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A QTAIM and DFT study of the dizinc bond in non-symmetric [CpZn2Ln] complexes
Journal of Organometallic Chemistry 898 (2019) 120878
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Journal of Organometallic Chemistry journal homepage: www.elsevier.com/locate/jorganchem
A QTAIM and DFT study of the dizinc bond in non-symmetric [CpZn2Ln] complexes Regla Ayala a, b, **, Agustín Galindo a, * a b
nica, Facultad de Química, Universidad de Sevilla, Aptdo 1203, 41071, Sevilla, Spain Departamento de Química Inorga Instituto de Ciencia de Materiales de Sevilla-CSIC. Avda. Am erico Vespucio 49, 41092, Sevilla, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 June 2019 Received in revised form 23 July 2019 Accepted 24 July 2019 Available online 31 July 2019
Several [Zn2L2] and [CpZn2Ln] dizinc compounds have been studied by density functional theory (DFT) and quantum theory of atoms in molecules (QTAIM) in order to compare the nature and topology of the ZneZn bond in symmetrical and non-symmetrical complexes. The stability of these complexes have been evaluated on the basis of the formation energies. The disproportionation reaction has also been analysed indicating that symmetric complexes are less stable than non-symmetric ones. To certain extent, the properties of the [CpZn2Ln] complexes are between those of the [Zn2L2] and [Zn2Cp2] compounds. The asymmetry of the [CpZn2Ln] compounds is illustrated in terms of the topological properties, especially in the Source Function (SF) and Natural Bond Orbital (NBO) analysis. © 2019 Elsevier B.V. All rights reserved.
Keywords: Zinc DFT QTAIM Dizinc Organometallic complexes Cyclopentadienyl
1. Introduction The first ZneZn bond was authenticated in the complex [Cp*2Zn2] (Cp* ¼ h5-C5Me5), which was reported by Carmona and co-workers in 2004 [1,2]. After this finding, the same research group [3e7] and others [8e11] expanded the number of wellcharacterized complexes containing the, until then unidentified, ZneZn bond [12,13]. The chemical stabilization of this bond towards disproportionation is kinetic and, with some remarkable exceptions [14,15], this stabilization can be achieved by means of bulky ligands, as cyclopentadienyl [4,5], terphenyl [8], or chelating N-donor ligands [16]. Recent experimental advances in dizinc chemistry are, for example, the synthesis of different type of heterometallic clusters [17], the characterization of a heterotetrametallic Re-Zn-Zn-Re complex [18] or the evidence of a h2 dizinc ligand in a palladium complex [19]. From a theoretical point of view and in a parallel way to experimental results, the nature of the dizinc bond has been investigated in a variety of complexes [20]. Essentially, the dizinc single bond is constructed from an s-s
* Corresponding author. nica, Facultad de Quí** Corresponding author. Departamento de Química Inorga mica, Universidad de Sevilla, Aptdo 1203, 41071, Sevilla, Spain. E-mail addresses: [email protected] (R. Ayala), [email protected] (A. Galindo). https://doi.org/10.1016/j.jorganchem.2019.120878 0022-328X/© 2019 Elsevier B.V. All rights reserved.
overlap and, for this reason, these compounds have been isolobally related to the dihydrogen molecule [21]. Significant recent developments in this area are, for example, the existence of a double bond between two zinc atoms, which has been theoretically proved in several dizinc(0) complexes [22,23], the theoretical analysis of the formation of [Cp*2Zn2] [24], and the cubic aromaticity found in multicentre [ZnI]8 clusters [25]. The most studied dizinc compounds are symmetric molecules that fit to the general formula [Zn2L2] (where L is whatever ligand). In these cases, the topology of the dizinc bond is, as expected, symmetric. Following our interest in the theoretical aspects of dizinc molecules [23,26], we decide to explore the nature of this bond in non-symmetric complexes of general composition [CpZnZnLn]. Here, we report DFT [27] and QTAIM [28] studies of model [CpZn2Ln] complexes and, for comparison, related symmetric [Zn2L2] compounds. 2. Computational details Quantum chemical optimizations on the basis of DFT at the BP86 [29]/Def2TZVPP [30] level of theory together with the D3(BJ) [31] correction by Grimme were carried out in gas-phase. The need for dispersion corrections has already been demonstrated by previous results on similar compounds [15]. The optimised geometries of all
2
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
Scheme 1. Occupied frontier orbitals of selected d10s1-metal fragments.
the compounds were characterized as energy minima by nonexistent imaginary frequencies. Electronic calculations were performed using Gaussian09 rev. D01 program [32] and topology parameters were studied within the framework QTAIM method as implemented in AIMALL [33] and Multiwfn [34] programs. Cartesian coordinates of all optimised compounds are collected in the Supplementary Material (Table S1).
