Quantum Mechanical Design and Structures of Hexanuclear

Article pubs.acs.org/JPCA

Quantum Mechanical Design and Structures of Hexanuclear Sandwich Complex and Its Multidecker Sandwich Clusters (Li6)n([18] Annulene)n+1 (n = 1−3) Shu-Jian Wang,*,† Ying Li,† Di Wu,*,† Yin-Feng Wang,‡ and Zhi-Ru Li† †

Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun 130023, P. R. China ‡ Jiangxi Province Key Laboratory of Coordination Chemistry, Institute of Applied Chemistry, School of Chemistry and Chemical Engineering, Jinggangshan University, Ji’an, Jiangxi 343009, China S Supporting Information *

ABSTRACT: By means of density functional theory, a hexanuclear sandwich complex [18]annulene-Li6-[18]annulene which consists of a central Li6 hexagon ring and large face-capping ligands, [18]annulene, is designed and investigated. The large interaction energy and HOMO−LUMO gap suggest that this novel charge-separated complex is highly stable and may be experimentally synthesized. In addition, the stability found in the [18]annulene-Li6-[18]annulene complex extends to multidecker sandwich clusters (Li6)n([18]annulene)n+1 (n = 2−3). The energy gain upon addition of a [18]annulene-Li6 unit to (Li6)n−1([18]annulene)n is pretty large (96.97−98.22 kcal/mol), indicating that even larger multideckers will also be very stable. Similar to ferrocene, such a hexanuclear sandwich complex could be considered as a versatile building block to find potential applications in different areas of chemistry, such as nanoscience and material science.

1. INTRODUCTION Since the discovery of ferrocene (Fe(η5-C5H5)2) in 1951,1 studies of organometallic complexes with sandwich-like structures have been an active area. Now, a number of sandwich complexes, ions, multidecker sandwich clusters, and infinitely long sandwich complexes (or nanowires) with unusual physical and chemical properties have been studied both experimentally and theoretically, such as metallocenes, TMCp2 (TM = V, Cr, Mn, Co, Ni, Zn);2 inorganic metallocene ion [Ti(η5-P5)2]2− in the salt form [K(18-crown-6)]2[Ti(η5-P5)2];3 multidecker sandwich clusters Ni 2 Cp 3 + and Fe 2 Cp 3 + , 4 TMn(FeCp2)n+1 (TM = V, Ti),5 TMnBzn+1 (Bz = C6H6),6 and lanthanide-1,3,5,7-cyclooctatetraene Lnn(COT)n+1 (COT = C8H8; Ln = Ce, Nd, Eu, Ho, and Yb);7 infinitely long sandwich complexes (or nanowires) (TMBz)∞ (TM = transition metal, Bz = C6H6),8 (TMCp)∞ (TM = first raw transition metal),9 and (TM-FeCp2)∞ (TM = Sc, Ti, V, Mn).10 Prior to 2003, most sandwich complexes possessed only a mononuclear M center between two small carbocyclic ligands, and sandwich complexes with two or more central metal atoms were few. Burdett and Canadell11 had theoretically designed “extended polymetallic sandwich complexes” in 1985. Surprisingly, in 200312 and 2006,13 Murahashi et al. successfully synthesized multinuclear sandwich complexes with a central four-atom palladium chain as well as monolayer palladium sheets with three or five palladium atoms. Afterward, they reported again two multinuclear sandwich complexes with triangular14 and square15 platinum sheets as centers. Since then, © 2012 American Chemical Society

there has been increasing interest in multinuclear sandwich complexes.16 So far, almost all of the sandwich complexes are designed with transition-metal (TM) and small carbocyclic ligands. Is it possible to design a multinuclear sandwich complex or several multidecker multinuclear sandwich clusters with multiple nontransition metal atoms and larger carbocyclic ligands such as [18]annulene? Motivated by the above fascinating achievements, a novel sandwich-like complex [18]annulene-Li6-[18]annulene is theoretically designed for the first time with the larger face-capping ligand [18]annulene17 and six alkali metal Li atoms. In addition, its multidecker sandwich clusters (Li6)n([18]annulene)n+1 (n = 2−3) are also predicted and characterized in this paper. For the hexanuclear sandwich complex [18]annulene-Li6[18]annulene, the geometrical structure, electronic structure, aromaticity, binding nature between [18]annulene and Li6 ring subunits, and the mechanical stability are investigated and discussed in detail. For multidecker multinuclear sandwich clusters (Li6)n([18]annulene)n+1 (n = 2−3) or larger clusters (n > 3), their stabilities are also discussed. This work might expand the knowledge of multinuclear sandwich complexes and promote the development of the chemistry of metal sandwich clusters. Received: July 7, 2012 Revised: July 31, 2012 Published: August 8, 2012 9189

