Article pubs.acs.org/JPCA
Nature of Chemical Bonding and Metalloaromaticity of Na2[(MArx′)3] (M = B, Al, Ga; Arx′ = C6H3-2,6-(C6H5)2) Xiaoyan Li, Jie Sun, Yanli Zeng, Zheng Sun, Shijun Zheng, and Lingpeng Meng* College of Chemistry and Material Science, Hebei Normal University, Yuhua Road, Shijiazhuang, 050016, China S Supporting Information *
ABSTRACT: The nature of chemical bonding and metalloaromaticity of Na2[(MArx′)3] (M = B, Al, Ga) have been studied within the framework of the atoms in molecules (AIM) theory and using electron localization function (ELF) analysis. The π electrons of the studied systems were separated from the total electron density and analyzed. The calculated results indicate that there are closed-shell weak interactions between the sodium atom and the M3 (M = B, Al, Ga) ring, between the sodium atom and the terminal phenyl group on each Arx′, and between the terminal phenyl groups on Arx′ in Na2[(MArx′)3]. The Na2[(MArx′)3] has metalloaromatic nature, and the sodium atoms have an active role in determining the computed aromatic properties of the three-numbered cycle.
1. INTRODUCTION One of the most challenging areas of modern chemistry is the synthesis of stable molecules containing multiply bonded atoms of the main group elements.1 However, it was thought that the electron deficient nature of group 13 elements precluded the formation of homonuclear multiple bonds.2 In the 1980s and early 1990s, a number of groups showed that multiple bonds between boron atoms could be synthesized.3 Soon afterward, numerous molecules that contain group 13 double or triple bonds that were previously thought unable to exist have been synthesized.4−12 Utilization of the 2,6-dimesitylphenyl moiety, C6H3-2,6-(C6H2-2,4,6-Me3)2, as an extraordinarily bulky ligand for heavier group 13 complexes afforded compounds with unusual and intriguing structural, physical, and chemical properties.13,14 In 1995, Robinson and co-workers reported the synthesis of a novel compound, Na2[(GaAr′)3] (Ar′ = C6H3-2,6-(C6H2-2,4,6-Me3)2), as the first cyclogallane.15 Most striking is the fact that this highly symmetrical compound resided about an unprecedented, and inherently planar, Ga3 ring with Ga−Ga−Ga bond angles of 60.0°. The metallic core of Na2[(GaAr′)3] is completed by two sodium atoms perfectly centered about the centroid of the Ga3 ring (Ga···Na, 3.220(2) Å).16 In addition to being the first cyclogallane, Na2[(GaAr′)3] expands the metalloaromaticity concept17,18 into the arena in which an aromatic cycle is completely made up by metal atoms.15 In 2006, Philip and co-workers synthesized the first cyclotrialuminene, Na2[(AlAr′)3] (Ar′ = C6H3-2,6-(C6H2-2,4,6Me 3 ) 2 ). 19 The structure of Na2 [(AlAr′) 3 ] bears some resemblance to that of the previously described gallium salts Na2[(GaAr′)3].19 Robinson and co-workers examined M2(GaH)3 (M = Li, Na, K) compounds using ab initio quantum mechanical techniques. The computed equilibrium geometries, harmonic vibrational frequencies, and chemical shifts are reported.13 The large negative nuclear independent chemical shifts (NICS) clearly support the proposed aromatic character of M2(GaH)3 (M = Li, Na, K).13 Philip and co-workers discussed the bond order of © 2012 American Chemical Society
the Al−Al and Na−Al bonds in Na 2 [(AlAr′) 3 ] and Na2[(AlMe)3].19 The Na−Al bond orders in Na2[(AlMe)3] are calculated to be 0.34 and are indicative of incomplete electron transfer to the Al3 ring. Most of the prior studies mainly discussed simplified model systems;13,15,16,19−21 the contribution of bulky ligands to shortening the M−M bond length and the interaction between sodium atoms and the two terminal phenyl groups have not been considered. Takagi22 and Cotton23 suggested that ,in Na2[Ar*GaGaAr*], the short Ga− Ga bond length is due to an interaction between Na cations and two terminal phenyl groups on each Ar*. In this study, we report the electronic structure, the metal− metal bonding characteristics, and metalloaromaticity of Na2[(MArx′)3] (Arx′ = C6H3-2,6-(C6H5)2) (M = B, Al, Ga) in which the molecules have very similar structural parameters to their real chemical structure but whose flanking aryl rings do not carry the methyl-substituents. We also discuss the contribution of bulky ligands to shortening the M−M bond length, the role of sodium atoms in the complexes, the metalloaromaticity of these complexes, and the effects of the two terminal phenyl groups, with a particular emphasis on metal−metal bonding and metalloaromaticity. These calculations should improve understanding of the properties of Na2[(MArx′)3] (Arx′ = C6H3-2,6-(C6H5)2) (M = B, Al, Ga).