3. Results and discussion In order to analyse a non-symmetric dizinc bond, we selected the common [CpZn] fragment for all model [CpZn2Ln] complexes. The features of this neutral [CpM] fragment, in which the zinc atom is d10s1, are well known (see Scheme 1) [4,26,35]. As the second zinc fragment, [ZnLn], we have chosen three representative metalfragment types: [ML] (L ¼ Ph anion), [ML2] (L2 ¼ eda, k2N,N0 -
HNCHCHNH dianion; and Nacnac, k2N,N0 -b-diketiminato anion) and [ML3] (L3 ¼ Tp, k3N,N0 ,N00 -hydridotris(1-pyrazolyl)borate anion; and Cpz3, k3N,N0 ,N00 -tris(1-pyrazolyl)methanide anion [36]). For the sake of completeness, the charged [Zn(eda)]- fragment was saturated by a sodium cation as it can be found in well-characterized similar complexes [37e39]. In all cases, the frontier MOs of these d10s1-[ZnLn] fragments are similar, being the SOMO constituted by a s hybrid with an important s contribution (Scheme 1). The formation of the zinc-zinc bond in [CpZn2Ln] compounds can be qualitatively rationalized by FMO analysis as the overlap between the SOMOs of [CpZn] and [ZnLn] fragments and this interaction is essentially an s-s overlap (see below). We have theoretically analysed the selected complexes [CpZn2Ph], 1, Na[CpZn2(eda)], 2a, [CpZn2(Nacnac)], 2b, [CpZn2Tp], 3a, and [CpZn2(Cpz3)], 3b (Scheme 2). For comparative purposes, the symmetric dizinc model compounds [Zn2Cp2], 4, [Zn2Ph2], 5, Na2[Zn2(eda)2], 6, [Zn2(Nacnac)2], 7, [Zn2Tp2], 8, and [Zn2(Cpz3)2], 9, were also computed at the same level of theory (Scheme 3). Fig. 1 shows the resulting optimised structures of non-symmetric [CpZn2Ln] complexes, 1e3, while those of [Zn2L2] type, 4e9, are depicted in Fig. 2. Selected structural data for all these complexes are collected in Table S2 (Supplementary Material). Energetic estimations for reactions of formation and disproportion are collected in Tables 1e2 and S3-S4. Values of topological properties for ZneZn bond of compounds 1e9 can be found in Tables 3 and S5, while MOs for the dizinc bond are drawn in Fig. S1 (Supplementary Material). Topological graphs showing bond paths (BPs) and critical points (CPs) are collected in Fig. S2. The selected combination of method and basis sets provides, in general, a good structural description of the dizinc complexes according to the comparison of the structural parameters of the optimised structures with experimental data. Thus, for example, the ZneZn distance in these complexes is between 2.30 and 2.41 Å (Table 3) and these values are within the experimental range of 2.29e2.48 Å found in X-ray characterized complexes (mean value of
Scheme 2. Studied non-symmetric dizinc model complexes.
Scheme 3. Studied symmetric dizinc model complexes.
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
3
Fig. 1. Optimised structures for model complexes [CpZn2Ln], 1e3.
Fig. 2. Optimised structures of [Zn2L2] compounds, 4e9.
2.38 Å from a CSD search [40]). Complexes 1e3 have not experimental counterparts and only there is a structurally characterized example related to 2b, namely compound [Cp*Zn2L] where L is a bidentate ligand of bis(iminodi(phenyl)phosphorano)methane type (L ¼ CH(Ph2P]N-2,6-i-Pr2C6H3)2 anion) [41]. The ZneZn distance for 2b of 2.336 Å is slightly longer than that experimentally observed in [Cp*ZnZnL] (2.3272(2) Å), but shorter than the value of 2.381 Å obtained by DFT calculations (B3LYP/SVP) by the same authors [41]. Conversely, there are several X-ray characterized compounds of [Zn2L2] type, which can be compared with theoretical data. Besides the parent [Zn2Cp2], 4, for which the computed value fits quite well with experimental X-ray data (2.303 versus 2.305(3) Å [1]), model complex [Zn2Ph2], 5, display a computed dizinc bond of 2.403 Å, which is slightly longer than the value reported for [Zn2Ar’2] (2.3591(9) Å, Ar’ ¼ C6H3-2,6-(C6H3-2,6-iPr2)2) [8]. Compounds [Zn(Nacnac)2], 7, and [Zn2Tp2], 8, have
Table 1 Formation free energies (DGf) of [CpZn2Ln] and [Zn2L2] complexes in kcal/mol. Complex
DGf
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b
55.75 57.27 60.92 62.19 62.26
[Zn2Cp2], 4 [Zn2Ph2], 5 Na2[Zn2(eda)2], 6 [Zn2(Nacnac)2], 7 [Zn2Tp2], 8 [Zn2(Cpz3)2], 9
60.55 47.56 48.57 53.81 58.54 58.92
experimental analogues in [Zn2[{(R)NC(Me)}2CH]2] (R ¼ 2,6-iPr2C6H3 [42] and 2,4,6-Me3C6H2 [43]) and [Zn2Tp’2] (Tp’ ¼ hydridotris(3,5-dimethylpyrazolyl)borate anion [44]) complexes, respectively. Concerning model [Zn2Tp2], 8, the dizinc bond length is quite well described by our calculations (2.354 versus 2.3560(9) Å), while for model [Zn(Nacnac)2] 7, the calculated value of 2.362 Å is between the experimental ZneZn distances found in [Zn2[{(R)NC(Me)}2CH]2] complexes (2.3586(7) and 2.3813(8) Å). Finally, with respect to Na2[Zn2(eda)2], 6, there are several complexes containing N-substituted a-ene-diamido ligands bonded the dizinc bond in which the resulting dianionic species is additionally stabilized by alkali ions with coordinated solvent molecules [37,38] or crown ethers [39]. The dizinc bond in 6, 2.364 Å, is within the observed 2.36e2.45 Å range of experimental data. From an energetic point of view, the energies (DEf, Table S3) and free energies (DGf, Table 1) for the formation of these complexes from their monomers were calculated as DXf ¼ Xdim-Xmon-Xmon’, in which X is E or G, Xdim is the energy of [Zn2Cp2] or [Zn2CpLn] complexes and Xmon and Xmon’ are the energies of [ZnLn] and/or [CpZn] monomers. As it can be seen in Table 1, the stability of the species is larger when the Cp ligand is present in the complex. In
