Stability Rules of Main-Group Element Compounds with Planar

Jul 9, 2010 - ring and conjugated three-membered ring, as well as π electrons. These rules ... compounds containing ptC to obtain the stability rules...
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J. Phys. Chem. A 2010, 114, 7960–7966

Stability Rules of Main-Group Element Compounds with Planar Tetracoordinate Carbons Congjie Zhang,*,† Wenhong Jia,† and Zexing Cao*,‡ Key Laboratory of Macromolecular Science of Shaanxi ProVince, School of Chemistry & Materials Science, Shaanxi Normal UniVersity, Xi’an 710062, China, and Department of Chemistry and State Key Laboratory of Physical Chemistry of Solid Surface, Xiamen UniVersity, Xiamen 361005, China ReceiVed: March 24, 2010; ReVised Manuscript ReceiVed: June 20, 2010

We have investigated the structures, stabilities, aromaticities, and Wiberg bond indices of four types of compounds (8-like, trapezia, umbrella-like, and quadrangle) containing planar tetracoordinate carbon (ptC), and the stability rules for the compound with ptC were concluded on the basis of extensive calculations. Generally, the stability or viability of compound with ptC strongly depends on the number of three-membered ring and conjugated three-membered ring, as well as π electrons. These rules can be successfully used to identify the stability of other compounds reported in previous studies. On the basis of these rules, eight stable compounds with planar tetracoordinate nitrogen (ptN) are successfully constructed. Introduction In 1970, Hoffmann, Alder, and Wilcox investigated the electronic structure of the planar methane with an electron pair orthogonal to the molecular plane,1 and their calculations indicated that the planar methane is not stable. Recently, many efforts have been conducted to obtain a stable compound with ptC, both experimentally and theoretically, and remarkable progress has been made in this domain. These compounds can be classified into two kinds: one kind is that the ptC is confined within a cage,2-5 and the other is that ptC is incorporated into a conjugated system.6-37 Generally, the cage molecules with ptC are not easily synthesized due to the remarkable strain between atoms. Conjugated molecules with ptC have four types of structures: 8-like,6-22 trapezia,14,18,21,23,24 umbrella-like,6,21 and quadrangle24-36 (as shown in Scheme 1). In this Article, we have investigated the bonding model of the four types of compounds containing ptC to obtain the stability rules. Moreover, we will validate these stability rules in those compounds with ptC in previous papers and design many novel molecules with ptN in terms of these stability rules. Computational Methods We have constructed four types of compounds with ptC and eight molecules with ptN on the basis of the stability rules of the compounds with ptC. Full geometry optimization and vibrational analysis of all compounds are carried out at the B3LYP/6-311++G** level of theory. Predicted energies, zeropoint energies (ZPEs), natural charge populations on ptC, dipole moments, and smallest vibrational frequencies of these compounds are listed in Table 1. The nucleus-independent chemical shifts (NICS) of the lowest energy structures are calculated by the gauge-independent atomic orbital (GIAO) method. Wiberg bond indices (WBIs) of the lowest energy molecules have been achieved by natural bond orbital (NBO) analyses. All calculations in the present work have been performed via the Gaussian 03 program.38 The number of π electrons in these compounds are counted according to the valence bond theory (VBT).