dx.doi.org/10.1021/jp306749a | J. Phys. Chem. A 2012, 116, 9189−9196

The Journal of Physical Chemistry A

Article

Figure 1. Optimized geometry of the hexanuclear sandwich complex [18]annulene-Li6-[18]annulene.

2. COMPUTATIONAL DETAILS The geometry of the novel hexanuclear sandwich molecule [18]annulene-Li6-[18]annulene was optimized by the density functional CAM-B3LYP method (the corrected version of B3LYP using the Coulomb-attenuating method which has recently been developed by Handy and co-workers for chargetransfer and long-range interaction systems)18 with the 631+G(d) basis set. Frequency analysis was performed at the same computational level, and the vibrational frequencies are all real. For the purpose of comparison, the geometry of [18]annulene (C2) with alternating localized single CC and double CC bonds was also obtained at the same level. The results are listed in Tables S1 and S2 in the Supporting Information. It has previously been demonstrated by Wannere and his co-workers17c that neither the X-ray19 nor the electroncorrelated MP2 and various DFT [18]annulene geometries, namely, a highly delocalized D6h structure with nearly equal CC bond lengths, are correct. Owing to the steric repulsion between the inner hydrogen atoms, the [18]annulene prefers a bond-length alternating C2 structure with the lowest energy. As shown in Tables S1 and S2 in the Supporting Information, the bond length data computed at the CAM-B3LYP/6-31+G(d) level is also close to the corresponding X-ray data19 (1995) measured at 111 K and the corresponding data at other levels of theory,17c which means that the CAM-B3LYP method with the 6-31+G(d) basis set is appropriate to predict the geometry of the sandwich-like complex. The total interaction energy ΔEint and binding energy ΔEb between the [18]annulene···[18]annulene subunit and Li6 subunit were calculated at the CAM-B3LYP/6-31+G(d) level. To eliminate the basis set superposition error (BSSE),20 the counterpoise (CP) procedure21 was adopted. The total interaction energy ΔEint is the difference between the energy of the hexanuclear sandwich complex and the sum of the energies of two [18]annulene and six Li atoms, and the binding energy ΔEb is the difference between the energy of the complex and the sum of the energies of the [18]annulene···[18]annulene subunit and Li6 subunit, as given below by eqs 1 and 2:

ΔE b = Ecomplex (Xcomplex ) − E[18]annulene···[18]annulene(Xcomplex ) − E Li6(Xcomplex )

The same basis set, Xcomplex, was used for the subunit calculation as for the complex calculation. In order to assess the accuracy of the calculated interaction energy ΔEint and binding energy ΔEb, the bond dissociation energies (BDE) of ferrocene (Fe(η5-C5H5)2) and the lithium−benzene sandwich complex Li·(C6H6)2 were calculated because their theoretical and experimental BDE values are available and they exhibit similar structural features with [18]annulene-Li6-[18]annulene. The results are listed in Tables S3 and S4 in the Supporting Information. The experimental BDE value of ferrocene is 158 ± 2 kcal/mol.22 Roos and co-workers reported a BDE of De = 156 kcal/mol without ZPE correction using the CASPT2 method.23 Our calculated BDE value is Do = 131.5 kcal/mol with ZPE correction (De = 137.3 kcal/mol without ZPE correction), which is lower by about 27 kcal/mol for Do and 19 kcal/mol for De. By comparison with the experimental value and ab initio CASPT2 data, it can be seen that the calculated BDE values at the CAM-B3LYP level of theory are underestimated to some extent. As shown in Table S4 in the Supporting Information, the BDE value of Li·(C6H6)2 is De = 15.8 kcal/mol at the CAM-B3LYP level, which agrees very well with that (De = 15.5 kcal/mol) at the QCISD(T)//MP2 level. Besides, the zeropoint corrected BDE value of Li·(C6H6)2 is 18.0 kcal/mol at the CAM-B3LYP level, which is quite near that (Do = 19.6 kcal/mol) at the G3(MP2) level. This means that our predicted values (interaction energy ΔEint and binding energy ΔEb) for the investigated system at the CAM-B3LYP level of theory should be reliable. The NBO charge analysis24 was performed at the same level. It has been reported that the 1H NMR chemical shifts of many arenes computed by the GIAO-B3LYP/6-311+G(d,p) method are generally within 0.2−0.5 ppm of the experimental values.25 Furthermore, the NICS value (−10.92 ppm) at the center of the aromatic Li3+ ring computed by GIAO-B3LYP/6-311+G(d,p) agrees very well with that (−11 ppm) at the MP2/aug-ccpVDZ level.26 Thus, the GIAO-B3LYP/6-311+G(d,p) method is considered proper to calculate the nucleus-independent chemical shifts (NICS)27 of the [18]annulene-Li6-[18]annulene complex. All calculations were performed by using the Gaussian 09 (revision A.02) program package.28 The molecular structure