Table 2 Free energies for the disproportionation reaction in kcal/ mol. Complex
DGr
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b
3.40 5.44 7.49 5.06 5.30
4
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
Table 3 Selected topological properties for zinc-zinc bond of [CpZn2Ln] and [Zn2L2] complexes.a Complex
ZneZn distance
rBCP
V2rBCP
d(Zn,Zn)
jVBCPj/GBCP
HBCP/rBCP
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b
2.344 2.334 2.336 2.337 2.336
0.064 0.062 0.063 0.063 0.063
0.045 0.060 0.057 0.056 0.056
0.917 0.914 0.924 0.890 0.897
1.636 1.551 1.567 1.580 1.578
0.310 0.298 0.300 0.306 0.305
[Zn2Cp2], 4 [Zn2Ph2], 5 Na2[Zn2(eda)2], 6 [Zn2(Nacnac)2], 7 [Zn2Tp2], 8 [Zn2(Cpz3)2], 9
2.303 2.403 2.364 2.362 2.354 2.354
0.065 0.062 0.059 0.062 0.063 0.063
0.069 0.019 0.050 0.045 0.044 0.044
0.960 0.882 0.901 0.935 0.887 0.895
1.530 1.884 1.584 1.624 1.648 1.643
0.299 0.320 0.298 0.303 0.317 0.315
a All dimensioned quantities are in atomic units (a.u.) except ZneZn distances which are in Angstroms (Å). The subscript BCP implies that the value is reported at the bond critical point. d(Zn,Zn) denotes the delocalization index between zinc atoms. jVBCPj/GBCP is an adimensional ratio (see text). HBCP/rBCP is the total energy ratio at the BCP.
addition, formation energies are less negative when decreases the coordination number of the [ZnLn] monomer following the sequence L > L2 > L3. This is also related with the fragment electron count, which is maximum for L3 (18 e), then L2 and minimum for L (compound 5). The values for non-symmetric complexes, 1e3, are between the parent symmetric compounds, 4e9, and they are more negative than the simple mean average indicating that the asymmetry of the complexes introduces a stabilizing component. Based on these formation free energies, the combination of dizinc Zn2þ 2 ion with the ligands selected in this work gives rise to nonsymmetric dizinc complexes that can be good candidates to be prepared in the laboratory. It is also interesting to analyse the stability of [Zn2CpLn] complexes towards the disproportionation reaction. To assess this proposal, the reaction free energies for the process 2 [CpZn2Ln] / [Zn2Cp2] þ [Zn2Ln] have been calculated (Table 2). These values indicate that in all cases the disproportionation reaction is not favoured and the non-symmetric complexes are preferred. The additional stabilization induced by the asymmetry favours these compounds. Table 3 shows a summary of selected topological properties of the ZneZn bond. All complexes present a BCP between Zn atoms (see Fig. S2). As expected for heavy metal atoms, rBCP and V2rBCP at ZneZn bonds give rise to low values what rules out their use for a bonding classification. It is well-known the need for additional magnitudes at the BCP to characterise bond types involving transition metals [45e47]. In this sense, all the complexes correspond to a transient region between ionic and covalent ZneZn bonds where 1 < jVBCPj/GBCP> 2, V2rBCP > 0 and HBCP < 0, being VBCP, GBCP and HBCP the potential, kinetic and total energies at the BCP. The bonding degree, HBCP/rBCP, indicates the degree of covalency, in such a way that the greater its magnitude, the more covalent and strong the bond is. Another interesting property is the delocalization index, d(Zn,Zn). This parameter hints the number of electron pairs that are exchanged or shared between the two atomic Zn basins and can be interpreted as the covalent bond order and related to bonding mechanism. The inspection of Table 3 shows that, in general, the topological properties of the dizinc bond are not very different for symmetric and non-symmetric compounds, having the latter compounds intermediate values respect to their corresponding symmetric species. In fact, the comparison of the Laplacian of the charge density, V2r, in a molecular plane containing the dizinc bond does not display significant differences. For example, the comparison of V2r for several related complexes [CpZn2Ph], 1, versus [Zn2Ph2], 5, and [CpZn2Tp], 3a, versus [Zn2Tp2], 8, is shown in Fig. 3. Additional graphs of the electronic density, r, the gradient vector field of r and the Laplacian of the charge density, V2r, for [CpZn2Ln] and [Zn2L2]
complexes are collected in Fig. S3 (Supplementary Material). In spite of fact that the figures collected in Table 3 are similar in all the complexes, it is expected certain influence by the different ligands involved in each [ZnLn] fragment. The ZneZn BCP in the symmetric complexes is located in the midpoint between both atoms (see Fig. S2). However, there is a deviation in the nonsymmetric ones that entails a displacement of the BCP of ca. 0.03 Å towards the Zn atom of the [ZnLn] fragment. This is also evidenced by the Source Function (SF) [48]. This magnitude provides a measure of the importance of the contribution of an atom or group of atoms to the density at a given point. In practice, the SF is evaluated at the BCPs, the integration being carried out over atomic
Fig. 3. Comparison of V2r, in the molecular plane containing the ZneZn bond, for [CpZn2Ph], 1, and [Zn2Ph2], 5, (up) and [CpZn2Tp], 3a, and [Zn2Tp2], 8, (bottom).