2. COMPUTATIONAL DETAILS The hybrid density functional B3LYP method has proven to be an accurate technique for reproducing metal−ligand bond lengths, particularly metal−metal bond distances.24 Thus, the geometries of the studied complexes were optimized using density functional theory (DFT) at the B3LYP/6-311G(d,p) level using the Gaussian03 program package.25 Received: March 23, 2012 Revised: May 21, 2012 Published: May 21, 2012 5491
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Figure 1. Geometry and molecular graph of Na2[(MArx′)3] (M = B, Al, Ga).
suite of programs.29,30 The latter quantities are useful to single out the localization zones dominated by σ and π electrons as suggested by Santos et al.,31 even though it should be kept in mind that, according with Kohout and Savin,32 the total ELF cannot be rigorously partitioned into orbital contributions. The
A detailed topological analysis of electron density was made according to atoms in molecules (AIM) theory,26,27 as proposed by Bader, using the program AIMALL.28 The π and σ orbitals have been identified and used to compute the respective π and σ charge densities. Then, the corresponding ELFσ and ELFπ contributions were obtained using the TopMod 5492
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the substitution of methyl groups has a limited influence on the geometry of the studied compounds. 3.2. Na···π, CH···π, and H···H Interactions in Na2[(MArx′)3] (M = B, Al, Ga). In order to discuss the roles of sodium atoms and the bulky ligands in the Na2[(MArx′)3] (M = B, Al, Ga) system, an AIM analysis was performed. According to AIM theory,26,27 a chemical structure is represented by a network of bond paths. The presence of a bond path provides a universal indicator of the bonding that exists between the linked atoms. The molecular graphs of Na2[(MArx′)3] (M = B, Al, Ga) are also presented in Figure 1. It can be seen that there is a bond critical point (BCP) located between the midpoint of the M atoms and that two bond paths link the BCP to these two M atoms. Three M atoms form a planar M3 three-membered ring, and the sodium atoms are linked by the bond path to the ring critical point (RCP); the Na atoms are faced to the π cloud of M3 ring. The topological structures mean that these are interactions between the sodium atoms and the M3 ring, that is, the Na···π(M3) interactions. Meanwhile, the molecular graphs show that, in Na2[(BArx′)3], there are BCPs located between the Na atoms and C(11) atoms of the Arx′ and the C(12′) atoms of another Arx′ (the geometry of Arx′ with the atom numbering scheme are shown in Figure S1, Supporting Information); In Na2[(AlAr′)3] and Na2[(GaArx′)3], the BCPs are located between Na atoms and the C(2) atoms of Arx′ and the C(9′) atoms of another Arx′. Overall, in Na2[(MArx′)3], each Na atom faces two phenyl groups, the interactions between them also belong to Na···π(phenyl) interactions. Except for the interaction between Na atom and phenyl groups, in Na2[(BArx′)3], there are weak interactions between H(2) and H(2′), H(5) and H(5′), and H(9) and H(9′); they belong to the H···H interaction. In Na2[(AlAr′)3] and Na2[(GaArx′)3], there are weak interactions between the faceto-face phenyl groups; the −C(2)H(2) and −C(9)H(9) group of one Arx′ are linked to the C(4′) and C(7′) atoms of another Arx′, and these interactions belongs to CH···π interactions, which is discussed in detail by Nishio.33 The topological data from the BCPs calculations for Na···π(M3), Na···π(phenyl) and CH···π (H−H), such as the values of the electron density ρ(rc), the Laplacian of the electron density ∇2ρ(rc), the total energy density Hc (the sum of the Lagrangian kinetic energy density Gc and the virial energy density Vc) and -Gc/Vc of Na2[(MArx′)3] (M = B, Al,
NICS analysis were determined at both HF/6-311G(d,p) and B3LYP/6-311G(d,p) levels.
