10048
J. Phys. Chem. 1994,98, 10048-10053
Theoretical Resonance Energies of Benzene, Cyclobutadiene, and Butadiene Yirong Mo," Wei W U , ~and Qianer Zhang Department of Chemistry and the Institute of Physical Chemistry, Xiamen University, Xiamen 361005, People's Republic of China Received: April 12, 1994; In Final Form: July 8, 1994@
A valence bond method, namely the bonded tableau unitary group approach, is applied to analyze the n electron delocalization of benzene, cyclobutadiene, and butadiene, and the resonance energies are also calculated and extensively compared with experimental data and theoretical results in the literature. In the frame of a b initio calculations, we optimize the geometries of hypothetical molecules with localized nonresonating double bonds without any artificial approximation. Our results show that the Csp2-Csp2 single bond length (1 SO9 8, with the 6-31G basis set) is only about 0.021 8, shorter than the Csp3-Csp3 bond, and the delocalization is a driving force in conjugated systems. If the delocalization energy can compensate the energy needed by the shortening of some Csp2-Csp2 bonds, the system will prefer a regular geometry with uniform C-C bond lengths, otherwise the system will be stable toward an alternate geometry where delocalization is still important. An interesting result is that even in cyclobutadiene the delocalization is energetically beneficial and the theoretical resonance energy is 3.16 kcal/mol with the STO-6G basis set or 5.67 kcal/mol with the 6-31G basis set, which is close to the value of butadiene. Moreover, the n orders of the long bonds in C4& and C4H6 are very close. Thus it can be concluded that the antiaromacity of C4& is a direct outcome of the (5 frame's ring strain rather than n electronic delocalization.
Introduction The concept of resonance energy (RE) for conjugated systems is rather confused and troublesome for theoretical chemists.'*2 Experimentally the RE of a conjugated system can be estimated from the heats of hydrogenation of the conjugated system and its reference state containing localized nonresonating double bond^.^-^ For example, the heats of hydrogenation of cyclohexene and benzene with respect to cyclohexane are 28.7 and 50.0 kcaymol respectively, however, since the hypothetical cyclohexatriene consists of three independent double bonds, its fictitious heat of hydrogenation is 3 times the value of cyclohexene, 86.1 kcaymol. The difference between the above value and 50.0 kcaymol, 36 kcdmol, is called the experimental RE (ERE) of benzene. Nevertheless, the controversy over the stabilization of conjugated systems is still u n ~ e t t l e dand ~ ? ~the theoretical RE (TRE) cannot be strictly defined since there is no unique and undisputed method to make the ERE and the TRE comparable. In his earlier calculations, Pauling8 conceived that the RE is the difference between the energy of a single KekulC valence bond (VB) wave function and the energy of the actual ground state. Later, %eland4 as well as Mulliken and Parr9 noted that the compression energy is involved when a Kekul6 structure with six equal CC bond lengths is changed to the bond-alternate structure of cyclohexatriene, and they also defined Pauling's RE as vertical RE (VRE) (VRE is easily mistaken as TRE'O) which measures the degree of x electronic delocalization. The latter authors calculated the RES of benzene and butadiene based on a LCAO MO method. Many authors' 1-14 used semiempirical methods to study the electronic delocalization in conjugated systems. Adopting the concept of RE per n electron (REPE), Dewar and de Llano's PPP computationsllb revealed that the REPEs were 0.145 and -0.193 eV for benzene and cyclobutadiene, respectively, while
* Author to whom correspondence should be addressed.