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
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Table 4 Source Function contributions (%) to the electron density at ZneZn BCPs as referenced point and NBO analysis (%) of the ZneZn bond.a Complex
%SF Zn1
%SF Zn2
NBO Zn1b
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b [Zn2Cp2], 4 [Zn2Ph2], 5 Na2[Zn2(eda)2], 6 [Zn2(Nacnac)2], 7 [Zn2Tp2], 8 [Zn2(Cpz3)2], 9
45.4 44.5 45.6 45.0 45.1 43.0 44.1 41.1 41.6 40.8 40.9
42.9 40.1 37.6 38.3 37.2 43.0 44.1 41.1 41.6 40.8 40.9
62.32 55.90 56.12 55.37 55.12 50.00 50.00 50.00 50.00 50.00 50.00
a b
(s (s (s (s (s (s (s (s (s (s (s
79.55 85.10 84.51 84.34 84.08 79.16 40.69 48.00 43.20 69.93 70.33
NBO Zn2b p p p p p p p p p p p
19.71) 14.06) 14.67) 14.92) 15.18) 20.21) 58.46) 51.56) 56.28) 29.60) 29.18)
37.68 44.10 43.88 44.63 44.88 50.00 50.00 50.00 50.00 50.00 50.00
(s (s (s (s (s (s (s (s (s (s (s
41.74 70.19 68.86 64.43 65.17 79.16 40.69 48.00 43.20 69.93 70.33
p p p p p p p p p p p
57.60) 29.02) 30.47) 35.19) 34.44) 20.21) 58.46) 51.56) 56.28) 29.60) 29.18)
Zn1 refers to [CpZn] unit, while Zn2 refers to [ZnLn] fragment in complexes 1e3. Total % and, in parenthesis, partial s and p contributions. Percentages lower than 1% are not included.
basins and the value is given as a percentage. In the symmetriccomplexes, the percentage of r at the BCP from the two Zn basins alone is more than 80% and the same for both atoms, indicating that the Zn atoms are the main responsible for this bond and in an equal proportion. However, when the non-symmetric complexes are analysed the Zn atom of the [CpZn] fragment participates to larger extent in the bond in spite of being further displaced with respect to the BCP (Table 4). In addition, another variance between symmetric and nonsymmetric complexes is found in the NBO analysis of these compounds (Table 4). In agreement with the % SF, the [CpZn] fragment participates to larger extent in the bond in non-symmetric complexes 1e3 and this unit shows higher contribution of the s orbital than the [ZnLn] fragment. The participation in the dizinc bond is obviously the same for the two Zn atoms in symmetric compounds 4e9, with a typical increase of the s percentage when the coordination number of the zinc atom rises. The values for the s contribution to the dizinc bond compare well with those described in theoretical calculations of related compounds [12a]. 4. Conclusions A DFT and QTAIM study of the dizinc bond in several [CpZn2Ln] and [Zn2L2] compounds has been carried out. Non-symmetric [CpZn2Ph], 1, Na[CpZn2(eda)], 2a, [CpZn2(Nacnac)], 2b, [CpZn2Tp], 3a, and [CpZn2(Cpz3)], 3b, and symmetric [Zn2Cp2], 4, [Zn2Ph2], 5, Na2[Zn2(eda)2], 6, [Zn2(Nacnac)2], 7, [Zn2Tp2], 8, and [Zn2(Cpz3)2], 9, dizinc model complexes were selected for this study. From an energetic point of view, the formation of these complexes from their corresponding monomers is clearly exergonic, while the possible disproportionation of non-symmetric compounds 1e3 into the symmetric species is thermodynamically disfavoured. The inspection of these data reveals that the presence of Cp substituent favours the strength of the dizinc bond and this interaction is also stabilized by increasing the steric protection of the [ZnLn] fragment (higher n value that also implies higher zinc electron count). Furthermore, values for non-symmetric complexes, 1e3, are between the parent symmetric compounds, 4e9, but they are more negative than the simple mean average indicating that asymmetry introduces a stabilizing factor. The topologic properties of all compounds are quite similar and the main difference between symmetric and non-symmetric compounds come from the SF and NBO analysis. Acknowledgements Financial support from the University of Sevilla (VI Plan Propio) and Junta de Andalucía (FQM-223 and FQM-282) are gratefully
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Journal of Organometallic Chemistry journal homepage: www.elsevier.com/locate/jorganchem
A QTAIM and DFT study of the dizinc bond in non-symmetric [CpZn2Ln] complexes Regla Ayala a, b, **, Agustín Galindo a, * a b
nica, Facultad de Química, Universidad de Sevilla, Aptdo 1203, 41071, Sevilla, Spain Departamento de Química Inorga Instituto de Ciencia de Materiales de Sevilla-CSIC. Avda. Am erico Vespucio 49, 41092, Sevilla, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 June 2019 Received in revised form 23 July 2019 Accepted 24 July 2019 Available online 31 July 2019
Several [Zn2L2] and [CpZn2Ln] dizinc compounds have been studied by density functional theory (DFT) and quantum theory of atoms in molecules (QTAIM) in order to compare the nature and topology of the ZneZn bond in symmetrical and non-symmetrical complexes. The stability of these complexes have been evaluated on the basis of the formation energies. The disproportionation reaction has also been analysed indicating that symmetric complexes are less stable than non-symmetric ones. To certain extent, the properties of the [CpZn2Ln] complexes are between those of the [Zn2L2] and [Zn2Cp2] compounds. The asymmetry of the [CpZn2Ln] compounds is illustrated in terms of the topological properties, especially in the Source Function (SF) and Natural Bond Orbital (NBO) analysis. © 2019 Elsevier B.V. All rights reserved.
