ARTICLE pubs.acs.org/JPCA
Structures, Energetics, and Aromaticities of the Tetrasilacyclobutadiene Dianion and Related Compounds: (Si4H4)2, (Si4H4)2 3 2Liþ, [Si4(SiH3)4]2 3 2Liþ, [Si4(SiH3)4]2 3 2Naþ, and [Si4(SiH3)4]2 3 2Kþ Sunghwan Kim, Suyun Wang, and Henry F. Schaefer, III* Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
bS Supporting Information ABSTRACT: In light of the important recent synthesis of a stable tetrasilacyclobutadiene dianion compound by Sekiguchi and co-workers and the absence of theoretical studies, ab initio methods have been used to investigate this dianion and a number of related species. These theoretical methods predict multiple minima for each compound, and most minima contain folded and bicyclic silicon rings. For (Si4H4)2, (Si4H4)2 3 2Liþ, [Si4(SiH3)4]2 3 2Liþ, [Si4(SiH3)4]2 3 2Naþ, and [Si4(SiH3)4]2 3 2Kþ, respectively, the energetically lowestlying structures are designated A-3 (C2v symmetry), B-8 (C1 symmetry), C-1 (C2 symmetry), D-1 (C2 symmetry), and E-1 (C2h symmetry). None of these structures satisfies both the ring planarity and the cyclic bond equalization criteria of aromaticity. However, all of the representative NICS values of these lowest-lying structures are negative, indicating some aromatic character. Especially, structures C-1 and D-1 of C2 symmetry effectively satisfy the criteria of aromaticity due to the slightly trapezoidal silicon rings, which are nearly planar with nearly equal bond lengths. SiH3 substitution for hydrogen in (Si4H4)2 3 2Liþ significantly reduces the degree of aromaticity, as reflected in the substantially smaller NICS absolute values for [Si4(SiH3)4]2 3 2Liþ than those of (Si4H4)2 and (Si4H4)2 3 2Liþ. The aromaticity is further weakened in [Si4(SiH3)4]2 3 2Naþ and [Si4(SiH3)4]2 3 2Kþ by replacing lithium with the sodium and potassium cations.
I. INTRODUCTION It has recently become possible to synthesize tetrasilacyclobutadiene dianion compounds, which are skeletal silicon homologues of the analogous carbon compounds.1 The tetrasilacyclobutadiene dianion species provides an important new type of ligand for transition metal complexes.2 Similar to the cyclobutadiene dianion (CBD2), for the related compounds incorporating silicon atoms, it is of interest to investigate questions related to structure and aromaticity. This is partly due to the fact that multiply charged 6π-aromatic cyclic systems behave quite differently from neutral and singly charged systems, due to the Coulombic repulsion of the two or one additional electrons.3,4 Measures of aromaticity are based on many different criteria, among which the H€uckel (4nþ2) rule5 affords perhaps the simplest test. According to the H€uckel rule, the tetrasilacyclobutadiene dianion should be considered aromatic because the number of π electrons is six (n = 2 for the 4nþ2 rule). However, aromaticity is a much more complex phenomenon than is suggested by a simple electron count. Currently, the most widely accepted measures of aromaticity are structural, energetic, and magnetic.6,7 Conventional aromatic molecules generally have planar ring skeletons with equal bond lengths, in contrast to the r 2011 American Chemical Society
marked alternation of bond length in singlet antiaromatic molecules.8 The aromatic stabilization energy (ASE) can be evaluated both experimentally and theoretically, but depends on the choice of reference standards.9,10 The nucleus-independent chemical shift (NICS), one of the characteristic magnetic properties of aromaticity, was introduced by Schleyer, Maerker, Dransfeld, Jiao, and Hommes11 in 1996 and has routinely been used to probe the aromatic character of mono- and polycyclic molecules.1,1216 NICS is based on the negative of the computed absolute shielding, typically at or above ring centers. Hence, negative NICS values of significant magnitude suggest aromaticity, and positive values suggest antiaromaticity. Many theoretical studies1723 have been reported for the structure and aromaticity of the parent carbon compound CBD2. Some of the results show folded and trapezoidal geometries,17,18 while Schleyer and co-workers19,20 predicted a planar delocalized CBD2 structure stabilized by coordination of two lithium cations. Sekiguchi and co-workers2427 recently succeeded in Received: March 21, 2011 Revised: April 22, 2011 Published: May 10, 2011 5478
dx.doi.org/10.1021/jp202671u | J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A isolating the first stable Me3Si-substituted CBD2 3 2Liþ, which has a square-planar delocalized aromatic structure. This structure was subsequently supported by Shainyan and Sekiguchi21 in 2005 using second-order MøllerPlesset (MP) perturbation theory. Very few explorations have been carried out on the valence isoelectronic tetrasilacyclobutadiene dianion, the CBD2 analogue composed of skeletal silicon atoms. As compared to the large number of theoretical studies related to neutral tetrasilacyclobutadiene,2838 there is apparently only one report involving the dianion. In 1989, Glukhovtsev, Simkin, and Minkin28 performed a semiempirical MINDO/3 investigation on tetrasilacyclobutadiene, its dication, and dianion. Their results showed a singlet minimum corresponding to the Cs nonplanar bicyclic structure of the dianion. In 2004, Lee, Takanashi, Matsuno, Ichinohe, and Sekiguchi1 synthesized the first tetrasilacyclobutadiene dianion, tetrakis(di-tert-butylmethylsilyl)-1,2,3,4-tetrasilacyclobutadiene dianion, stabilized by coordination to two potassium cations. This compound has a significantly folded four-membered ring (folding angle 34°) of highly pyramidalized skeletal silicon atoms, with the two potassium cations accommodated above and below the ring.1 The structural feature of the compound does not meet the classical criteria for aromaticity (ring planarity, cyclic bond equalization), thus apparently providing evidence for the nonaromatic nature. In light of the absence of theoretical insights for the tetrasilacyclobutadiene dianion, we have applied ab initio HartreeFock (HF) methods and density functional theory (DFT) to investigate the structure and aromaticity of the parent Si4H42 and range of related compounds.