'
Present address: Dipartimento di Chimica e Chimica Industriale, Universita di Pisa, 56100 Pisa, Italy. Abstract published in Advance ACS Abstracts, September 1, 1994. @
Hess and Schaad's values12bwere 0.0658 and -0.2688 based on the simple Hiickel method where' the RES had been normalized. These values are believed to be able to describe the difference between aromaticity and antiaromaticity. A common feature for these schemes is that the reference states are a classical polyene rather than a hypothetical model compound with nonresonating double bonds. On the level of ab initio SCF theory, some authors15J6 introduced an approximate scheme to evaluate x conjugation in a given conformation, where the x MOs in the SCF wave function are replaced by nonresonating localized n MOs obtained by a calculation of ethylene in the same basis or by Boys's localization method.17 This method may be a most elaborate and direct way to analyze the properties of n electrons up to now. Recently, Janoschek2 reviewed the different possibilities for the definition of the stabilization energy of the benzene molecule and found that the definition is only a matter of taste since different values are possible with different definitions. Obviously, the key reason is that neither a molecular nor an electronic structure is assumed for the fictitious reference molecules. In order to circumvent rather than solve the above bottleneck, some authors defined the stabilization energy by means of homodesmotic18 and isodesmic reaction^'^ which involve actual molecular structures only. However, as pointed by Janoschek,2 the choice of structures is also somewhat arbitrary. Compared with the molecular orbital (MO) method,21 VB theory still enjoys some a d v a n t a g e ~in~elucidating ~~~ the bonding features of molecules, thus the revival of the VB method is hopefully e x p e ~ t e d . ~By ~ , means ~ ~ of VB methods, we can easily construct a wave function for a hypothetical molecule and investigate its electronic structure as well as its molecular structure. However, to our knowledge, there is no detailed report on the theoretical study of the hypothetical molecules in the frame of ab initio calculations. In the present paper, we will address our attention to the RES of benzene, cyclobutadiene, and butadiene and correlate them with thermodynamic data and
0022-3654/94/2098-10048$04.50/0 0 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 40, 1994 10049
Theoretical Resonance Energies other theoretical results. In addition we will discuss the delocalization of n electrons.
Also, we define the VB bond order Bi(pq) between AOs p and q:
Method for the Calculation of the TREs
M
In the VB terminology, the real molecular structure can be described by some resonance structures, which is the main idea of the resonance theory.4,8,24,25 A simple way26,27to construct VB structure functions is to use the standard projection operator which may be called the "bonded tableau unitary group approach" (BTUGA).28 In view of the idea of adopting bonded tableaux (BTs) as the state functions of a system, while these state functions can describe corresponding resonance structures, BTUGA is much closer to classical conceptions and ideas than are other many-body theories. In the BTUGA, for a system with N electrons and m oneelectron orbitals and spin quantum number S, a BT is defined as
where is a standard projection operator while [A] = [2(N/2)-s12s] is an irreducible representation of the permutation group 3 ~ Ak . is a normalization coefficient, and Wo(k) is a primitive function which is expressed as a successive product of one-electron orbitals. Though the one-electron orbitals can take the form of overlap-enhanced orbital^,^^,^^,^^ in the present paper, we will employ fixed atomic orbitals (AOs). Thus, the above BT corresponds to a VB resonance structure or a Lewis structure where two AOs uzi-1 and u2i overlap to form a bond (i 5 (N/2) - S, and if u2i-l = uzi, the "bond" is a lone pair of electrons) and the latter 2s electrons are unpaired. Subsequently, a state wave function of the system can be written as a superposition of canonical BTs (CBTs), namely M
k=l
where
(7) where mp,(k) = 2 if p and q are in the same row in the BT W(k),otherwise mpq= 0. It should be noted that the bond orders defined in this way can be negative and the values are dependent on the choice of BTs since all possible BTs form an overcomplete set of structure functions. Presently we use Rumer structures30as the CBTs which are a complete set of structure functions. In order to investigate the bonding between n AOs as well as to reduce the time of calculation, for conjugated systems we normally adopt the (T-nseparability appr~ximation,~~ and the (T electrons are confined in the (T MOs from the SCF calculation. The influence of the potential provided by the (T frame on the n electrons is i n t r ~ d u c e d ,and ~ ~ procedures like this33 are analogous to the n MO-CI method. Unequivocally, the full CBT interaction (BTI)34 and the full n MO-CI give identical results. For a hypothetical molecule (generalized Kekult) with n nonresonating double bonds, its appropriate electronic structure can be described by 3" Lewis structures when a minimal basis set is applied, since every double bond has three Lewis structures, namely, one covalent structure >C=C< and two ionic structures, >C--C+< and >C+-C-m,(k)
(6)
k=l
where m,(k) = 0, 1, or 2 is the number of electrons occupying the A 0 q in the BT W(k).