3. RESULTS AND DISCUSSION 3.1. Equilibrium Geometry. The optimized geometries of Na2[(MArx′)3] (M = B, Al, Ga, Arx′ = C6H3-2,6-(C6H5)2)) are shown in Figure 1, and their structural parameters are given in Table 1, along with the experimental values. Table 1. Geometry Parameters of Na2[(MArx′)3] (M = B, Al, Ga),a Optimized and Experimental Valuesb Na2[(BArx′)3] BL(M− M)c BL(M− Na)c BL(M− C)c A(M− M−M)c A(M− Na− M)c
Na2[(AlArx′)3]
Na2[(GaArx′)3] b
2.4886
2.441(1)b
1.6136
2.5226
2.520(2)
2.8248
3.1916
3.285(2)b
3.1543
3.229(2)b
1.5672
2.0679
2.021(3)b
2.1014
2.037(3)b
60.00
60.00
60.0b
60.00
60.0(1)b
33.19
46.56
45.12(3)b
46.47
44.4(1)b
a
The metal radii of B, Al, and Ga are 0.95, 1.43, and 1.40 Å, respectively. bThe experimental value comes from refs 15 and 17. cBL: bond length, in angstrom. A: bond angle, in degree.
As shown in Figure 1 and Table 1, the calculated geometries of Na2[(MArx′)3] (M = B, Al, Ga; Arx′ = C6H3-2,6-(C6H5)2) are similar to those found experimentally. 15,17 The Na2[(MArx′) 3] molecule resides about a planar threemembered M3 core with M−M−M angles of 60.0°. The metallic core of Na2[(MArx′)3] is completed by two sodium atoms perfectly centered above and beneath the center of the M3 plane, thus constituting a Na2M3 metallic trigonal bipyramid. The lengths of the M−M bond in the Na2[(MArx′)3] (M = B, Al, Ga) systems are smaller than the sum of the two metal radii and increase in the following sequence: B−B < Ga−Ga < Al−Al, an order that is consistent with the atomic radii of the group 13 crystal structures. The calculated bond lengths of the Ga−Ga, Ga−Na, and Ga−C bonds in Na2[(GaArx′)3] are 2.4886, 3.1543, and 2.1014 Å, respectively. These parameters are very close to the experimental parameters.15,17 The results also mean that our calculated level is suitable for the complexes studied and that
Table 2. Topological Properties at the BCPs of the Various Bonds in Na2[(MArx′)3] (M = B, Al, Ga)a cmpd
bond
ρ(rc)
∇2ρ(rc)
Gc
Vc
Hc
−Gc/Vc
Na2[(BArx′)3]
B−B Na···π(M3) Na···π(phenyl) H−H Al−Al Na ···π(M3) Na···π(phenyl) CH···π Ga−Ga Na ···π(M3) Na···π(phenyl) CH···π
0.1480 0.0151 0.0085 0.0062 0.0477 0.0137 0.0056 0.0043 0.0543 0.0133 0.0054 0.0043
−0.2096 0.0544 0.0364 0.0204 −0.0434 0.0253 0.0215 0.0113 0.0280 0.0273 0.0206 0.0115
0.0559 0.0118 0.0074 0.0040 0.0072 0.0066 0.0043 0.0023 0.0238 0.0069 0.0041 0.0024
−0.1642 −0.0100 −0.0057 −0.0030 −0.0253 −0.0068 −0.0032 −0.0018 −0.0407 −0.0069 −0.0031 −0.0019
−0.1083 0.0018 0.0017 0.0010 −0.0181 −0.0002 0.0010 0.0005 −0.0169 0.0001 0.0010 0.0005
0.3404 1.1800 1.2982 1.3333 0.2846 0.9706 1.3438 1.2778 0.5848 1.0000 1.3226 1.2632
Na2[(AlArx′)3]
Na2[(GaArx′)3]
a
All values are in a.u. 5493
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Ga) are collected in Table 2. The ρ(rc) at the BCP of Na···π(M3), Na···π(phenyl) and CH···π (H−H) bond range from 0.013−0.015, 0.005−0.008, and 0.004−0.006 au, respectively. These values mean that the Na···π(M3), Na···π(phenyl), and CH···π (H−H) interactions are weak interactions. These weak interactions play important stabilizing roles in the complexes studied, and the bulky ligands play a passive role in shielding the reactive M−M bonds, which