ΔE int = Ecomplex (Xcomplex ) − 2E[18]annulene(Xcomplex ) − 6E Li(Xcomplex )

(2)

(1) 9190



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Table 1. The Important Geometrical Parameters (Å), HOMO−LUMO Gap (eV), the Averaged Binding Energies ΔELi6‑[18] between Ligand Subunits and Li6 Subunits, and the Energy Gain, ΔE(n, n − 1), with Addition of a Li6·[18]annulene Subunit to (Li6)n−1([18]Annulene)n for the Hexanuclear Sandwich Complex and Its Multidecker Sandwich Clusters (Li6)n([18]Annulene)n+1 (n = 1, 2, 3)

annulene

1a

1b

2b

3b

C2 1.382−1.442(1.412)c 1.382−1.442(1.412)

C2h 1.407−1.424(1.417) 1.407−1.424(1.417)

C2v 1.404−1.432(1.418) 1.405−1.445(1.428) 1.404−1.432(1.418)

2.874

2.798

3.138 3.136

3.732

3.729

3.952 3.950

3.732 1.087 2.768

3.729 1.088 3.211

7.901 1.089 1.635 96.97 −126.99

C2h 1.405−1.432(1.419) 1.406−1.443(1.429) 1.406−1.443(1.429) 1.405−1.432(1.419) 3.097 3.129 3.097 3.942 3.958 3.942 11.841 1.089 3.031 98.22 −126.49

(Li6)n([18]annulene)n+1 PG symmetry C−C bond length of [18]annulene

averaged RLi−Li

averaged layer distance L

total layer distance L averaged RC−H HOMO−LUMO gap ΔE(n, n − 1) ΔELi6‑[18]annulene a

1 2 3 4 1 2 3 1 2 3

−137.34

−131.61

b

Obtained at the CAM-B3LYP/6-31+G(d) level. The important geometrical parameters are obtained at the B3LYP/6-31G(d) level, and the HOMO−LUMO gap, the averaged binding energies ΔELi6‑[18]annulene, and the energy gain, ΔE(n, n − 1), are computed at the CAM-B3LYP/631G(d) level. cThe values in parentheses for the average C−C bond length. The average C−C bond length for isolated [18]annulene with C2 symmetry is 1.401 Å at the CAM-B3LYP/6-31+G(d) level.