Results and Discussion A. 8-like Compounds with ptC. According to the valence bond theory, the planar methane is not stable due to the lone electron pair on the carbon atom, which roots in that the dication of methane is of planar but not tetrahedral structure.39 In general, if the lone electron pair on the carbon atom of a molecule can properly be distributed, the molecule with ptC will probably exist. First, we optimized five molecules 1, 2, 3, 4, and 5 shown in Figure 1. As can be seen from Figure 1, the left part of these five molecules is a conjugated three-membered moiety formed by two boron atoms and a center carbon, while the right part consists of hydrogen atoms or saturated hydrocarbon units. Optimized geometries indicate that 1 and 2 are in C2V symmetry, and the sum of the four angles associated with the center carbon in 3, 4, and 5 is 359.9°, 370.0°, and 378.3°, respectively. Although the initial structures of compounds 3-5 with C1 symmetry are considered in full geometry optimization, the optimized structure of 3 still exhibits a mirror perpendicular to the molecule, and the further optimization within Cs symmetry leads to an isoenergetic species with the structure of 3 in C1 symmetry. However, the optimized structures of 4 and 5 are slightly spiral, indicating that they have no ptC atoms. Therefore, the dihedral angles associated with center carbon decrease as the increase of the size of right rings in 2-5. Compound 2 has C2V symmetry, and it obviously contains a ptC, and the center carbon in compound 3 has dominant character of a ptC. As Table 1 shows, the smallest vibrational frequencies of 2, 3, 4, and 5 are 92, 32, 12, and 127 cm-1, respectively, while the smallest vibrational frequency of 1 is 205i cm-1. Accordingly, 2 and 3 with ptC are minima on the potential energy surface. Analyzing the electronic structure of the five compounds (1-5) as shown in Figure 1, there is a conjugated three-membered ring of BCB and two π electrons on ptC in the five molecules. They should SCHEME 1: Four Types of Structures with ptC

* Corresponding author. E-mail: [email protected] (C.Z.); zxcao@ xmu.edu.cn (Z.C.). † Shaanxi Normal University. ‡ Xiamen University.

10.1021/jp102678v  2010 American Chemical Society Published on Web 07/09/2010

Main-Group Element Compounds with ptC

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TABLE 1: Total Energies (E, hartree), Symmetries (symm), Zero-Point Energies (ZPE, eV), Natural Charges on ptC and ptN (q, e), Dipole Moments (µ, debye), and the Smallest Vibrational Frequencies (Wmin, cm-1) of Compounds 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

symm

Ea

ZPE

q

µ

Vmin

Eb

C2V C2V Cs C1 C1 C2V C2V Cs D2h D2h C2V C2V C2V C2V C2V C2V C2V C2V C2V C2V C2V C2V Cs Cs C2V C2V Cs Cs Cs Cs D4h C2V D2h C2V C2V C2V Cs Cs Cs C2V

-90.15148 -167.56033 -206.87729 -246.22493 -285.55642 -166.29485 -166.36362 -160.66296 -154.96098 -139.81117 -165.22637 -195.30827 -192.96921 -222.98048 -218.39310 -244.97894 -271.44567 -190.65437 -217.29143 -243.77855 -165.07969 -165.04500 -165.04370 -165.07987 -138.59756 -166.31527 -167.58953 -153.72672 -181.39129 -180.15753 -1007.83819 -1170.26701 -156.57370 -164.07590 -155.30544 -154.98416 -168.48155 -183.97574 -170.11722 -1186.95218

29.44 52.25 70.72 89.25 107.27 36.57 37.60 36.35 35.23 32.58 40.44 45.04 59.72 61.68 67.85 73.20 76.62 48.39 55.25 59.91 26.18 22.85 24.46 24.59 22.76 41.45 53.69 44.54 61.04 45.28 2.28 5.01 32.56 34.34 20.68 22.17 23.43 53.82 44.85 4.87

-0.84 -0.52 -0.44 -0.45 -0.45 -0.45 -0.24 -0.48 -0.75 -1.17 -1.23 -1.15 -0.64 -0.88 -1.20 -1.19 -0.47 -0.72 -0.96 -0.24 -0.08 -0.03 -0.22 -0.05 -0.86 -0.27 -0.32 -0.57 -0.27 0.08 -3.05 -2.67 -0.96 -0.96 -0.83 -1.04 -0.69 -0.64 -0.83 -2.32

1.87 3.34 3.02 2.56 2.95 4.39 0.41 6.89 0.00 0.00 0.33 3.83 4.71 0.74 5.54 3.15 6.20 0.35 2.39 1.23 0.86 0.57 2.35 0.85 1.23 1.63 2.26 2.05 0.66 2.42 0.00 7.03 0.00 7.94 0.98 0.20 0.93 1.13 0.70 8.08