II. THEORETICAL METHODS Quantum mechanical methods were used to study the structure and aromaticity of the tetrasilacyclobutadiene dianion (Si4H4)2, its dilithium salt (Si4H4)2 3 2Liþ, and the dilithium, disodium, and dipotassium salts of tetrakis(silyl)-1,2,3,4-tetrasilacyclobutadiene dianion [Si4(SiH3)4]2 3 2Mþ (M = Li, Na, and K). The Gaussian 94 software package39 was used in this study. For each compound, a thorough conformational search was initially performed at the HF level of theory because it was the simplest with reasonable accuracy among theoretical methods available in the software package. In addition, electron correlation effects were also taken into account by using the B3LYP density functional, a generalized gradient approximation (GGA) that employs the dynamical correlation functional of Lee, Yang, and Parr (LYP)40 in conjunction with the three-parameter HF/DFT hybrid exchange functional (B3) of Becke.41 The stationary points for the constrained planar four-membered silicon ring were also predicted, and the energy barriers between the planar and minimum structures were computed. The lowestlying minima have been identified for each of the tetrasilacyclobutadiene dianion compounds. On the basis of the optimized geometries at the lowest-lying stationary points, NICS values were obtained to analyze the aromaticity of the studied compounds. A double-ζ basis set with polarization and diffuse functions, denoted DZPþþ,4245 was used for the Si (12s8p1d/7s5p1d) and H (5s1p/3s1p) atoms with both the HF and the B3LYP methods. This basis set was constructed by augmenting the HuzinagaDunningHay sets4244 of contracted double-ζ Gaussian functions with one set of p polarization functions for each H atom and one set of d polarization functions for each
ARTICLE
silicon atom (Rd(Si) = 0.5, Rp(H) = 0.75). To complete the DZPþþ basis, one diffuse s function was added to each H atom, and a set of diffuse s and p functions was added to each silicon atom (Rs(Si) = 0.02729, Rp(Si) = 0.025, Rs(H) = 0.04415). These diffuse “even-tempered” orbital exponents were determined following the guidelines of Lee.45 For the lithium atom, the basis set was that of Thakkar, Koga, Saito, and Hoffmeyer, Li (9s5p/4s2p).46 For the sodium atom, the basis set was Na (11s5p/7s2p),4244,47 plus two sets of even-tempered p functions used as polarization functions (Rp(Na) = 0.163, 0.050).48 For the potassium atom, Wachters’s basis set (14s9p/10s6p)49 was augmented with one set of d polarization function (Rd(K) = 0.1) and two sets of even-tempered p functions (Rp(K) = 0.085202, 0.031737),48 which may be regarded as describing the 4p orbital. The final basis sets are thus designated Si (13s9p1d/8s6p1d), H (5s1p/3s1p), Li (9s5p/4s2p), Na (11s7p/7s4p), and K (14s11p1d/10s8p1d).
III. RESULTS AND DISCUSSION All optimized stationary-point geometries of the tetrasilacyclobutadiene dianion and related compounds are reported in the Supporting Information, and selected structures are depicted in Figures 14. The bond angles for the skeletal silicon ring of the dianion salts are summarized in the Supporting Information. Figure 5 illustrates the representative NICS values of the dianion compounds. The relative energies of the minimum structures with respect to the constrained planar stationary points are shown in Table 1. Note that, according to the vibrational frequency analysis, these constrained structures of D4h or C4h symmetry for all five compounds considered in the present study were not minima on the potential energy surface (PES), with at least three imaginary frequencies, which are also summarized in the Supporting Information.
A. Geometries. i. Tetrasilacyclobutadiene Dianion (Si4H4)2.
Stationary-point geometries for (Si4H4)2 at the HF and B3LYP DFT levels of theory are presented in Figure 1. According to the vibrational frequency analysis, all are minima, except for the (Si4H4)2 D4h structure (A-0). With the HF method, seven minima have been found for the parent (Si4H4)2 structures, including two of C2v symmetry (structures A-2 and A-3), one of Ci symmetry (A-4), one of C2 symmetry (A-5), and three of Cs symmetry (A-6A-8). Only six minima (A-1A-4, A-6, and A-7) have been discovered at the B3LYP level of theory. Instead of having a C2 structure as with the HF method, B3LYP results indicate the existence of a C2h geometry. Additionally, only two structures of Cs symmetry are predicted by B3LYP. Both HF and B3LYP show two minimum structures (A-4 and A-8 with HF; A-1 and A-4 with B3LYP) that contain the planar four-membered ring. However, these structures do not have equalized cyclic bond lengths, because the A-1 ring is a rectangle, the A-8 ring is actually a trapezoid, and the A-4 ring is a parallelogram. Except A-1, A-4, and A-8, all of the other geometries are folded to some degree. Nevertheless, A-5 shows a nearly planar structure [τe(Si1Si2Si3Si4) = τe(Si2 Si1Si4Si3) = 7.9°, τe(Si3Si2Si1Si4) = 8.3°, and τe(Si2 Si3Si4Si1) = 7.2°]. Structures A-2 and A-3 exhibit equal cyclic bond distances, although they are not planar. In addition, structures A-2, A-3, A-4, A-6, and A7 are predicted to be bicyclic with respect to the skeletal silicon ring. The lowest-lying (Si4H4)2 minimum that has been found exhibits C2v symmetry at both the HF and the B3LYP levels of 5479
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
Figure 1. Stationary-point geometries for the parent (Si4H4)2 optimized at the HF and B3LYP DFT levels of theory. Bond distances are in angstroms, and bond angles are in degrees. All except structure A-0 are equilibrium geometries.