with alternating localized single CC and double CC bonds ranges from 1.355 to 1.454 Å (δ = 0.099 Å). This means that, by interacting with the planar metal Li6 ring, there is a tendency toward bond length equalization for [18]annulene and the delocalization extent of two [18]annulene molecules is enhanced. The averaged CC bond length (1.412 Å) of [18]annulene in sandwich complex is larger than that (1.401 Å) of isolated [18]annulene molecule, which means that the ring plane of [18]annulene gets slightly larger upon the interaction with Li6 ring. The average layer distance L (3.732 Å) between two [18]annulene's is comparable to that (3.744 Å at the B3LYP/6-31G(d) level) in the benzene-Li-benzene32 sandwich complex and that (3.88 Å) in a one-dimensional crystal of lithium-aromatic sandwich complex R-nLi-R33 (R is naphthalene or pyrene). The six lithium atoms that are sandwiched between two [18]annulene ligands are cyclically conjugated into an approximate regular hexagon (see Figure 1). The average Li−Li bond length (2.874 Å) of the Li6 ring subunit is shorter in comparison with that (2.953 Å at the CAM-B3LYP/ 6-31+G(d) level) of the aromatic Li3+ ring, indicating that the lithium atoms bind each other more tightly in the former. 3.2. Electronic Structure and the Charge-Separated Character of [18]Annulene-Li6-[18]Annulene. To explore the electronic structure of the novel hexanuclear sandwich complex [18]annulene-Li6-[18]annulene and the interaction among the [18]annulene ligands and Li6 hexagon ring, the molecular orbitals (MO) of [18]annulene-Li6-[18]annulene are analyzed in detail. As shown in Figure 2, the molecular orbitals of the sandwich complex originate from the overlap of the fragment orbitals of three subunits. The bonding and antibonding interaction between two [18]annulene fragments and the σ delocalized bonding interaction among six lithium atoms are observed. The planar Li6 ring possesses six 2s valence electrons. Upon combination, the charge transfer (CT) happens among three fragments, namely, four electrons transfer

and orbitals were plotted with the Molden and GaussView programs.29 Moreover, to quantitatively describe the metal− ligand bonding, a charge decomposition analysis (CDA)30 was carried out from the Gaussian results with the program AOMix.31 In the CDA, the wave function of a donor−acceptor complex is considered as a linear combination of the fragment orbitals of the ligand and the remaining metal-containing moiety. This method dissects the following primary contributions: ligand → metal donation (d), ligand ← metal backdonation (b), and ligand ↔ metal repulsive polarization (r).

3. RESULTS AND DISCUSSION 3.1. Geometrical Structure of the Hexanuclear Sandwich Complex. The optimized structure of [18]annulene-Li6-[18]annulene with all real frequencies was obtained at the CAM-B3LYP/6-31+G(d) level, and is displayed in Figure 1. The important geometrical parameters are collected in Table 1. The details of the geometrical structure can be seen in Table S5 in the Supporting Information. As shown in Figure 1, the optimized structure of [18]annulene-Li6-[18]annulene with C2 symmetry is a nearly perfect sandwich-like structure. For the purpose of comparison, the high symmetrical D2h structure is also computed at the same level. Its relative energy Erel with respect to the energetically more stable C2 structure is only 0.12 kcal/mol, which indicates that the higher symmetrical sandwich molecule may exist at a slightly high temperature. Due to the steric interactions, the internal protons of [18]annulene are slightly upturned, and the [18]annulene subunit with slight deformation remains an approximatly planar structure. Two [18]annulene planes are approximately parallel. By comparison with the isolated [18]annulene molecule, as shown in Tables S1 and S2 in the Supporting Information, we can find that the CC/CC bond length of [18]annulene in sandwich-like complex ranges from 1.382 to 1.442 Å (δ = Rsingle − Rdouble = 0.060 Å), while that in the isolated [18]annulene 9191



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subunits calculated at the CAM-B3LYP/6-31+G(d) level with counterpoise (CP) correction are −334.87 and −266.65 kcal/ mol, respectively. Note that the total interaction energy (−334.87 kcal/mol) of [18]annulene-Li6-[18]annulene is very large and more than 2 times the bond dissociation energy (−158 ± 2 kcal/mol) for ferrocene reported experimentally22 in 1992, suggesting the stability of such a hexanuclear sandwich complex. The averaged binding energy ΔE Li 6 ‑[18]annulene (−137.34 kcal/mol) between one [18]annulene and Li6 subunit is also large, indicating a strong interaction between the metallic Li6 moiety and the large organic ligand [18]annulene, which is consistent with the charge-separated nature of [18]annulene-Li6-[18]annulene from the molecule orbital analyses. Next, we analyzed the binding nature of the sandwich complex in two aspects: the interactions between ligands and the metal Li6 hexagon ring and the binding among Li atoms in the Li6 ring itself. The NBO charge analysis was performed to explore the nature of the metal−ligand interactions. The computed results are listed in Table S6 in the Supporting Information. As shown in Table S6 (Supporting Information), the NBO charges of six Li atoms are almost equal (from 0.449 to 0.476 e). The NBO charge of the Li6 subunit is +2.770 e, and the NBO charge of each [18]annulene subunit distinctly deviates from the formal charge, namely, −2. Therefore, remarkable donating and back-donating interactions may also exist between the ligands and the middle Li6 moiety. To reveal that, we performed a CDA study at the CAM-B3LYP/631G(d) level on the CAM-B3LYP/6-31+G(d) geometry and summarized the results in Table S6 (Supporting Information). The CDA results clearly show that considerable charge donation (+3.498 e) and slight back-donation (+0.105 e) occur in the sandwich complex. These results are in line with the NBO charge distribution listed above. Note that all the repulsive polarization items are negligible (−0.134), indicating the slight amount of charge in the overlapping area of the occupied molecular orbitals of the planar Li6 ring and [18]annulene ligand fragments. To analyze the binding among Li atoms in the Li6 ring itself, their WBIs are computed. The results are also listed in Table S6 (Supporting Information). The small WBIs (0.0448−0.0497) imply weak Li−Li interactions, which is consistent with the σ delocalized bonding orbital of the planar Li64+ hexagon ring. 3.4. Aromaticity of the Hexanuclear Sandwich Complex. The nucleus-independent chemical shift (NICS), proposed by Schleyer and co-workers,27 is an efficient and simple criterion in probing the aromaticity of a molecule. It is based on the negative value of the magnetic shielding computed, for example, at or above the geometrical centers