205i(b2) 92(a2) 32(a′′) 12(a) 127(a) 119(b2) 193(a2) 115(a′′) 90(b3u) 493i(b3u) 466i(b1) 158i(b1) 295i(b1) 390i(b1) 338i(a2) 341i(a2) 541i(a2) 426i(a2) 198i(b1) 44i(a2) 455(b1) 339(b1) 326(a′′) 320(a′′) 256(a2) 229(b1) 181(a′′) 23(a′′) 363i(a′′) 458i(a′′) 479i(eu) 65(b1) 122(au) 97(b1) 244(b2) 266(b1) 324(a′′) 168(a′′) 24(a′′) 69(b1)

-90.12650 (2) -167.54431 (2) -206.85097 (2) -246.22493 (0) -285.53587 (2) -166.25991 (1) -166.26797 (0)c -160.55250 (1)c -154.75118 (8) -139.81725 (2) -165.22695 (4) -195.29277 (2) -192.98428 (2) -223.05609 (0)

-156.53855 (0)c -163.98620 (3)

a

The total energies of the compounds with ptC (ptN). b The total energies of the tetrahedral isomers of the corresponding compounds with ptC (ptN). c The energies of the triplet of tetrahedral isomers of 7 (3B), 8 (3A′′), and 27 (3A1).

be stable according to the 4n + 2 rule from Huckel molecular theory, but only 2 is viable40 and strictly contains a ptC. Therefore, the 8-like viable molecule with ptC depends on the number of delocalized π electron. Additionally, it should contain two three-membered rings, in which one three-membered ring should be conjugated. Second, we change the saturated -CH2-CH2- of 2 into the unsaturated -CHdCH- to obtain compound 6, which has two conjugated three-membered rings. Again, compound 7 as the isomer of 6 is also constructed. The vibrational frequencies of 6 and 7 in Table 1 indicate that the two molecules are stable without imaginary frequency, and 7 is lower in energy than 6 by 42.96 kcal/mol, indicating that 7 is more stable than 6. The two molecules have four delocalized π electrons. In addition, 8 and 9 with four delocalized electrons are designed, and calculated vibrational frequencies show that the two compounds are viable. Compound 10 with two delocalized π electrons, which is derived from 9, is not stable. Figure 2 displayed the resonance structures of 102-, and each resonance structure has two double bonds. Therefore, the viable molecule with two opposite conjugated three-membered rings should be Π54 but not Π52.

Third, the right part of 2 is changed into a conjugated fourmembered ring with zero and two delocalized π electrons to obtain compounds 11 and 12, respectively. Similarly, the left part of 2 is changed into a conjugated four-membered ring with zero and two delocalized π electrons to obtain compounds 13 and 14, respectively. The four molecules 11, 12, 13, and 14 are not stable, in which their smallest vibrational frequencies correspond to 466i, 158i, 295i, and 390i cm-1, respectively. Further, the right part of 11-14 is changed into a conjugated five-membered ring with zero, two, and four delocalized π electrons to yield compounds 15-20. Calculated frequencies in Table 1 indicate that all of them have imaginary frequencies. Therefore, conjugated four- and five-membered ring is disadvantageous to form a stable molecule with ptC. Fourth, the tetrahedral carbon isomers of compounds 1-14 are optimized, and their total energies are listed in Table 1. As can be seen from Table 1, the energies of the tetrahedral isomers of only 13 and 14 are lower than those of 13 and 14 with ptC, while the energies of tetrahedral isomers of other compounds 1-12 are higher than those of corresponding compounds with ptC. So such types of viable compounds with ptC are more stable than those with tetrahedral carbon.

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Figure 1. Optimized geometries of the compounds with ptC.

Figure 2. Five resonance structures of compound 102-.