theory, that is, the A-3 structure shown in Figure 1. Although A-3 is folded and bicyclic, the four bond lengths of the silicon ring are predicted to be the same. With the approximate inclusion of correlation effects, the B3LYP method gives longer bond distances than HF, but similar bond angles of the silicon ring are predicted for both methods. At the B3LYP level of theory, the optimized geometries for the silicon ring of A-3 are predicted to be re(Si1Si2) = re(Si2Si3) = re(Si3Si4) = re(Si4Si1) = 2.411 Å, θe(Si1Si2Si3) = θe(Si3Si4Si1) = 64.1°, and θe(Si2Si3Si4) = θe(Si4Si1Si2) = 110.3°. ii. Tetrasilacyclobutadiene Dilithium (Si4H4)2 3 2Liþ. For the neutral system (Si4H4)2 3 2Liþ, the HF method predicted nine minima, including one in C2 symmetry (structure B-1), one in Cs symmetry (B-2), and seven in C1 symmetry (B-4B-10), while the B3LYP method also gave rise to nine minima (B-1 B-8 and B-10), but with one more structure of Cs symmetry and one less structure of C1 symmetry (see the Supporting
Information). Figure 2 illustrates selected optimized structures, with the constrained stationary-point structure (B-0) of D4h symmetry. Unlike CBD2 3 2Liþ, which has a square-planar delocalized aromatic structure,1921 no genuine minimum structure with an exactly planar silicon ring has been found for (Si4H4)2 3 2Liþ with either the HF or the B3LYP method. Generally, all of the predicted minima are to some degree folded. However, the skeletal silicon ring in the C2 symmetry structure B-1 is very close to planarity [τe(Si1Si2Si3Si4) = τe(Si2Si1Si4Si3) = 8.3°, τe(Si3Si2Si1Si4) = 8.7°, and τe(Si2Si3Si4Si1) = 8.1° at the B3LYP level of theory]. For the other structures (B-2B-10), the four-membered ring is both folded and bicyclic. In particular, B-3, which introduces two lithium cations to structure A-3 of (Si4H4)2, is predicted by B3LYP to have nearly equal cyclic bond lengths. The B-10 geometry (reported in the Supporting Information) differs from the others by forming a hydrogen bridge 5480
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
Figure 2. Selected stationary-point geometries for (Si4H4)2 3 2Liþ, optimized at the HF and B3LYP DFT levels of theory. Bond distances are in angstroms. All except B-0 are equilibrium geometries.
(Si1HSi2) between two skeletal silicon atoms, in addition to the Si1Si2 bond. The structure B-8 of C1 symmetry is predicted to be the lowest-lying minimum found, with both the HF and the B3LYP methods. Interacting with two lithium atoms, the (Si4H4)2 part of the lowest-lying B-8 structure has a shape similar to A-7 rather than A-3 [the lowest-lying structure for (Si4H4)2] in Figure 1. As compared to the HF predictions, the B3LYP method for B-8 gives longer Si1Si2, Si1Si3, and Si1Si4 bond distances, but shorter Si2Si3 and Si3Si4 lengths. Accordingly, all of the internal bond angles (Si1Si2Si3, Si2Si3Si4, and Si3Si4Si1) in B-8 are widened (except the Si4Si1Si2 angle) at the B3LYP level with respect to the HF results (see the Supporting Information). With the B3LYP method, the optimized geometries for the silicon ring of B-8 are predicted to be re(Si1Si2) = 2.372 Å, re(Si2Si3) = 2.443 Å, re(Si3Si4) = 2.412 Å, re(Si4Si1) = 2.402 Å, θe(Si1 Si2Si3) = 65.6°, θe(Si2Si3Si4) = 102.5°, θe(Si3Si4Si1) = 65.6°, and θe(Si4Si1Si2) = 104.9°. iii. Tetrakis(silyl)-1,2,3,4-tetrasilacyclobutadiene Dilithium [Si4(SiH3)4]2 3 2Liþ. In addition to [Si4H4]2 3 2Liþ, we have also studied the structure and aromaticity of the tetra SiH3 compounds, [Si4(SiH3)4]2 3 2Mþ (M = Li, Na, and K). Note that the dianion synthesized by Sekiguchi and co-workers1 has