Figure 2. Origin of molecule orbitals of the hexanuclear sandwich complex [18]annulene-Li6-[18]annulene.

from the Li6 hexagon ring to two [18]annulene molecules. Therefore, the σ delocalized bonding orbital of the Li6 ring becomes the HOMO level of the sandwich complex, and the other four electrons are filled in the HOMO-1 and HOMO-2 levels of the sandwich complex. As shown in Figure 2, the HOMO-1 (bonding) level is derived from the interaction between two LUMOs of the [18]annulene molecules and the HOMO-2 (bonding) level is derived from the interaction between two LUMO+1's of the [18]annulene molecules. Similarly, the overlap of HOMOs of two [18]annulene's leads to HOMO-3 (antibonding) and HOMO-5 (bonding) of the sandwich complex, the overlap of HOMO-1's leads to HOMO4 (antibonding) and HOMO-6 (bonding) of the sandwich complex, etc. In a word, the sandwich complex is chargeseparated and the interaction among the three subunits can be explained in terms of electrostatic interaction and the [18]annulene-Li6-[18]annulene complex can be written as R−2-Li64+-R−2 (the dianion34 of [18]annulene reduced by potassium has been experimentally prepared and investigated). In addition, the novel sandwich complex exhibits a considerable HOMO−LUMO gap energy of 2.76 eV, which is larger compared with the HOMO−LUMO gap of about 1.9 eV in C6035 and implies the substantial kinetic stability of such a sandwich complex. As shown in Figure 2, the large HOMO− LUMO gap in this sandwich complex originates from the gap between the σ delocalized bonding orbital of the planar Li6 ring and the antibonding LUMO orbital derived from the interaction between the LUMOs of two [18]annulene's. 3.3. Interaction Energy and Binding Nature among the Subunits. The total interaction energy ΔEint and binding energy ΔEb between the [18]annulene···[18]annulene and Li6

Table 2. Distribution of Nucleus-Independent Chemical Shift (NICS, in ppm) in the Hexanuclear Sandwich Complex at the GIAO-B3LYP/6-311+G(d,p) Level of Theory distance over the plane

0.00a

0.45

0.90

1.35

1.80

2.25

2.70

3.15

3.80

4.80

6.00

1.87

sandwich complex [18]annulene in sandwichb [18]annulene benzene Li3+

−11.60 −13.32 −6.66 −8.03 −10.92

−11.31 −13.04 −6.64 −9.63 −9.92

−10.42 −12.49 −6.54 −10.48 −7.39

−9.51 −11.65 −6.30 −8.52 −4.55

−8.91 −10.58 −5.89 −5.87 −2.32

−8.48 −9.35 −5.33 −3.84 −0.96

−7.95 −8.09 −4.69 −2.54 −0.30

−7.25 −6.90 −4.04 −1.73 −0.05

−6.11

−4.43

−2.86

−8.73

a NICS(0.00) is for the geometric center of the Li6 ring in the sandwich complex/isolated [18]annulene/benzene/Li3+. NICS(1.87) is for the center of the [18]annulene in the sandwich complex. bThe NICS values of [18]annulene in the sandwich are obtained by simply removing the planar Li6 hexagon ring and another [18]annulene.