Compound 2 here is the same as species 47 in ref 6. The C52-, C5Na-, and C5Na2 belong to the 8-like compound with two conjugated three-membered rings, in which each structure has four π electrons.9-11 The C5+nHn with a ptC in ref 13 and

C5+nH2n (n ) 2-5) with a ptC in ref 16 also fall into the 8-like configuration with two conjugated three-membered rings. Furthermore, the two kinds of structures show that the stability mainly depends on the 8-like moiety, in which the number of π electrons in the 8-like subunit is four. Similarly, compound 31 in ref 20 is an 8-like structure too. We optimized this structure and its saturated structure at the B3LYP/6-311++G** level, and both compounds S1 and S2 are displayed in Figure 3. As seen from Figure 3, the two compounds are viable, and the smallest frequencies are 98 and 83 cm-1, respectively. Their

Main-Group Element Compounds with ptC

Figure 3. Optimized geometries of (CB2C2H2)3 and (CB2C2H4)3 with ptC.

resonance structures have three double bonds, so each structure has six delocalized π electrons. This further confirms that the viable 8-like molecules with ptC mainly depend upon the conjugated three-membered ring, and they have little relationship with the delocalization of the whole molecule. Especially, many 8-like compounds with ptC, C4N-, C3N2, C5H2, C5F2, C5Cl2, C7H6, C13H18, C5H4, and C9H12 in refs 14 and 18 are viable. Analyzing their electronic and geometrical structures, we found that all of compounds have four π electrons and contain two three-membered rings, in which the number of the conjugated three-membered ring is not less than one. B. Trapezia Compounds with ptC. Six trapezia compounds with ptC are designed and displayed in Figure 1, which are 21, 22, 23, 24, 25, and 26. 21, 22, 23, and 24 are the isomers of C3B2H2, and the relative energy order of these isomers is 24 < 21 < 22 < 23. The vibrational frequencies of the four structures (21-24) in Table 1 indicate that they are minima on the PES. Isomer 24 is the lowest energy structure, while the isomer 21 is only slightly higher in energy than 24 by 0.11 kcal/mol. Each structure has four π electrons, where two π electrons come from ptC and the rest are from the other two carbon atoms. Compounds 25 and 26 with two π electrons have the smallest frequencies of 256 and 229 cm-1, respectively, indicating that the two molecules are viable. Thus, the viable trapezia structures with ptC may have two or four π electrons. Moreover, the geometries and vibrational frequencies of the six trapezia compounds with ptC are performed at the MP2/6-311++G** level, and they are collected in Table 2. As Table 2 shows, the smallest frequencies of the six structures at the B3LYP level are in good agreement with those at the MP2 level. The molecules 17-28 in ref 14 contain C5H22+, C4BH4, C3B2H4, C3B2, and CB4 moieties, in which 17, 27, and 28 have two π electrons, while 25 and 26 have four π electrons. Compound 22 in ref 14 is the same as the compound 26 here, and the other three isomers 21, 23, and 24 in ref 14 are higher in energy than 22.14 The number of π electrons of 5, 9-11, and 14 in ref 18 are two. C6H62+ in ref 19 can be considered as a trapezia structure with four π electrons, in which each ptC provides two π electrons. Therefore, the previous results are in good agreement with the stability rules of trapzia compound with ptC. C. Umbrella-like Compounds with ptC. Compounds 27 and 28 in Figure 1 are umbrella-like molecules with ptC, where each molecule has two π electrons. Compound 28 can be considered as that one -CH2- unit in 27 is changed into -BH-. Both -BH- subunits in 27 are changed into -CH2to obtain compound 29. Similarly, the two -BH- units in 28 are replaced by -CH- to yield compound 30. The smallest vibrational frequencies of 27, 28, 29, and 30 in Table 1 show the species 27 and 28 are viable, while compounds 29 and 30

