (1998). Acta Cryst. A54, 646–652. Timoshkin, A. & Schaefer III, H. F. (2005). Organometallics,24, 3343–3345. Van der Maelen Urı ´a, J. F. (1999). Crystallogr. Rev. 7, 125–180. Van der Maelen Urı ´a, J. F., Ruiz, J. & Garcı ´a-Granda, S. (2003). J. Appl. Cryst. 36, 1050–1055. Van der Maelen Urı ´a, J. F., Ruiz, J. & Garcı ´a-Granda, S. (2005). J. Theor. Comput. Chem. 4, 823–832. Van der Maelen Urı ´a, J. F. & Sheldrick, G. M. (1996). Anal. Quim. Int. Ed. 92, 7–12. Volkov, A., Macchi, P., Farrugia, L. J., Gatti, C., Mallison, P. R., Richter, T. & Koritsanszky, T. (2006). XD2006. University of New York at Buffalo, USA. Vosko, S. H., Wilk, L. & Nusair, M. (1980). Can. J. Phys. 58, 1200– 1211. Wang, Y., Quillian, B., Wei, P., Wang, H., Yang, X. J., Xie, Y., King, R. B., Scheleyer, P. R., Schaefer III, H. F. & Robinson, G. H. (2005). J. Am. Chem. Soc. 127, 11944–11945. Wilkinson, C., Cowan, J. A., Myles, D. A. A., Cipriani, F. & McIntyre, G. J. (2002). Neutron News,13, 37–41. Wilkinson, C., Khamis, H. W., Stansfield, R. F. D. & McIntyre, G. J. (1988). J. Appl. Cryst. 21, 471–478. Xie, Y., Schaefer III, H. F. & Jemmis, E. D. (2005). Chem. Phys. Lett. 402, 414–421. Xie, Y., Schaefer III, H. F. & King, R. B. (2005). J. Am. Chem. Soc. 127, 2818–2819. Xie, Z.-Z. & Fang, W.-H. (2005). Chem. Phys. Lett. 404, 212–216. Zhu, Z., Wright, R. J., Olmstead, M. M., Rivard, E., Brynda, M. & Power, P. P. (2006). Angew. Chem. Int. Ed. 45, 5807–5810. research papers 868 Juan F. Van der Maelen et al. Characterization of the Zn—Zn bond Acta Cryst. (2007). B63, 862–868