Keywords: Zinc DFT QTAIM Dizinc Organometallic complexes Cyclopentadienyl
1. Introduction The first ZneZn bond was authenticated in the complex [Cp*2Zn2] (Cp* ¼ h5-C5Me5), which was reported by Carmona and co-workers in 2004 [1,2]. After this finding, the same research group [3e7] and others [8e11] expanded the number of wellcharacterized complexes containing the, until then unidentified, ZneZn bond [12,13]. The chemical stabilization of this bond towards disproportionation is kinetic and, with some remarkable exceptions [14,15], this stabilization can be achieved by means of bulky ligands, as cyclopentadienyl [4,5], terphenyl [8], or chelating N-donor ligands [16]. Recent experimental advances in dizinc chemistry are, for example, the synthesis of different type of heterometallic clusters [17], the characterization of a heterotetrametallic Re-Zn-Zn-Re complex [18] or the evidence of a h2 dizinc ligand in a palladium complex [19]. From a theoretical point of view and in a parallel way to experimental results, the nature of the dizinc bond has been investigated in a variety of complexes [20]. Essentially, the dizinc single bond is constructed from an s-s
* Corresponding author. nica, Facultad de Quí** Corresponding author. Departamento de Química Inorga mica, Universidad de Sevilla, Aptdo 1203, 41071, Sevilla, Spain. E-mail addresses: [email protected] (R. Ayala), [email protected] (A. Galindo). https://doi.org/10.1016/j.jorganchem.2019.120878 0022-328X/© 2019 Elsevier B.V. All rights reserved.
overlap and, for this reason, these compounds have been isolobally related to the dihydrogen molecule [21]. Significant recent developments in this area are, for example, the existence of a double bond between two zinc atoms, which has been theoretically proved in several dizinc(0) complexes [22,23], the theoretical analysis of the formation of [Cp*2Zn2] [24], and the cubic aromaticity found in multicentre [ZnI]8 clusters [25]. The most studied dizinc compounds are symmetric molecules that fit to the general formula [Zn2L2] (where L is whatever ligand). In these cases, the topology of the dizinc bond is, as expected, symmetric. Following our interest in the theoretical aspects of dizinc molecules [23,26], we decide to explore the nature of this bond in non-symmetric complexes of general composition [CpZnZnLn]. Here, we report DFT [27] and QTAIM [28] studies of model [CpZn2Ln] complexes and, for comparison, related symmetric [Zn2L2] compounds. 2. Computational details Quantum chemical optimizations on the basis of DFT at the BP86 [29]/Def2TZVPP [30] level of theory together with the D3(BJ) [31] correction by Grimme were carried out in gas-phase. The need for dispersion corrections has already been demonstrated by previous results on similar compounds [15]. The optimised geometries of all
2
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
Scheme 1. Occupied frontier orbitals of selected d10s1-metal fragments.
the compounds were characterized as energy minima by nonexistent imaginary frequencies. Electronic calculations were performed using Gaussian09 rev. D01 program [32] and topology parameters were studied within the framework QTAIM method as implemented in AIMALL [33] and Multiwfn [34] programs. Cartesian coordinates of all optimised compounds are collected in the Supplementary Material (Table S1).