di-tert-butylmethylsilyl groups, tBu2MeSi, which are bulkier than the silyl substituents, SiH3, considered in the present study. For [Si4(SiH3)4]2 3 2Liþ, the HF predictions present eight minimum structures, consisting of one in C2 symmetry (structure C-1), one in Cs symmetry (C-2), and six in C1 symmetry (C-4C-9), and the B3LYP method leads to nine minima (C-1C-9) with one additional structure of Cs symmetry. Figure 3 shows selected optimized geometries of [Si4(SiH3)4]2 3 2Liþ, with the C4h stationary point (C-0). Shainyan and Sekiguchi21 theoretically proposed a squareplanar delocalized aromatic structure of SiH3-substituted CBD2 3 2Liþ. However, we find no fully planar silicon-ring structure on the PES for its all-silicon analogue, [Si4(SiH3)4]2 3 2Liþ, at either the HF or the B3LYP level of theory. Our C-1 structure (with C2 symmetry) does exhibit a silicon ring that is almost planar [τe(Si1Si2Si3Si4) = τe(Si2Si1Si4Si3) = 10.5°, τe(Si3Si2Si1Si4) = 11.0°, and τe(Si2Si3Si4Si1) = 10.0° at the B3LYP level of theory]. All of the other equilibrium geometries (C-2C-9) are folded to some extent, and also bicyclic. Similar to B-3 of (Si4H4)2 3 2Liþ, structure C-3 contains nearly equal cyclic bond lengths with the B3LYP method. No hydrogenbridged structure similar to B-10 of (Si4H4)2 3 2Liþ has been found for the tetrakis(silyl) system. 5481
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
Figure 3. Selected stationary-point geometries for [Si4(SiH3)4]2 3 2Liþ, optimized at the HF and B3LYP DFT levels of theory. Bond distances are in angstroms. All except structure C-0 are equilibrium geometries.
The lowest-lying structure for [Si4(SiH3)4]2 3 2Liþ is determined to be C-1 of C2 symmetry at both the HF and the B3LYP levels of theory. The SiH3 substitution for the H atoms of the lowest structure for (Si4H4)2 3 2Liþ (i.e., B-8) corresponds to structure C-8, in which there may be stronger steric repulsion among the SiH3 groups, as compared to the H atoms in B-8. This might be the reason why the lowest-lying minimum of [Si4(SiH3)4]2 3 2Liþ is C-1, which possesses a silicon ring similar to B-1, rather than B-8. Nearly planar, the silicon ring in C-1 is almost trapezoidal with equal bond lengths for the Si1Si4 and Si2Si3 bonds. As compared to the HF method, for structure C-1, B3LYP elongates re(Si1Si2) and shortens re(Si3Si4), but shows similar bond distances for Si1Si4 and Si2Si3, indicating more nearly equalized bond distances for the silicon ring. At the B3LYP level of theory, the silicon-ring related optimized geometries of C-1 are predicted to be re(Si1Si2) = 2.240 Å, re(Si2Si3) = re(Si4Si1) = 2.357 Å, re(Si3Si4) = 2.471 Å, θe(Si1Si2Si3) = θe(Si4Si1Si2) = 92.3°, and θe(Si2Si3Si4) = θe(Si3Si4Si1) = 86.7°.
iv. Tetrakis(silyl)-1,2,3,4-tetrasilacyclobutadiene Disodium [Si4(SiH3)4]2 3 2Naþ and Dipotassium [Si4(SiH3)4]2 3 2Kþ. Replacing lithium with sodium in [Si4(SiH3)4]2 3 2Liþ, seven minima have been optimized for [Si4(SiH3)4]2 3 2Naþ, and further replacing sodium with potassium resulted in six minima of [Si4(SiH3)4]2 3 2Kþ (see the Supporting Information). Selected structures of the two compounds are shown in Figure 4. Similar to [Si4(SiH3)4]2 3 2Liþ, [Si4(SiH3)4]2 3 2Naþ possesses a structure (D-1) of C2 symmetry with nearly planar silicon ring [τe(Si1Si2Si3Si4) = τe(Si2Si1Si4Si3) = 5.6°, τe(Si3Si2Si1Si4) = 5.8°, and τe(Si2Si3Si4Si1) = 5.4° at the B3LYP level of theory], while the structures D-2D-7 are folded and bicyclic. At the B3LYP level of theory, the Cs symmetry structure D-2 is found to have nearly equal bond distances for the silicon ring, although the ring is strongly folded. The D-1 geometry is predicted by both HF and B3LYP to be the lowest-lying among the [Si4(SiH3)4]2 3 2Naþ structures. Again, the silicon ring in D-1 is almost trapezoidal with equal bond lengths for Si1Si4 and Si2Si3 bonds. At the B3LYP level of 5482
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
Figure 4. Selected equilibrium geometries for [Si4(SiH3)4]2 3 2Naþ and [Si4(SiH3)4]2 3 2Kþ, optimized at the HF and B3LYP DFT levels of theory. Bond distances are in angstroms.