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the enhanced delocalization extent of [18]annulene in the sandwich complex. In addition, it can be demonstrated that the aromaticity at the center of the sandwich complex is comparable with those of the benzene molecule (−8.03 ppm) and aromatic Li3+ ring (−10.92 ppm). 3.5. Mechanical Stability of the Hexanuclear Sandwich Complex. Here, we also study the mechanical stability of the hexanuclear sandwich complex. Three different potential energy curves are shown in Figure 4. To examine the stability of the sandwich complex with respect to the sliding motion of the [18]annulene molecule, one [18]annulene ring is artificially translated, which is accompanied by the variation of the horizontal distance d between the centers of the Li6 plane and the [18]annulene plane. Meanwhile, the six lithium atoms and another [18]annulene molecule are fixed at their equilibrium positions. The relationship between the distance d and the relative energy of the model structure with respect to the equilibrium structure is obtained. As shown in Figure 4a, the potential energy curve is very steep and the total energy of the model structure at d = 1.5 Å is about 90 kcal/mol higher than the corresponding value of the equilibrium structure, indicating that the sandwich complex is indeed stable with respect to the sliding motion of the [18]annulene ligand. To examine the stability of the sandwich complex with respect to the stretching motion of two [18]annulene planes, two [18]annulene rings are artificially pulled or pushed with the change of the layer distance L. The relationship between the distance L and the relative energy of the model structure with respect to the equilibrium structure is exhibited in Figure 4b. As is shown in the figure, the potential energy curve is very deep, and the total energy of the model structure at L = 5.0 Å is about 120 kcal/ mol higher than the corresponding value of the equilibrium structure, which indicates the stability of the sandwich complex upon the stretching motion of two [18]annulene ligands. In addition, like the famous sandwich complex ferrocene, the stability of the [18]annulene-Li6-[18]annulene sandwich complex should be examined with respect to the rotating motion of two [18]annulene ligands. In the model structure, two [18]annulene rings are artificially rotated along the perpendicular axis through the center of the Li6 ring. The potential energy curve of the model structure as a function of the rotation angle θ is exhibited in Figure 4c. From Figure 4c, the rotation potential barrier (about 150 kcal/mol) of the sandwich complex is the largest at an angle θ of about 60°, which is quite larger than that (about 1 kcal/mol) in ferrocene37 and means that the rotation of the [18]annulene ligands is unlikely to occur.

of rings or clusters. Systems with negative NICS values are aromatic, and systems with strongly positive NICS values are antiaromatic. Nonaromatic cyclic systems should therefore have NICS values around zero. The more negative the NICS value, the more aromatic the system. As shown in Figure 2, two 2s electrons of six lithium atoms occupy the σ delocalized bonding orbital (HOMO) of the sandwich complex. The Li64+ hexagon ring with two delocalized electrons satisfies the 4n+2 electron counting rule of Hückel, which indicates that the cyclic conjugated Li64+ hexagon ring is aromatic like the all-metal aromatic unit Al42−.36 For analyzing the aromaticity of the sandwich complex, the NICS values are evaluated at the GIAOB3LYP/6-311+G(d,p) theoretical level by placing the ghost atoms at and above the geometric centers of the Li6 hexagon ring and the [18]annulene plane in sandwich complex. The computed NICS values are listed in Table 2 and depicted in Figure 3. As shown in Table 2, the NICS values at different

Figure 3. Diagram of the NICS values varying along the z axis of the hexanuclear sandwich complex.

points are all negative (−2.86 to −11.60 ppm), suggesting the aromaticity of [18]annulene-Li6-[18]annulene. From Figure 3, the aromaticity is strongest at the geometric center of the Li6 hexagon ring, and decreases toward the [18]annulene ligands. In order to further analyze the aromaticity of the sandwich complex, the aromaticity of [18]annulene in the sandwich complex, isolated [18]annulene molecule, benzene, and metal cluster cation Li3+ ring are computed at the same level. In comparison with the isolated [18]annulene molecule, we find that the aromaticity of [18]annulene is enhanced due to combination with the metal Li6 ring, which is consistent with

Figure 4. The mechanical stability of the hexanuclear sandwich complex with respect to the (a) sliding, (b) stretching, and (c) rotating motion of [18]annulene. 9193



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Figure 5. The geometrical structures of the hexanuclear sandwich complex and its multidecker multinuclear sandwich clusters (Li6)n([18]annulene)n+1 (n = 1, 2, 3).