3. Results and discussion In order to analyse a non-symmetric dizinc bond, we selected the common [CpZn] fragment for all model [CpZn2Ln] complexes. The features of this neutral [CpM] fragment, in which the zinc atom is d10s1, are well known (see Scheme 1) [4,26,35]. As the second zinc fragment, [ZnLn], we have chosen three representative metalfragment types: [ML] (L ¼ Ph anion), [ML2] (L2 ¼ eda, k2N,N0 -
HNCHCHNH dianion; and Nacnac, k2N,N0 -b-diketiminato anion) and [ML3] (L3 ¼ Tp, k3N,N0 ,N00 -hydridotris(1-pyrazolyl)borate anion; and Cpz3, k3N,N0 ,N00 -tris(1-pyrazolyl)methanide anion [36]). For the sake of completeness, the charged [Zn(eda)]- fragment was saturated by a sodium cation as it can be found in well-characterized similar complexes [37e39]. In all cases, the frontier MOs of these d10s1-[ZnLn] fragments are similar, being the SOMO constituted by a s hybrid with an important s contribution (Scheme 1). The formation of the zinc-zinc bond in [CpZn2Ln] compounds can be qualitatively rationalized by FMO analysis as the overlap between the SOMOs of [CpZn] and [ZnLn] fragments and this interaction is essentially an s-s overlap (see below). We have theoretically analysed the selected complexes [CpZn2Ph], 1, Na[CpZn2(eda)], 2a, [CpZn2(Nacnac)], 2b, [CpZn2Tp], 3a, and [CpZn2(Cpz3)], 3b (Scheme 2). For comparative purposes, the symmetric dizinc model compounds [Zn2Cp2], 4, [Zn2Ph2], 5, Na2[Zn2(eda)2], 6, [Zn2(Nacnac)2], 7, [Zn2Tp2], 8, and [Zn2(Cpz3)2], 9, were also computed at the same level of theory (Scheme 3). Fig. 1 shows the resulting optimised structures of non-symmetric [CpZn2Ln] complexes, 1e3, while those of [Zn2L2] type, 4e9, are depicted in Fig. 2. Selected structural data for all these complexes are collected in Table S2 (Supplementary Material). Energetic estimations for reactions of formation and disproportion are collected in Tables 1e2 and S3-S4. Values of topological properties for ZneZn bond of compounds 1e9 can be found in Tables 3 and S5, while MOs for the dizinc bond are drawn in Fig. S1 (Supplementary Material). Topological graphs showing bond paths (BPs) and critical points (CPs) are collected in Fig. S2. The selected combination of method and basis sets provides, in general, a good structural description of the dizinc complexes according to the comparison of the structural parameters of the optimised structures with experimental data. Thus, for example, the ZneZn distance in these complexes is between 2.30 and 2.41 Å (Table 3) and these values are within the experimental range of 2.29e2.48 Å found in X-ray characterized complexes (mean value of
Scheme 2. Studied non-symmetric dizinc model complexes.
Scheme 3. Studied symmetric dizinc model complexes.
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
3
Fig. 1. Optimised structures for model complexes [CpZn2Ln], 1e3.
Fig. 2. Optimised structures of [Zn2L2] compounds, 4e9.
2.38 Å from a CSD search [40]). Complexes 1e3 have not experimental counterparts and only there is a structurally characterized example related to 2b, namely compound [Cp*Zn2L] where L is a bidentate ligand of bis(iminodi(phenyl)phosphorano)methane type (L ¼ CH(Ph2P]N-2,6-i-Pr2C6H3)2 anion) [41]. The ZneZn distance for 2b of 2.336 Å is slightly longer than that experimentally observed in [Cp*ZnZnL] (2.3272(2) Å), but shorter than the value of 2.381 Å obtained by DFT calculations (B3LYP/SVP) by the same authors [41]. Conversely, there are several X-ray characterized compounds of [Zn2L2] type, which can be compared with theoretical data. Besides the parent [Zn2Cp2], 4, for which the computed value fits quite well with experimental X-ray data (2.303 versus 2.305(3) Å [1]), model complex [Zn2Ph2], 5, display a computed dizinc bond of 2.403 Å, which is slightly longer than the value reported for [Zn2Ar’2] (2.3591(9) Å, Ar’ ¼ C6H3-2,6-(C6H3-2,6-iPr2)2) [8]. Compounds [Zn(Nacnac)2], 7, and [Zn2Tp2], 8, have
Table 1 Formation free energies (DGf) of [CpZn2Ln] and [Zn2L2] complexes in kcal/mol. Complex
DGf
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b
55.75 57.27 60.92 62.19 62.26
[Zn2Cp2], 4 [Zn2Ph2], 5 Na2[Zn2(eda)2], 6 [Zn2(Nacnac)2], 7 [Zn2Tp2], 8 [Zn2(Cpz3)2], 9
60.55 47.56 48.57 53.81 58.54 58.92
experimental analogues in [Zn2[{(R)NC(Me)}2CH]2] (R ¼ 2,6-iPr2C6H3 [42] and 2,4,6-Me3C6H2 [43]) and [Zn2Tp’2] (Tp’ ¼ hydridotris(3,5-dimethylpyrazolyl)borate anion [44]) complexes, respectively. Concerning model [Zn2Tp2], 8, the dizinc bond length is quite well described by our calculations (2.354 versus 2.3560(9) Å), while for model [Zn(Nacnac)2] 7, the calculated value of 2.362 Å is between the experimental ZneZn distances found in [Zn2[{(R)NC(Me)}2CH]2] complexes (2.3586(7) and 2.3813(8) Å). Finally, with respect to Na2[Zn2(eda)2], 6, there are several complexes containing N-substituted a-ene-diamido ligands bonded the dizinc bond in which the resulting dianionic species is additionally stabilized by alkali ions with coordinated solvent molecules [37,38] or crown ethers [39]. The dizinc bond in 6, 2.364 Å, is within the observed 2.36e2.45 Å range of experimental data. From an energetic point of view, the energies (DEf, Table S3) and free energies (DGf, Table 1) for the formation of these complexes from their monomers were calculated as DXf ¼ Xdim-Xmon-Xmon’, in which X is E or G, Xdim is the energy of [Zn2Cp2] or [Zn2CpLn] complexes and Xmon and Xmon’ are the energies of [ZnLn] and/or [CpZn] monomers. As it can be seen in Table 1, the stability of the species is larger when the Cp ligand is present in the complex. In