has also been confirmed by Cotton23 and Takagi.22 Meanwhile, for all of the weak interactions, the ∇2ρ(rc) and Hc are positive, and the −Gc/Vc is greater than 1. On the basis of Bader’s24 and Cremer’s criteria,34 the quantities of ∇2ρ(rc), Hc, and −Gc/Vc indicate that all of the weak interactions are closed-shell interactions. Furthermore, the ∇2ρ(rc) and Hc of the weak interactions in Na2[(BArx′)3] are greater than those of in Na2[(AlArx′)3] and Na2[(GaArx′)3]. Furthermore, the Bader’s AIM integral atomic charge of Na atom, which is calculated based on AIM theory, is +0.8652e in Na2[(BArx′)3], while that of Na2[(AlArx′)3] and Na2[(GaArx′)3] is +0.8145e and +0.8206e, respectively. The larger the positive atomic charge means the more the ionic character of the Na···π interaction. Therefore, the ∇2ρ(rc), Hc, and the atomic charge of the Na atom all indicated that the weak interaction in Na2[(BArx′)3] have more dominant ionic character than in Na2[(AlArx′)3] and Na2[(GaArx′)3]. 3.3. Metal−Metal Bonding. 3.3.1. Topological Analysis of Electron Density. 3.3.1.1. AIM Analysis of the Total Electron Density. Figure 1 also presents the molecular graph of Na2[(MArx′)3]. It can be seen that the three M atoms form a planar M3 three-membered ring and that there is a BCP located between the midpoint of the M atoms; two bond paths link the BCP to these two M atoms. The topological properties at the BCPs of the M−M bond, such as the values of the electron density ρ(rc), the Laplacian of the electron density ∇2ρ(rc), and the total energy density Hc (the sum of Lagrangian kinetic density Gc and the virial energy density Vc) of Na2[(MArx′)3] (M = B, Al, Ga) are also collected in Table 2. The value of ∇2ρ(rc) for the B−B and Al−Al bonds are −0.2096 and −0.0434, respectively. Although the value of ∇2ρ(rc) for the Ga−Ga bond is positive, the value of Hc is negative; this means that the B−B, Al−Al, and Ga−Ga bonds are covalent. The values of ρ(rc) decrease in the following sequence: B−B > Ga−Ga > Al−Al, which is the inverse of the order of the changes of M−M bond lengths. However, for the Al−Al and Ga−Ga bonds, the values of ρ(rc) are surprisingly low for a homonuclear shared interaction compared to the value of 0.14 a.u. for the B−B bond. In addition, the value of Hc for the Al−Al and Ga−Ga bonds are −0.0181 and −0.0169, respectively. The low values of electron density ρ(rc) at the BCP of the M−M bond as well as for the Hc make classification of the metal−metal bond using only AIM criteria somewhat ambiguous. This circumstance has been already pointed out for other metal−metal bonding in transition metal complexes.35,36 3.3.1.2. ELF Analysis of the Total and π Electron Density. The complexity of the terphenyl ligands makes the use of ELF methods for the study of the complete Na2[(MArx′)3] (M = B, Al, Ga) molecule difficult.37 It is generally believed that these bulky ligands play a passive role, serving only to shelter the reactive M−M bonds, but not otherwise altering the essential structural and electronic features of the molecule;21 the calculations by Li38 and Kuznetsov39 also show that the Na+ coordination to the metal cluster does not affect them.