theory, the silicon-ring related optimized geometries of D-1 are predicted to be re(Si1Si2) = 2.272 Å, re(Si2Si3) = re(Si4Si1) = 2.338 Å, re(Si3Si4) = 2.422 Å, θe(Si1Si2 Si3) = θe(Si4Si1Si2) = 91.7°, and θe(Si2Si3Si4) = θe(Si3Si4Si1) = 88.0°. The three unique SiSi distances differ from the analogous Li structure by þ0.032, 0.019, and 0.049 Å, respectively. All predicted minima of [Si4(SiH3)4]2 3 2Kþ are folded and bicyclic, except for E-1 and E-2. Note that E-2 (C2 symmetry), which is a nearly planar structure, is found only at the HF level. E-1 (C2h symmetry) is exactly planar (or more specifically, rectangular) and determined to be the lowest-lying of [Si4(SiH3)4]2 3 2Kþ. For comparison, C-1 (Figure 3) and D-1 (Figure 4) have C2 symmetry for the SiH3-substituted tetrasilacyclobutadiene dianions with coordination of two lithium or sodium cations. With the B3LYP method, the silicon-ring related optimized geometries
of E-1 are predicted to be re(Si1Si2) = re(Si3Si4) = 2.351 Å, re(Si2Si3) = re(Si4Si1) = 2.318 Å, and θe(Si1Si2Si3) = θe(Si2Si3Si4) = θe(Si3Si4Si1) = θe(Si4Si1Si2) = 90.0°. This dipotassium structure has SiSi distances much closer (Δr = 0.033 Å) to each other than is the case for the analogous Li and Na structures. While the lowest-energy structure of [Si4(SiH3)4]2 3 2Kþ, E-1, has a rectangular Si4 ring skeleton, the dipotassium salt of tetrakis(di-tert-butylmethylsilyl)-1,2,3,4-tetrasilacyclobutadiene dianion, [Si4(tBu2MeSi)4]2 3 2Kþ, synthesized by Sekiguchi and coworkers,1 has a folded ring. Note that the tBu2MeSi groups are much bulkier than the SiH3 substituents considered in the present study. Therefore, replacing the SiH3 groups in structure E-1 with the bulkier tBu2MeSi groups may cause steric repulsion between the substituents, which is energetically unfavorable. To minimize this unfavorable interaction, [Si4(tBu2MeSi)4]2 3 2Kþ 5483
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
Figure 5. Representative NICS values shown as solid dots for the lowest-lying minima of the tetrasilacyclobutadiene dianion compounds at the B3LYP level of theory. The absolute NICS values are proportional to the size of the dots.
has a folded Si4 ring, with its tBu2MeSi groups occupying alternating up and down positions. B. Energetics. The relative energies of the minimum structures with respective to the constrained D4h/C4h stationary points are reported in Table 1 at the HF and B3LYP levels of theory for the tetrasilacyclobutadiene dianion compounds. The larger is the energy difference relative to the 4-fold symmetry stationary point, the more readily distinguished is the lower-lying minimum geometry predicted for the compound. All of the minima in Table 1 are associated with negative relative energies, except for the [Si4(SiH3)4]2 3 2Liþ structures
C-4, C-5, and C-7, which lie higher than the corresponding C4h saddle point. The energy separations between minima and the constrained planar structures become much smaller with the addition of two lithium cations to (Si4H4)2. These separations decrease more dramatically or are even reversed; that is, some minima are energetically located above the planar saddle point, when substituting the hydrogens of (Si4H4)2 3 2Liþ with SiH3. However, these energy deviations become larger, relative to the dilithium salts, for the disodium system and more so for the dipotassium salts of [Si4(SiH3)4]2. 5484
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
Table 1. Relative Energies (in kcal mol1) of the Tetrasilacyclobutadiene Dianion Compounds With Respect To the Constrained D4h/C4h Stationary Point at the HF and B3LYP DFT Levels of Theory HF R group counterion structures H
none
A-0
E 0.0
B3LYP
EþZPVE 0.0
A-1
H
Liþ
SiH3
SiH3
Liþ
Naþ
Kþ
EþZPVE
0.0
0.0
46.0
46.1
A-2
55.6
55.1
54.9
54.3
A-3
65.4
63.9
63.2
61.6
49.2
48.1
49.1 59.1
48.1 58.1
A-4
49.3
48.3
A-5
42.2
42.1
A-6 A-7
49.4 60.7
48.5 59.8
A-8
42.1
42.4
B-0
0.0
0.0
0.0
0.0
B-1
15.2
15.0
14.3
14.4
B-2
16.5
16.5
B-3
SiH3
E
18.4
18.4
18.9
18.3
B-4
8.7
8.5
8.2
8.2
B-5 B-6
4.3 5.1
4.9 5.1
8.0 5.4
8.2 5.3
B-7
7.7
7.3
9.8
9.7
B-8
17.1
17.1
19.9
19.8
B-9
16.8
16.5
B-10
0.9
1.5
4.2
4.7
C-0
0.0
0.0
0.0
0.0
C-1
9.0
8.8
12.4
11.9
C-2 C-3
2.6
2.0
8.6 7.1
7.9 6.5
C-4
þ5.3
5.6
þ1.4
1.8
C-5
þ8.3
8.3
þ2.8
3.1 1.2
C-6
þ2.1
2.0
1.6
C-7
þ19.3
19.5
þ7.5
7.8
C-8
þ0.4
0.9
8.0
7.4
C-9
3.4
3.1
7.4
7.0
D-0 D-1
0.0 18.3
0.0 18.0
0.0 19.3
0.0 19.0 13.9
D-2
11.6
11.1
14.6
D-3
5.2
4.9
7.8
7.6
D-4
2.9
2.8
6.1
6.1
D-5
10.4
10.2
11.9
11.8
D-6
5.3
5.0
10.7
10.5
D-7
14.5
14.3
16.7
16.4
E-0 E-1
0.0 23.4
0.0 23.2
0.0 27.9
0.0 27.4 13.9
E-2
22.9
22.7
E-3
14.2
13.9
14.1
E-4
7.4
7.4
9.3
9.3
E-5
10.8
10.7
13.6
13.6
E-6
18.9
18.7
19.9
19.6
It appears that some minimum structures with very different geometries exhibit small energy variations of 0.1 kcal mol1, for example, A-4 and A-6 of (Si4H4)2 with the HF and B3LYP