Li6·[18]annulene subunit to (Li6)n−1([18]annulene)n, and the HOMO−LUMO gap computed at the CAM-B3LYP/6-31G(d) level for these multidecker sandwich clusters are listed in Table 1. The average binding energy ΔELi6‑[18]annulene is defined as

In a word, the novel hexanuclear sandwich complex [18]annulene-Li6-[18]annulene not only possesses a large interaction energy and HOMO−LUMO gap but also exhibits high mechanical stability. Due to the small interlayer distance (3.732 Å), the [18]annulene-Li6-[18]annulene complex would be protected from the direct contact with other chemical reagents and may be inactive at room temperature. Such a sandwich complex may be synthesized in the gas phase by a combination of laser vaporization and molecular beam methods, which has been successfully applied to synthesize [Lnn(C8H8)n+1] (Ln = Ce, Nd, Eu, Ho, and Yb).7a It has been demonstrated that this new approach should open up an area of organometallic chemistry and physics that can be studied quite nicely in the gas phase. If the hexanuclear sandwich [18]annulene-Li6-[18]annulene complex could be analyzed in experiment, it would expand the investigation of the multinuclear sandwich complexes and promote the development of the chemistry of metal multinuclear sandwich complexes. Besides, it could be expected to find potential applications in different areas of chemistry, such as material science. Note that the abundance of polarizable π delocalized electrons in the sandwich complex could yield species with large first hyperpolarizability if the centrosymmetry is broken; hence, it may be a good candidate for nonlinear optical (NLO) material design. 3.6. Multidecker Multinuclear Sandwich Clusters (Li6)n([18]Annulene)n+1 (n = 2−3). The unexpectedly large binding energy ΔEb between the [18]annulene···[18]annulene and Li6 subunits raises the question of whether the strong binding in this system can extend to larger (Li6)n([18]annulene)n+1 complexes. To answer this question, we optimized the structures of multidecker multinuclear sandwich clusters (Li6)n([18]annulene)n+1 (n = 1−3) at the B3LYP/6-31G(d) level, and their structures confirmed by all real frequencies are displayed in Figure 5. It has been reported in ref 32 by Vollmer et al. that, due to the unpaired spin on the lithium atoms, the complexes Lin·(C6H6)n+1 (n = 2−6) with multiple lithium atoms can have several different spin states, and the high spin states were found to be slightly more stable than the corresponding low spin predictions. Different from the case in the Lin·(C6H6)n+1 complexes, the multidecker multinuclear sandwich clusters (Li6)n([18]annulene)n+1 do not contain isolated Li atoms, so we only considered the singlet state of these species in the present work. The important geometrical parameters, including average binding energies (average metal− ligand interactions) ΔELi6‑[18]annulene between [18]annulene and Li6 subunits, the energy gain, ΔE(n, n − 1), with addition of a

ΔE Li6‐ [18]annulene = (Ecomplex (Xcomplex ) n+1

−

n

∑ E[18]annulene(Xcomplex) − ∑ E Li (Xcomplex))/2n , 6

i=1

i=1

(3)

n = 1−3

To eliminate the BSSE effect in the average binding energy ΔELi6‑[18]annulene, we also use the same basis set, Xcomplex, for the subunits’ calculation as for the complex’s calculation. The energy gain ΔE(n, n − 1) is given by ΔE(n , n − 1) = {E Li6‐ [18]annulene + E(Li6)n − 1([18]annulene)n} − E(Li6)n([18]annulene)n + 1,

n = 2−3

(4)