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7963 are not stable. Compound 29 has no conjugated three-membered ring. Thus, the viable umbrella-like molecules with ptC should have two π electrons and a conjugated three-membered ring at least. Compound 27 will obtain 26 by dehydrogenization, that is, 27 ) 26 + H2. The reaction thermal enthalpies and thermal free energies are 54.67 and 47.24 kcal/mol, respectively, indicating that this reaction is an exothermic reaction. The species 52 in ref 6 is predicted to be viable at the B3LYP/6311+G* level. In fact, it is an umbrella structure and accords with the rule of umbrella-like compound with ptC. D. Quadrangle Compounds with ptC. Experimentally, the quadrangle structures with ptC, Al4C-, CAl3Si-, CAl3Ge-, and CAl4Na- have been observed.24-27 In addition, CAl42-, cisCSi2Al2, trans-CSi2Ga2, and cis-CGe2Al2 were investigated theoretically and indentified to be stable.28,29,34 Here, we choose CAl4 and CAl4Na- (31 and 32 in Figure 1) to investigate their structures and electronic properties. The planar structure of CAl4 with two π electrons has three imaginary frequencies of 478i (eu) and 65i cm-1 (b2u), and thus this cluster corresponds to a third-order saddle point. However, the CAl4Na- species with ptC contains four π electrons, and it is stable with the smallest vibrational frequency of 65 cm-1. Accordingly, the calculated results show that the stable quadrangle structure with ptC should have four π electrons. Analyzing the previous experimental results, we note that CAl3Si-, CAl3Ge-, and CAl4Na- have four π electrons, and Al4C- with three π electrons corresponds to an open shell state. Because of the coulomb repulsive energy between electrons, Al4C- easily forms CAl4Na- with Na atom, instead of accepting an electron to form Al4C2-. Because such typical structures require that the atoms around ptC should have very proper atom radius, usually some transition metal atoms are very promising candidates, such as Cu, Ni, and so on, and their compounds have been investigated in previous studies.30-32 According to the stability of the four types of compounds with ptC, we can conclude five stability rules. First, the viable compounds with ptC should have two three-membered rings at least, and the conjugated three-membered ring is not less than one. Second, the 8-like compound should have two and four π electrons for one and two conjugated three-membered rings, respectively. Third, the trapezia structure with ptC will be viable whether it has two or four π electrons. Fourth, the umbrellalike compound should have two π electrons. Fifth, the number of π electrons of the quadrangle compound should have four π electrons; moreover, the atom around ptC must be suitable because the ptC must be confined within the center formed with the four atoms, and, generally, Al, Cu, and Ni are suitable. Except for the four basic types of compounds with ptC, there are other derivatives with multi-ptCs constructed by one of the four types, such as (C3B2)nH4 (n ) 2-6),17 C6H62+,19 and (CB2CH2)3.20 Thus, according to the five stability rules, some novel compounds with multi-ptCs can be constructed by using the four basic structures. The adiabatic singlet-triplet energy differences of the lowest energy structures with ptC, ES-T ) ES - ET, are reported in Table 3. As see from Table 3, the singlet state of the compound is generally lower in energy than its triplet state. Especially, the adiabatic singlet-triplet energy differences of compounds 24-26 are calculated at the MP2/6-311++G** level and also listed in Table 3. Table 3 shows that the adiabatic singlet-triplet energy differences of compounds 24-26 by B3LYP and MP2 methods are well consistent. Thus, the closed-shell structures may dominate these compounds with ptC.

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TABLE 2: Total Energies of Trapezia Structures with ptC symm

Ea

ZPEa

Vmina

Eb

ZPEb

Vminb

C2V C2V Cs Cs C2V C2V

-165.07969 -165.04500 -165.04370 -165.07987 -138.59756 -166.31527

26.18 22.85 24.46 24.59 22.76 41.45

455(b1) 339(b1) 326(a′′) 320(a′′) 256(a2) 229(b1)

-164.54278 -164.51337 -164.51129 -164.54469 -138.09762 -165.76335

26.12 22.87 24.43 24.55 22.78 41.72

417(b1) 340(b1) 300(a′′) 315(a′′) 250(a2) 189(b1)

21 22 23 24 25 26 a

B3LYP method. b MP2 method.