methods, and D-3 and D-6 of [Si4(SiH3)4]2 3 2Naþ at the HF level of theory. The lowest-lying structures have been found to be A-3 (C2v symmetry in Figure 1), B-8 (C1 symmetry in Figure 2), C-1 (C2 symmetry in Figure 3), D-1 (C2 symmetry in Figure 4), and E-1 (C2h symmetry in Figure 4) for (Si4H4)2, (Si4H4)2 3 2Liþ, [Si4(SiH3)4]2 3 2Liþ, [Si4(SiH3)4]2 3 2Naþ, and [Si4(SiH3)4]2 3 2Kþ, respectively. The energy lowerings as compared to 4-fold symmetry of these lowest-lying minima are predicted to be 63.2 (A-3), 19.9 (B-8), 12.4 (C-1), 19.3 (D-1), and 27.9 (E-1) kcal mol1, respectively, at the B3LYP level of theory, with respect to the corresponding constrained planar structures. C. Nucleus-Independent Chemical Shifts. Representative NICS values at the B3LYP level of theory are illustrated as solid dots in Figure 5 for the five global minima (A-3, B-8, C-1, D-1, and E-1) of the tetrasilacyclobutadiene dianion compounds. The size of each dot is proportional to the absolute NICS values, and some of the NICS values are listed alongside the corresponding dots in the figure. All of the representative NICS values are predicted to be negative, indicating that the tetrasilacyclobutadiene dianion compounds may have aromatic character according to Schleyer’s definition.11 For example, the NICS values at the midpoint of the Si1Si3 bond are 29.0 for A-3 of (Si4H4)2 and 33.7 for B-8 of (Si4H4)2 3 2Liþ; the NICS values at the center of the four-membered silicon ring are 14.4 for C-1 [Si4(SiH3)4]2 3 2Liþ, 12.9 for D-1 [Si4(SiH3)4]2 3 2Naþ, and 13.9 for E-1 [Si4(SiH3)4]2 3 2Kþ. The dilithium salt of the tetrasilacyclobutadiene dianion (B-8) provides NICS values that are similar to those the parent dianion (A-3), that is, without the metal cations. Of course, we cannot exactly compare the NICS values of these two species due to the different structures. Yet it is safe to conclude that the addition of lithium cations to (Si4H4)2 does not particularly enhance the aromaticity. Substituting hydrogen with SiH3 in (Si4H4)2 3 2Liþ substantially decreases the absolute NICS values, although the more nearly planar silicon ring is obtained at the C-1 (lowestlying energetically) geometry, indicating significant weakening of the aromatic effect. With the analogous sodium C2 structure [Si4(SiH3)4]2 3 2Naþ (D-1), one sees a further reduction in the absolute NICS values, suggesting a lower degree of aromaticity than that for [Si4(SiH3)4]2 3 2Liþ (C-1). The [Si4(SiH3)4]2 3 2Kþ structure (E-1, C2h symmetry) has an exactly planar silicon ring. However, the aromaticity is not enhanced with respect to the sodium analogue as the NICS values are comparable. We conclude that [Si4(SiH3)4]2 3 2Kþ is less aromatic than the “free” tetrasilacyclobutadiene dianion, while other comparisons are less clear-cut.
IV. CONCLUDING REMARKS We have investigated the structures and aromaticities of a range of tetrasilacyclobutadiene dianion compounds. A number of structures are found for each compound. Most minima have folded and bicyclic silicon rings. However, there are some structures with special characteristics for the skeletal ring. Structures A-1 (C2h symmetry), A-4 (Ci symmetry), A-8 (Cs symmetry), and E-1 (C2h symmetry) show precisely planar fourmembered silicon rings, while structures A-5 (C2 symmetry), B-1 (C2 symmetry), C-1 (C2 symmetry), D-1 (C2 symmetry), and E-2 (C2 symmetry) exhibit nearly planar rings. Structures A-1 and E-1 are both of the same C2h symmetry, and the two 5485
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A structures have rectangular silicon rings. With symmetries lower than A-1 and E-1, the A-4 and A-8 skeletal rings display parallelogram and trapezoid shapes, respectively. Structures A-2 and A-3, which possess similar C2v symmetries, are predicted to have equivalent cyclic silicon bond lengths. The B-3, C-3, D-2, and E-3 structures of Cs symmetry are found to contain nearly equal SiSi bond distances for the skeletal rings. The lowest-lying structures have been predicted to be A-3 (C2v symmetry), B-8 (C1 symmetry), C-1 (C2 symmetry), D-1 (C2 symmetry), and E-1 (C2h symmetry) for (Si4H4)2, (Si4H4)2 3 2Liþ, [Si4(SiH3)4]2 3 2Liþ, [Si4(SiH3)4]2 3 2Naþ, and [Si4(SiH3)4]2 3 2Kþ, respectively. Although structures A-3 and E-1 satisfy the cyclic bond equalization or ring planarity criterion of aromaticity, respectively, none of the five lowest-lying structures satisfy both criteria for aromaticity. However, all of the representative NICS values of these lowest-lying structures are predicted to be negative, indicating possible aromatic character. Especially, structures C-1 and D-1 of C2 symmetry effectively satisfy the criteria of aromaticity due to the slightly trapezoidal silicon rings, which are nearly planar with nearly equal bond lengths. The SiH3-substituted dilithium salt of tetrasilacyclobutadiene dianion displays a significantly lower degree of aromaticity, because of the substantially smaller absolute NICS values, than those of (Si4H4)2 and (Si4H4)2 3 2Liþ. The degree of aromaticity is further diminished by replacing the lithium cations by the sodium and potassium cations to form [Si4(SiH3)4]2 3 2Naþ and [Si4(SiH3)4]2 3 2Kþ.