From Table 1, it can be found that the average C−H bond length (RC−H) in the (Li6)n([18]annulene)n+1 (n = 2, 3) clusters is 1.089 Å, which is close to the value (1.088 Å) in the isolated [18]annulene-Li6-[18]annulene sandwich complex. The average C−C bond length (RC−C) of the [18]annulene subunit varies depending on the location of the [18]annulene ring in the clusters, that is, RC−C = 1.419 (1.405−1.432) Å for the two side [18]annulene rings, increases toward the center of the sandwich clusters, and reaches a maximum value of 1.429 (1.406−1.443) Å for (Li6)3([18]annulene)4. For the average Li−Li distance RLi−Li in each Li6 hexagon ring, it also increases toward the center of the sandwich cluster. For the average layer distance L between two [18]annulene's, the situation is the same as that of RLi−Li. From the results of the average binding energies ΔELi6‑[18] annulene (−126.49 to −131.61 kcal/mol), the energy gain ΔE(n, n − 1) (96.97−98.22 kcal/mol), and HOMO−LUMO gaps (1.635−3.211 eV), we can find that the multidecker multinuclear sandwich clusters (Li6)n([18]annulene)n+1 (n = 2−3) are also highly stable. Note that, for n = 2, the HOMO−LUMO gap (1.635 eV) is relatively small, which indicates that (Li6)2([18]annulene)3 is thermodynamically less stable than (Li6)n([18]annulene)n+1 (n = 1, 3). The stability found in the sandwich clusters (Li6)n([18]annulene)n+1 (n = 1−3) implies that larger (Li6)n([18]annulene)n+1 (n > 3) complexes may also be stable. 9194



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The intriguing structure of multidecker multinuclear sandwich clusters (Li6)n([18]annulene)n+1 (n = 2, 3) might expand the concept of multidecker sandwich complexes. The inclusion of multiple metallic centers into multidecker sandwich structures will make them possess promising properties. If the multidecker hexanuclear sandwich clusters (Li 6 ) n ([18] annulene)n+1 could be experimentally synthesized, such new species might have potential applications in many areas, such as nanomaterials, etc.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (S.-J.W.); [email protected]. edu.cn (D.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21173095 and 21173098).

4. CONCLUSIONS In this paper, a novel sandwich-like complex [18]annulene-Li6[18]annulene is theoretically designed with a Li6 ring and two face-capping [18]annulene ligands. The results suggest that the hexanuclear sandwich complex with large interaction energy and HOMO−LUMO gap are charged-separated and highly stable, and likely to be experimentally synthesized. A combination of laser vaporization and molecular beam methods may be a good approach for synthesizing macroscopic amounts of such a sandwich complex in the gas phase. The nucleusindependent chemical shift (NICS) values calculated at and above the geometric center of the Li6 hexagon ring and [18]annulene plane are all negative (−2.86 to −11.60 ppm), suggesting its aromaticity. In addition, the mechanical stability of the sandwich compound is also studied. It is shown that the hexanuclear sandwich complex is mechanically stable with respect to deformation. In view of the increasing interests in multidecker sandwich complexes, the multidecker sandwich clusters (Li6)n([18]annulene)n+1 (n = 2−3) are also presented in this paper. The results suggest that such multidecker multinuclear sandwich clusters may be highly stable, and the stability found in the sandwich clusters (Li6)n([18]annulene)n+1 (n = 1−3) implies that larger (Li6)n([18]annulene)n+1 (n > 3) complexes may also be stable. The finding of the hexanuclear sandwich complex and its multidecker sandwich clusters might expand the concept of multinuclear sandwich complexes and multidecker multinuclear sandwich clusters and promote the development of the chemistry of metal sandwich complexes. Like ferrocene, the investigated hexanuclear sandwich complex could also be considered as a versatile building block with potential applications in different areas of chemistry. For example, due to the abundance of polarizable π electrons, [18]annulene-Li6[18]annulene may be a good candidate for NLO material design.

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Article

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ASSOCIATED CONTENT

S Supporting Information *

Complete refs 10a and 28, optimized geometries of C2 and D6h [18]annulene at the CAM-B3LYP/6-31+G(d) level and comparisons of C−C distances for the structures of [18]annulene computed at different levels of theory with those from the X-ray results, details of the geometrical structure for [18]annulene-Li6-[18]annulene with C2 symmetry, NBO charges of lithium atoms, WBI of Li−Li bond, CDA results between two [18]annulene2− ligand fragments and metal Li64+ ring fragment, and Cartesian coordinates for (Li6)n([18]annulene)n+1 (n = 1−3). Reaction energy for the FeCp2 → Fe (3d64s2) + 2Cp dissociation channel. The bond dissociation energy BDE for the Li·(C6H6)2 → Li + 2C6H6 dissociation channel. This material is available free of charge via the Internet at http://pubs.acs.org. 9195



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Quantum Mechanical Design and Structures of Hexanuclear

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