TABLE 3: Total Energies of Singlet (ES, in au) and Triplet (ET, in au) of the Lowest Energy Structures with ptC, as well as Their Energy Differences between Singlet and Triplet (ES-T ) ES - ET, in eV) 2 3 7 8 9 24 25 26 27 28 32 a

ES

ET

ES-Ta

-167.56033 -206.87729 -166.36362 -160.66296 -154.96098 -165.07987 -138.59756 -166.31527 -167.58953 -153.72672 -1170.26701

-167.44128 -206.77922 -166.26252 -160.56534 -154.90466 -165.02202 -138.52364 -166.21150 -167.47660 -153.61256 -1170.23690

-3.24 -2.67 -2.75 -2.66 -1.53 -1.57 -2.01 -2.82 -3.07 -3.11 -0.82

ES-Tb

-1.67 -2.17 -4.04

B3LYP method. b MP2 method.

E. Application of the Stability Rules to Other Systems. We applied the above stability rules to the compounds with ptN. Eight molecules with ptN are constructed and displayed in Figure 4, which include 8-like, trapezia, umbrella-like, and quadrangle types. 33 and 34 in Figure 4 are derived from 9 in Figure 1; 35, 36, and 37 are from 25; 38 and 39 are from 27 and 28, respectively; and 40 is from 32. The optimized geometries of compounds 33-40 are displayed in Figure 4, and the smallest vibrational frequencies are incorporated into Table 1. As can be seen from Table 1, the eight molecules with ptN are viable, so the stability rules can be successfully applied to the compounds with ptN. Therefore, the universal rules are suitable for the compounds with ptC and ptN. F. Aromaticity of the Lowest Energy Compounds. The NICS(0) values on the center of the three- and four-membered rings of the lowest energy compounds with ptC and ptN are displayed in Figure 5. As seen from Figure 5, except for that the NICS(0) value on the center of the four-membered ring of 3 is only -1.90, the three-membered rings associated with ptC or ptN of the 8-like molecules with ptC or ptN have strong aromaticity, and their NICS(0) values are less than -20.00. As

Figure 4. Optimized geometries of the compounds with ptN.

Figure 5. NICS(0) values on the center of three- and four-membered rings of the most viable compounds with ptC (or ptN).

for the conjugated trapezia structures with two π electrons (25 and 36), the NICS(0) values at the middle of three-membered rings are -16.40 and -10.80, respectively, showing that the middle three-membered rings have strong aromaticity, while the two sides of three-membered rings have antiaromaticity due to positive NICS(0) values. Each three-membered ring in 26 and 37 with four π electrons has strong aromacity. The NICS(0) values on the side and middle three-membered rings of 26 are -26.34 and -51.09, respectively, and the NICS(0) value at the

Main-Group Element Compounds with ptC

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TABLE 4: Energies of HOMO and LUMO (hartree), Energy Gaps (gap, eV), and Wiberg Bond Indices of ptC(N)-X Bonds (WBIptC(N)-X) and Total WBIs of ptC(N) (TWBIptC(N)) of the Viable Molecules 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

EHOMO

ELUMO

gap

-0.27129 -0.24879 -0.25041 -0.24833 -0.23395 -0.22951 -0.24430 -0.18080 -0.13311 -0.23434 -0.25051 -0.24482 -0.21845 -0.18210 -0.22736 -0.20170 -0.17985 -0.23301 -0.24831 -0.23945 -0.24234 -0.22803 -0.23615 -0.23559 -0.26682 -0.26346 -0.25818 -0.26709 -0.18511 -0.17510 -0.20044 -0.02934 0.00718 -0.16656 0.02197 -0.53024 -0.22810 -0.53316 -0.53213 -0.16791

-0.04242 -0.02915 -0.03589 -0.06394 -0.04004 -0.05364 -0.03408 -0.05789 -0.04377 -0.14813 -0.16135 -0.06450 -0.07495 -0.01518 -0.10066 -0.07604 -0.07171 -0.16726 -0.11821 -0.09827 -0.06890 -0.09509 -0.08992 -0.07986 -0.13130 -0.04984 -0.02671 -0.06751 -0.03124 -0.06672 -0.15405 0.03478 0.11853 -0.06435 0.10787 -0.35211 -0.08228 -0.28720 -0.31317 -0.07201