’ ASSOCIATED CONTENT
bS
Supporting Information. All optimized stationary-point geometries of the tetrasilacyclobutadiene dianion and related compounds considered in the present study. The bond angles for the skeletal silicon ring of the dianion salts and the imaginary frequencies of the constrained planar stationary-point structures of D4h or C4h symmetry. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We would like to thank Professor Paul von Rague Schleyer for his suggestions of possible new minimum structures of the tetrasilacyclobutadiene dianion compounds. We also want to thank Dr. Yaoming Xie and Dr. Zhongfang Chen for helpful discussions on the NICS computations. This research was supported by the National Science Foundation, Grant CHE0749868. ’ REFERENCES (1) Lee, V. Y.; Takanashi, K.; Matsuno, T.; Ichinohe, M.; Sekiguchi, A. Cyclobutadiene dianions consisting of heavier group 14 elements: synthesis and characterization. J. Am. Chem. Soc. 2004, 126, 4758–4759. (2) Takanashi, K.; Lee, V. Y.; Matsuno, T.; Ichinohe, M.; Sekiguchi, A. Tetrasilacyclobutadiene (tBu2MeSi)4Si4: a new ligand for transitionmetal complexes. J. Am. Chem. Soc. 2005, 127, 5768–5769.
ARTICLE
(3) Feuerbacher, S.; Cederbaum, L. S. Influence of delocalization on the stability of dianions: study of a systematic series of dianions with growing electronic localization. J. Am. Chem. Soc. 2003, 125, 9531–9537. (4) Sommerfeld, T. A fresh look at aromatic dianions. J. Am. Chem. Soc. 2002, 124, 1119–1124. (5) H€uckel, E. Quantentheoretische beitr€age zum benzolproblem I. Die elektronenkonfiguration des benzols und verwandter verbindungen. Z. Phys. 1931, 70, 204–286. (6) Jung, Y.; Heine, T.; Schleyer, P. v. R.; Head-Gordon, M. Aromaticity of four-membered-ring 6π-electron systems: N2S2 and Li2C4H4. J. Am. Chem. Soc. 2004, 126, 3132–3138. (7) Schleyer, P. v. R. Introduction: aromaticity. Chem. Rev. 2001, 101, 1115–1118. (8) Krygowski, T. M.; Cyranski, M. K. Structural aspects of aromaticity. Chem. Rev. 2001, 101, 1385–1420. (9) Slayden, S. W.; Liebman, J. F. The energetics of aromatic hydrocarbons: an experimental thermochemical perspective. Chem. Rev. 2001, 101, 1541–1566. (10) Schaad, L. J.; Hess, B. A. Dewar resonance energy. Chem. Rev. 2001, 101, 1465–1476. (11) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Hommes, N. J. R. v. E. Nucleus-independent chemical shifts: a simple and efficient aromaticity probe. J. Am. Chem. Soc. 1996, 118, 6317–6318. (12) Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Which NICS aromaticity index for planar π rings is best? Org Lett. 2006, 8, 863–866. (13) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. Chem. Rev. 2005, 105, 3842–3888. (14) Pogodin, S.; Agranat, I.; Fetzer, J. C. A theoretical study of the conformations of tetrabenzo[A,CD,F,LM]perylene. An overcrowded LPAH. Polycyclic Aromat. Compd. 2004, 24, 151–160. (15) Zywietz, T. K.; Jiao, H.; Schleyer, P. v. R.; de Meijere, A. Aromaticity and antiaromaticity in oligocyclic annelated five-membered ring systems. J. Org. Chem. 1998, 63, 3417–3422. (16) Corminboeuf, C.; Heine, T.; Seifert, G.; Schleyer, P. v. R.; Weber, J. Induced magnetic fields in aromatic [n]-annulenes interpretation of NICS tensor components. Phys. Chem. Chem. Phys. 2004, 6, 273–276. (17) Hess, B. A.; Ewig, C. S.; Schaad, L. J. An ab initio study of the cyclobutadiene dianion and dication. J. Org. Chem. 1985, 50, 5869–5871. (18) van Zandwijk, G.; Jannsen, R. A. J.; Buck, H. M. 6π Aromaticity in four-membered rings. J. Am. Chem. Soc. 1990, 112, 4155–4164. (19) Balci, M.; McKee, M. L.; Schleyer, P. v. R. Theoretical study of tetramethyl- and tetra-tert-butyl-substituted cyclobutadiene and tetrahedrane. J. Phys. Chem. A 2000, 104, 1246–1255. (20) Kos, A. J.; Schleyer, P. v. R. Thionium ions as carbonyl substitutes. Synthesis of cyclic imino thioethers and lactams. J. Am. Chem. Soc. 1980, 102, 7929–7932. (21) Shainyan, B. A.; Sekiguchi, A. Computational study of tetrasilylcyclobutadiene dianion and its dilithium salt. 6e-6c three-dimensional aromaticity. J. Mol. Struct. 