Therefore, to make computation more convenient, [(MH)3]2− was chosen as the model molecule to analyze the nature of the M−M bond. In this model molecule, the bond length of the M−M bond and the bond angle of M−M−H are restricted to those found in Na2[(MArx′)3]. Table 3 lists the population in the metal basins of [(MH)3]2− (M = B, Al, Ga). The ELF calculation yields the core basin Table 3. Population in Various Basin of [(MH)3]2− (M = B, Al, Ga) total electron [(BH)3]2−
[(AlH)3]2−
[(GaH)3]2−
C(B1) C(B2) C(B3) V(B1,B2) V(B1,B3) V(B2,B3) total V(B, B) C(Al1) C(Al2) C(Al3) V(Al1,Al2) V(Al1,Al3) V(Al2,Al3) total V(Al, Al2) C(Ga1) C(Ga2) C(Ga3) V(Ga1,Ga2) V(Ga1,Ga3) V(Ga2,Ga3) total V(Ga,Ga)
2.07 2.07 2.07 2.50 2.48 2.51 7.49 9.98 9.98 9.98 2.62 2.62 2.63 7.88 27.46 27.43 27.42 2.93 2.93 2.93 8.79
σ electron
π electron
1.95 1.96 1.97 5.88
1.61
1.99 1.99 1.99 6.02
1.85
2.26 2.28 2.26 6.80
1.99
values for B, Al, and Ga as 2.07e, 9.98e, and 27.4e, respectively. The calculated population of core basin C(M) corresponds to the (1s)2, (1s)2(2s)2(2p)6, and (1s)2(2s)2(2p)6(3s)2(3p)6(3d)10 configurations of B, Al, and Ga. There are three valence basins (V(M, M)) in the studied compounds, and the population in each basin is about 2.5e, 2.6e, and 2.9e for B, Al, and Ga, respectively. The total population in the three valence basins is from 7.49e for B to 8.79e for Ga. In order to determine the properties of the electrons in the metal basins, we separate the π electrons from the total electron density. The isosurfaces of the total ELF, ELFσ, and ELFπ functions of the M3 cluster (M = B, Al, Ga) are shown in Figure S2, Supporting Information; the populations in the isosurfaces are calculated and listed in Table 3. For the B3 three-membered ring, the total population in the tetrasynaptic valence basins37 of the total ELF functions is equal to 7.49e, and the total population in the tetrasynaptic valence basins of the ELFσ functions is equal to 5.88e. Thus, there are about 1.61e in the π orbital located on the B3 three-membered ring. Similarly, the π electron in Al3 and Ga3 amount to 1.85e and 1.99e, respectively. With regard to the electronic properties and molecular structure of the M3 three-membered ring, we consider the M atoms as being three-coordinate with predominantly sp2 hybridization; the overlap of M atom sp2 hybridized orbitals form the M−M σ bond and, consequently, the M3 ring. Excluding the electrons that come from the three M−M σ bonds, there is some electron density left in the p orbitals of the M (M = B, Al, Ga) atoms, thus forming the π orbital. 5494
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Figure 2. Molecular graph of the π electron density of [(MH)3]2− (M = B, Al, Ga).