6.23 5.98 5.84 5.02 5.28 4.79 5.72 3.34 2.43 2.35 2.43 4.91 3.90 4.54 3.45 3.42 2.94 1.79 3.54 3.84 4.72 3.62 3.98 4.24 3.69 5.81 6.30 5.43 4.19 2.95 1.26 1.74 3.03 2.78 2.34 4.85 3.97 6.69 5.96 2.61

WBIptC(N)-X

TWBIptC(N)

0.8757(2), 1.0398(2) 0.9581(2),0.9819(2)

3.8708 3.9461

0.9813(2), 0.9266(2) 1.2758(2), 0.6558(2) 1.1821(1), 1.0193(1), 0.5964(1), 0.9615(1) 0.9116(4)

3.8825 3.9179 3.8312 3.7298

1.2604(2), 0.6786(2) 1.0691(2), 0.7153(2) 1.1644(1), 0.9268(1), 0.8254(1), 0.8859(1) 0.7278(1), 0.9869(1), 0.6664(1), 1.3794(1) 0.9903(2), 0.8580(2) 0.9898(2), 0.9642(2) 0.8820(1), 0.7919(1), 1.2021(1), 1.0109(1) 1.0004(2), 0.8235(1), 0.9968(1)

3.9125 3.5927 3.8323 3.7866 3.7131 3.9498 3.9366 3.8467

0.5218(2), 0.5943(2) 0.7453(4) 0.8325(2),0.6613(2) 0.7815(2), 0.7697(2) 0.7609(2),0.7067(2) 1.0554(1), 0.9195(1), 0.4505(1), 0.7959(1) 1.0750(1), 0.5208(1), 0.7809(1), 0.8742(1) 0.8902(2), 0.4862(1), 0.8636(1) 0.3005(2), 0.3460(2)

2.2669 3.0146 3.0248 3.1197 2.9440 3.2386 3.2916 3.1426 1.3095

middle of three-membered ring is the smallest. Three memberedrings of 35 both sides have strong aromaticity, while the middle three-membered ring has antiaromaticity. As for 27, 28, 38, and 39 containing two π electrons with umbrella-like structures, the two conjugated three-membered rings have strong aromacity, in which the NICS(0) values of 27 and 38 are remarkably less than those of 28 and 39. The NICS(0) values in the four threemembered rings of quadrangle structures 32 and 40 are less than -17.00, indicating that each three-membered ring has strong aromacity. The strong aromacity of the conjugated threemembered rings of the viable compounds with ptC and ptN indicates that the lone electron on ptC and ptN is delocalized. G. WBIs, Energy Gaps, and Natural Charges on ptC and ptN. The WBIs of the lowest energy compounds are calculated and listed in Table 4. Table 4 shows that the WBIs between ptC and its four bonding atoms in the viable 8-like, trapzia, and umbrella compounds with ptC are between 0.5964 and 1.2021, and the total WBIs of the ptC are close to 4.00, which obey the octal rule. As for the four kinds of compounds with ptN (33-40), the WBIs of between ptC and its four bonding atoms are between 0.4505 and 1.0750, indicating the presence of a ptN. The total WBIs of ptN in 33-40 are close to 3.00, in which the ptN atoms also obey the octal rule because the valence shell of N has a lone electron pair. The WBIs of ptC-Al bonds in 32 are 0.5218 and 0.5943, and the WBIs of ptN-Al bonds