2005, 728, 1–5. (22) Glukhovtsev, M. N.; Simkin, B. Y.; Minkin, V. I. Quantumchemical study of the cyclobutadiene dianion structure. Russ. J. Org. Chem. 1987, 23, 1317–1319. (23) Clark, T.; Wilhelm, D.; Schleyer, P. v. R. Y vs cyclic delocalization in small ring dications and dianions: the dominance of charge repulsion over Huckel aromaticity. Tetrahedron Lett. 1982, 23, 3547– 3550. (24) Sekiguchi, A.; Matsuo, T.; Watanabe, H. Synthesis and characterization of a cyclobutadiene dianion dilithium salt: evidence for aromaticity. J. Am. Chem. Soc. 2000, 122, 5652–5653. (25) Ishii, K.; Kobayashi, N.; Matsuo, T.; Tanaka, M.; Sekiguchi, A. Observation of the predicted negative Faraday A MCD term in a cyclobutadiene dianion. J. Am. Chem. Soc. 2001, 123, 5356–5357. (26) Matsuo, T.; Sekiguchi, A. Bull. Chem. Soc. Jpn. 2004, 77, 211. (27) Sekiguchi, A.; Matsuo, T.; Tanaka, M.; Watanabe, H.; Nakamoto, M. Russ. Chem. Bull. 2004, 53, 1109. 5486
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
The Journal of Physical Chemistry A
ARTICLE
(28) Glukhovtsev, M. N.; Simkin, B. Y.; Minkin, V. I. Quantum chemical study of the structure of tetrasilacyclobutadiene, its dication, and dianion. J. Struct. Chem. 1989, 30, 886–894. (29) Sax, A. F.; Kalcher, J. MC-SCF and CI calculations on the Si4H4 system. J. Comput. Chem. 1989, 10, 309–328. (30) Yates, B. F.; Schaefer, H. F. Tetrasilacyclobutadiylidene: the lowest energy cyclic isomer of singlet Si4H4? Chem. Phys. Lett. 1989, 155, 563–571. (31) Raahe, G.; Michl, J. In The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z., Eds.; Wiley: Chichester, 1989; pp 10151142. (32) Nagase, S.; Nakano, M. Is tetrasilatetrahedrane kinetically stable? Angew. Chem., Int. Ed. Engl. 1988, 27, 1081–1083. (33) Ohanessian, G.; Hiberty, P. C.; Lefour, J.-M.; Flament, J.-P.; Shaik, S. S. Is delocalization a driving force in chemistry? First- and second-row heteroannulenes. Inorg. Chem. 1988, 27, 2219–2224. (34) Yates, B. F.; Clabo, D. A.; Schaefer, H. F. Cyclic isomers of singlet Si4H4 related to tetrasilacyclobutadiene. Chem. Phys. Lett. 1988, 143, 421–427. (35) Sax, A. F.; Kalcher, J. Quantum chemical calculations on Si4H4. J. Chem. Soc., Chem. Commun. 1987, 809–810. (36) Clabo, D. A.; Schaefer, H. F. Tetrasilatetrahedrane. J. Am. Chem. Soc. 1986, 108, 4344–4346. (37) Suzuki, K.;A planar rhombic charge-separated tetrasilacyclobutadiene. Science 2011, 331, 1306–1309. (38) Apeloig, Y. The diamond within a silicon analog of cyclobutadiene. Science 2011, 331, 1277–1278. (39) Frisch, M. J.; et al. Gaussian 94, revision C.3; Gaussian, Inc.: Pittsburgh, PA, 1995. (40) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1998, 37, 785–789. (41) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648–5652. (42) Huzinaga, S. Gaussian-type functions for polyatomic systems. I. J. Chem. Phys. 1965, 42, 1293–1302. (43) Dunning, T. H. Gaussian basis functions for use in molecular calculations. I. Contraction of (9s5p) atomic basis sets for the first-row atoms. J. Chem. Phys. 1970, 53, 2823–2833. (44) Dunning, T. H.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum Press: New York, 1977; pp 128. (45) Lee, T. J.; Schaefer, H. F. Systematic study of molecular anions within the self-consistent-field approximation: OH, CN, C2H, NH2, and CH3. J. Chem. Phys. 1985, 83, 1784–1794. (46) Thakkar, A. J.; Koga, T.; Saito, M.; Hoffmeyer, R. E. Double and quadruple zeta contracted Gaussian basis sets for hydrogen through neon. Int. J. Quantum Chem., Quantum Chem. Symp. 1993, 27, 343–354. (47) Huzinaga, S. Department of Chemistry Report; University of Alberta: Edmonton, 1971. (48) Ma, B.; Meredith, C.; Schaefer, H. F. Pyrophosphate structures and reactions: evaluation of electrostatic effects on the pyrophosphates with and without alkali cations. J. Phys. Chem. 1994, 98, 8216–8223. (49) Wachters, A. J. H. Gaussian basis set for molecular wavefunctions containing third-row atoms. J. Chem. Phys. 1970, 52, 1033–1036.
5487
dx.doi.org/10.1021/jp202671u |J. Phys. Chem. A 2011, 115, 5478–5487