Table 2 Free energies for the disproportionation reaction in kcal/ mol. Complex
DGr
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b
3.40 5.44 7.49 5.06 5.30
4
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
Table 3 Selected topological properties for zinc-zinc bond of [CpZn2Ln] and [Zn2L2] complexes.a Complex
ZneZn distance
rBCP
V2rBCP
d(Zn,Zn)
jVBCPj/GBCP
HBCP/rBCP
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b
2.344 2.334 2.336 2.337 2.336
0.064 0.062 0.063 0.063 0.063
0.045 0.060 0.057 0.056 0.056
0.917 0.914 0.924 0.890 0.897
1.636 1.551 1.567 1.580 1.578
0.310 0.298 0.300 0.306 0.305
[Zn2Cp2], 4 [Zn2Ph2], 5 Na2[Zn2(eda)2], 6 [Zn2(Nacnac)2], 7 [Zn2Tp2], 8 [Zn2(Cpz3)2], 9
2.303 2.403 2.364 2.362 2.354 2.354
0.065 0.062 0.059 0.062 0.063 0.063
0.069 0.019 0.050 0.045 0.044 0.044
0.960 0.882 0.901 0.935 0.887 0.895
1.530 1.884 1.584 1.624 1.648 1.643
0.299 0.320 0.298 0.303 0.317 0.315
a All dimensioned quantities are in atomic units (a.u.) except ZneZn distances which are in Angstroms (Å). The subscript BCP implies that the value is reported at the bond critical point. d(Zn,Zn) denotes the delocalization index between zinc atoms. jVBCPj/GBCP is an adimensional ratio (see text). HBCP/rBCP is the total energy ratio at the BCP.
addition, formation energies are less negative when decreases the coordination number of the [ZnLn] monomer following the sequence L > L2 > L3. This is also related with the fragment electron count, which is maximum for L3 (18 e), then L2 and minimum for L (compound 5). The values for non-symmetric complexes, 1e3, are between the parent symmetric compounds, 4e9, and they are more negative than the simple mean average indicating that the asymmetry of the complexes introduces a stabilizing component. Based on these formation free energies, the combination of dizinc Zn2þ 2 ion with the ligands selected in this work gives rise to nonsymmetric dizinc complexes that can be good candidates to be prepared in the laboratory. It is also interesting to analyse the stability of [Zn2CpLn] complexes towards the disproportionation reaction. To assess this proposal, the reaction free energies for the process 2 [CpZn2Ln] / [Zn2Cp2] þ [Zn2Ln] have been calculated (Table 2). These values indicate that in all cases the disproportionation reaction is not favoured and the non-symmetric complexes are preferred. The additional stabilization induced by the asymmetry favours these compounds. Table 3 shows a summary of selected topological properties of the ZneZn bond. All complexes present a BCP between Zn atoms (see Fig. S2). As expected for heavy metal atoms, rBCP and V2rBCP at ZneZn bonds give rise to low values what rules out their use for a bonding classification. It is well-known the need for additional magnitudes at the BCP to characterise bond types involving transition metals [45e47]. In this sense, all the complexes correspond to a transient region between ionic and covalent ZneZn bonds where 1 < jVBCPj/GBCP> 2, V2rBCP > 0 and HBCP < 0, being VBCP, GBCP and HBCP the potential, kinetic and total energies at the BCP. The bonding degree, HBCP/rBCP, indicates the degree of covalency, in such a way that the greater its magnitude, the more covalent and strong the bond is. Another interesting property is the delocalization index, d(Zn,Zn). This parameter hints the number of electron pairs that are exchanged or shared between the two atomic Zn basins and can be interpreted as the covalent bond order and related to bonding mechanism. The inspection of Table 3 shows that, in general, the topological properties of the dizinc bond are not very different for symmetric and non-symmetric compounds, having the latter compounds intermediate values respect to their corresponding symmetric species. In fact, the comparison of the Laplacian of the charge density, V2r, in a molecular plane containing the dizinc bond does not display significant differences. For example, the comparison of V2r for several related complexes [CpZn2Ph], 1, versus [Zn2Ph2], 5, and [CpZn2Tp], 3a, versus [Zn2Tp2], 8, is shown in Fig. 3. Additional graphs of the electronic density, r, the gradient vector field of r and the Laplacian of the charge density, V2r, for [CpZn2Ln] and [Zn2L2]
complexes are collected in Fig. S3 (Supplementary Material). In spite of fact that the figures collected in Table 3 are similar in all the complexes, it is expected certain influence by the different ligands involved in each [ZnLn] fragment. The ZneZn BCP in the symmetric complexes is located in the midpoint between both atoms (see Fig. S2). However, there is a deviation in the nonsymmetric ones that entails a displacement of the BCP of ca. 0.03 Å towards the Zn atom of the [ZnLn] fragment. This is also evidenced by the Source Function (SF) [48]. This magnitude provides a measure of the importance of the contribution of an atom or group of atoms to the density at a given point. In practice, the SF is evaluated at the BCPs, the integration being carried out over atomic
Fig. 3. Comparison of V2r, in the molecular plane containing the ZneZn bond, for [CpZn2Ph], 1, and [Zn2Ph2], 5, (up) and [CpZn2Tp], 3a, and [Zn2Tp2], 8, (bottom).