in 40 are 0.3005 and 0.3460, which are remarkably less than those of other viable structures. In addition, the total WBIs of ptC and ptN in 32 and 40 are 2.2669 and 1.3095, respectively, and thus the ptC and ptN in the two clusters form a weak bond to the adjacent atoms. The energy gaps of compounds 1-40 are also listed in Table 4. As shown in Table 4, the gaps of 2, 3, 7, 26, 27, and 28 with ptC, as well as 38 and 39 with ptN, are larger than 5.70 eV. Also, the gaps of other viable compounds with ptC or ptN are between 1.70 and 4.90 eV, in which the gap of the quadrangle structure 32 with ptC has the smallest gap of 1.74 eV. The natural charges on ptC and ptN of the 40 compounds are calculated and listed in Table 1. As seen from Table 1, the natural charges on ptC and ptN of the quadrangle compounds are less than -2.00|e|, and the natural charges on ptC and ptN of other compounds are almost -1.00|e|. The more negative charges on ptC and ptN of the quadrangle species arise from considerable electron transfers from ligand Al atoms to ptC and ptN. Summary Structures, stabilities, aromaticities, and Wiberg bond indexes of four types of compounds with ptC (8-like, trapezia, umbrellalike, and quadrangle) have been investigated. We found the

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stability of the compounds with ptC depends on the number of π electron as well as three-membered ring and conjugated threemembered ring. On the basis of the predicted stability of the four type compounds with ptC, we concluded five stability rules for a stable compound with ptC: (i) inclusion of a conjugated three-membered ring and two three-membered rings at least; (ii) the 8-like compound should have two or four π electrons for one conjugated three-membered ring and two conjugated three-membered rings, respectively; (iii) containing two or four π electrons for the trapezia structure; (iv) containing two π electrons for the umbrella-like compound; and (v) the quadrangle compound should have four π electrons, and, moreover, the atom radius bonding to ptC must be suitable because the ptC must be confined within the center to bond the four atoms. These rules have been successfully used to identify other compounds with ptC reported in previous studies, and eight stable compounds with ptN have been designed on the basis of these stability rules. Acknowledgment. This work was financially supported by the start-up fund of Shaanxi Normal University and the excellent science preresearch project of Shaanxi Normal University in 2008, the National Science Foundation of China (20673087, 20733002, 20873105), and the Ministry of Science and Technology (2004CB719902). References and Notes (1) Hoffmann, R.; Alder, R. W.; Wilcox, C. F., Jr. J. Am. Chem. Soc. 1970, 92, 4992. (2) McGrath, M. P.; Radom, L. J. Am. Chem. Soc. 1993, 115, 3320. (3) Rasmussen, D. R.; Radom, L. Angew. Chem., Int. Ed. 1999, 38, 2876. (4) Wang, Z. X.; Schleyer, P. v. R. J. Am. Chem. Soc. 2001, 123, 994. (5) Wang, Z. X.; Schleyer, P. v. R. J. Am. Chem. Soc. 2002, 124, 11979. (6) Sorger, K.; Schleyer, P. v. R. J. Mol. Struct. (THEOCHEM) 1995, 338, 317. (7) Wang, Z. X.; Manojkumar, T. K.; Wannere, C.; Schleyer, P. v. R. Org. Lett. 2001, 3, 1249. (8) Liang, J.; Jia, W.; Zhang, C.; Cao, Z. Acta Phys. Chim. Sin. 2009, 25, 1847. (9) Merino, G.; Mendez-Rojas, M. A.; Vela, A. J. Am. Chem. Soc. 2003, 125, 6026. (10) Merino, G.; Mendez-Rojas, M. A.; Beltran, H. I.; Corminboeuf, C.; Heine, T.; Vela, A. J. Am. Chem. Soc. 2004, 126, 16160. (11) Pancharatna, P. D.; Mendez-Rojas, M. A.; Merino, G.; Vela, A.; Hoffmann, R. J. Am. Chem. Soc. 2004, 126, 15309. (12) Esteves, P. M.; Ferreira, N. B. P.; Correˆa, R. J. J. Am. Chem. Soc. 2005, 127, 8680. (13) Perez, N.; Heine, T.; Barthel, R.; Seifert, G.; Vela, A.; MendezRojas, M. A.; Merino, G. Org. Lett. 2005, 7, 1509. (14) Sateesh, B.; Reddy, A. S.; Sastry, G. N. J. Comput. Chem. 2007, 28, 335.

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