The molecular graph of the π electron density of the M3 (M = B, Al, Ga) ring, shown in Figure 2, also affirmed the existence of the π bond. It can be seen that there are two (3, −3) attractors above and beneath the M atom. In addition, there is a bond critical point (BCP) or (3, −1) critical point located between the midpoint of the (3, −3) attractors, and two bond paths link the BCP to these (3, −3) attractors, which mean that there are π interactions between the M atoms. 3.4. Metalloaromaticity. According to Hückel’s 4n + 2 rule, “when the number of π electrons of a cyclic ring molecule equals 4n + 2, where n is zero or any positive integer, the molecule will be aromatic,” [(MArx′)3]2−, with about two π electrons, clearly falls into the aromatic series. This means that Na2[(MArx′)3] has a metalloaromatic nature. To further assess the aromatic character of the studied complexes, the NICS values40−44 of [(MH)3]2− (M = B, Al, Ga) systems, the model molecules of Na2[(MArx′)3], were calculated at both HF/6311G(d,p) and B3LYP/6-311G(d,p) levels. According to the dissected NICS analysis on π aromaticity and antiaromaticity, the NICS(1) values (i.e., at 1 Å above) were recommended as better measures of π aromaticity than NICS(0) for benzene (i.e., at the ring centers).44 The calculated NICS(1) of [(MH)3]2− (M = B, Al, Ga) are listed in Table 4.
Na2[(GaArx′)3] have analogue features (as shown in Figure 3S, Supporting Information). There is only one occupied π orbital in all of the occupied orbitals in Na2[(MArx′)3], and the contributions of the sodium atoms to this π orbital in Na2[(BArx′)3], Na2[(AlArx′)3], and Na2[(GaArx′)3] are 8%, 58%, and 38%, respectively. Furthermore, the bond length differences of the M−M bond between the complexes and the atomic radii show the same tendency: the M−M bond length difference is 0.2864, 0.3374, and 0.3114 Å; the larger the bond length difference, the greater the Na contribution. In total, both the component of the π orbital and the bond length differences of the M−M bond mean that the two sodium atoms participate directly in the formation of the π bond; the contribution of sodium atoms to the short M−M bond is significant in Na2[(MArx′)3] (M = B, Al, Ga).
4. CONCLUSIONS The weak interactions and metal−metal bonding in Na2[(MArx′)3] (M = B, Al, Ga) have been discussed, using a combination of AIM and ELF techniques. The analyses carried out in this work lead to the following main conclusions: (1) There are Na···π, CH···π, and H···H interactions between the sodium atom and the M3 (M = B, Al, Ga) ring, between the sodium atom and the terminal phenyl group on each Arx′, and between the terminal phenyl groups on Arx′ in Na 2 [(MArx′) 3 ]. All of these interactions belong to closed-shell interactions. (2) The weak interactions in Na2[(BArx′)3] have more dominant ionic character than in Na2[(AlArx′)3] and Na2[(GaArx′)3]. (3) The Na2[(MArx′)3] has metalloaromatic nature, and the sodium atoms have an active role in determining the computed aromatic properties of the three-membered cycle.
Table 4. NICS(1) of [(MH)3]2− (M = B, Al, Ga) [(BH)3]2− [(AlH)3]2− [(GaH)3]2−
HF
B3LYP
−18.7 −13.7 −13.4
−16.9 −12.0 −11.0
As shown in Table 4, although the NICS(1) absolute values calculated at HF and B3LYP are different, the NICS(1) are all negative, which indicate that the [(MH)3]2− (M = B, Al, Ga) systems are metalloaromatic. 3.5. Orbital Analysis. Ab initio calculations for Na2[(MArx′)3] (M = B, Al, Ga) were performed at the HF/ 6-311G(d, p) level. In Na2[(MArx′)3] (M = B, Al, Ga), the HOMO − 2 is a π orbital delocalized over the three boron atom centers. The HOMOs in Na 2 [(AlArx′) 3 ] and
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ASSOCIATED CONTENT
S Supporting Information *
Geometry and atom numbering scheme of Arx′, ELF isosurfaces of [(MH)3]2− (M = B, Al, Ga), and orbital plots 5495
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of Na2[(MArx′)3] (M = B, Al, Ga); Cartesian coordinates of the optimized geometry for Na2[(MArx′)3] (M = B, Al, Ga). This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Tel/Fax: +86 311 80787402. E-mail:
[email protected]. cn. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Thanks are given to International Science Editing for the editing of this article. This work was supported by the National Natural Science Foundation of China (Contract No. 21102033, 21171047, 20973053, and 21073051), the Natural Science Foundation of Hebei Province (Contract No. B2010000371 and B2011205058), and the Education Department Foundation of Hebei Province (No. ZD2010126).
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