R. Ayala, A. Galindo / Journal of Organometallic Chemistry 898 (2019) 120878
5
Table 4 Source Function contributions (%) to the electron density at ZneZn BCPs as referenced point and NBO analysis (%) of the ZneZn bond.a Complex
%SF Zn1
%SF Zn2
NBO Zn1b
[CpZn2Ph], 1 Na[CpZn2(eda)], 2a [CpZn2(Nacnac)], 2b [CpZn2Tp], 3a [CpZn2(Cpz3)], 3b [Zn2Cp2], 4 [Zn2Ph2], 5 Na2[Zn2(eda)2], 6 [Zn2(Nacnac)2], 7 [Zn2Tp2], 8 [Zn2(Cpz3)2], 9
45.4 44.5 45.6 45.0 45.1 43.0 44.1 41.1 41.6 40.8 40.9
42.9 40.1 37.6 38.3 37.2 43.0 44.1 41.1 41.6 40.8 40.9
62.32 55.90 56.12 55.37 55.12 50.00 50.00 50.00 50.00 50.00 50.00
a b
(s (s (s (s (s (s (s (s (s (s (s
79.55 85.10 84.51 84.34 84.08 79.16 40.69 48.00 43.20 69.93 70.33
NBO Zn2b p p p p p p p p p p p
19.71) 14.06) 14.67) 14.92) 15.18) 20.21) 58.46) 51.56) 56.28) 29.60) 29.18)
37.68 44.10 43.88 44.63 44.88 50.00 50.00 50.00 50.00 50.00 50.00
(s (s (s (s (s (s (s (s (s (s (s
41.74 70.19 68.86 64.43 65.17 79.16 40.69 48.00 43.20 69.93 70.33
p p p p p p p p p p p
57.60) 29.02) 30.47) 35.19) 34.44) 20.21) 58.46) 51.56) 56.28) 29.60) 29.18)
Zn1 refers to [CpZn] unit, while Zn2 refers to [ZnLn] fragment in complexes 1e3. Total % and, in parenthesis, partial s and p contributions. Percentages lower than 1% are not included.
basins and the value is given as a percentage. In the symmetriccomplexes, the percentage of r at the BCP from the two Zn basins alone is more than 80% and the same for both atoms, indicating that the Zn atoms are the main responsible for this bond and in an equal proportion. However, when the non-symmetric complexes are analysed the Zn atom of the [CpZn] fragment participates to larger extent in the bond in spite of being further displaced with respect to the BCP (Table 4). In addition, another variance between symmetric and nonsymmetric complexes is found in the NBO analysis of these compounds (Table 4). In agreement with the % SF, the [CpZn] fragment participates to larger extent in the bond in non-symmetric complexes 1e3 and this unit shows higher contribution of the s orbital than the [ZnLn] fragment. The participation in the dizinc bond is obviously the same for the two Zn atoms in symmetric compounds 4e9, with a typical increase of the s percentage when the coordination number of the zinc atom rises. The values for the s contribution to the dizinc bond compare well with those described in theoretical calculations of related compounds [12a]. 4. Conclusions A DFT and QTAIM study of the dizinc bond in several [CpZn2Ln] and [Zn2L2] compounds has been carried out. Non-symmetric [CpZn2Ph], 1, Na[CpZn2(eda)], 2a, [CpZn2(Nacnac)], 2b, [CpZn2Tp], 3a, and [CpZn2(Cpz3)], 3b, and symmetric [Zn2Cp2], 4, [Zn2Ph2], 5, Na2[Zn2(eda)2], 6, [Zn2(Nacnac)2], 7, [Zn2Tp2], 8, and [Zn2(Cpz3)2], 9, dizinc model complexes were selected for this study. From an energetic point of view, the formation of these complexes from their corresponding monomers is clearly exergonic, while the possible disproportionation of non-symmetric compounds 1e3 into the symmetric species is thermodynamically disfavoured. The inspection of these data reveals that the presence of Cp substituent favours the strength of the dizinc bond and this interaction is also stabilized by increasing the steric protection of the [ZnLn] fragment (higher n value that also implies higher zinc electron count). Furthermore, values for non-symmetric complexes, 1e3, are between the parent symmetric compounds, 4e9, but they are more negative than the simple mean average indicating that asymmetry introduces a stabilizing factor. The topologic properties of all compounds are quite similar and the main difference between symmetric and non-symmetric compounds come from the SF and NBO analysis. Acknowledgements Financial support from the University of Sevilla (VI Plan Propio) and Junta de Andalucía (FQM-223 and FQM-282) are gratefully
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