The benzene molecule has been a subject of extensive investigations and controversies in theoretical chemistry. In respect to VB methods, notable are the ab initio calculations performed by Norbeck and Gallup36and by Simonetta et ~ l . , ~ ~ the latter used a Heitler-London-Slater-Pauling (HLSP) function as a VB function, which is essentially equivalent to the BT function. In the present calculation, the STO-6G basis set is adopted. For the 6 pn orbitals and 6 electrons in benzene, totally there are 175 CBTs whose Rumer diagrams are shown in previous paper^.^^^^' As a first step, we optimize the CC bond length in the ground state of benzene. The optimum value is 1.404 A, which is in good accordance with the experimental value 1.399 A.38Our VB description for the ground state of benzene is also identical with results of Simonetta et aL3' For cyclohexatriene, its molecular wave function is determined by 27 Lewis structures whose Rumer diagrams are as follows (in parentheses is the number of equivalent structures):
10050 J. Phys. Chem., Vol. 98, No. 40, 1994
Mo et al. TABLE 2: VB n Bond Orders in the Ground State of Benzene
SCHEME 1
0 'd
\
\
benzene molecule IVRE
0B
Kekule structure
stable cyclohexatriene
TABLE 1: Optimized Bond Lengths and Energies of CJ& with the STO-6G Basis SeP no. of molecular long CBTs energy (au) RE (kcdmol) 1.404 175 -230.238 77 1.404 27 -230.12041 74.28 1.521 27 -230.167 89 44.48
Rcc
short benzene 1.404 Kekult 1.404 cyclohexatriene 1.343
Total SCF energy of benzene is -230.128 81 au.
The relationship between TRE and VRE is shown in Scheme 1, where B represents the compression energy. Consequently our results show that cyclohexatriene has CC bond altemation. The C(sp2)-C(sp2) single bond length and C=C bond length are 1.521 and 1.343 A, respectively. The single bond length is in excellent agreement with the values 1.52 8, calculated by means of the semiempirical AM1 method39 and 1.51 8, determined by Kollmar16 where the C-C bond length was fixed at 1.34 8,, while the double bond length was near to the bond length 1.337 8, in ethylene.40 The energies of benzene, the KekulC structure, and cyclohexatriene are shown in Table 1. For the VRE, a value of 74.28 kcdmol was obtained, which is quite near to the value of 77 kcal/mol by Kollmar16 with the double-g basis when correlation is taken into account. This agreement strongly indicates that the method used by Kollmar and others,15 where localized JC MOs ascribed to the reference state are transferred from a SCF calculation of ethylene, is rather feasible. The VRE also indicates that the JC electron delocalization decreases the total energy of benzene significantly and is responsible for the enhanced stability of benzene. Mulliken and Parrg who used k2i-1 ~ 2 as~ the ) localized LCAO MOs for the KekulC structure got the VRE 73.1 kcdmol. Our TRE of benzene is 44.48 kcdmol, compared with the well-known data 36 kcal/mol. It should be pointed out that JC electrons in the benzene with alternate bonds of 1.343 and 1.521 8, will still delocalize remarkably since at the above geometry the VRE is 31.9 kcdmol, and maybe it is inappropriate to ascribe the JC electronic delocalization in benzene to the geometric constraint only.& It will be interesting to compare the TRE with the result obtained by means of homodesmotic reaction.'* For the following reaction
+
the energy difference is 21.2 kcdmol, which was used as the RE of benzene. However, since there is JC electron delocalization in butadiene, later, George et proposed butadiene with the C-C single bond rotated by 90" to be taken as the reference molecule for the definition of RE
Evidently, the homodesmotic stabilization energy, 42.65 f 2.95 kcal/mol, is exactly comparable with our result. The difference
benzene
0.5890
0.04138
0.1746
between TRE and VRE values is the compression energy, and the value is about 30 kcdmol, the same value as claimed by ~heiand.4 Now let us discuss the relationship between the TRE and the ERE. When the cyclohexene is hydrogenated to cyclohexane, besides the double bond, there is some changes in the u frame, where two Csp2-Csp3 single bonds tum to two Csp3Csp3 bonds. On the other hand, when the hypothetical cyclohexatriene is hydrogenated to cyclohexane, apart from the three localized double bonds, the three Csp2-Csp2 single bonds are changed to Csp3-Csp3 bonds. Thus, the difference between the ERE and the TRE is the following energy change 3Csp3-Csp3
+ 3Csp2-Csp2 - 6Csp2-Csp3
which amounts to -8.5 kcdmol, namely, an exothermic process. Table 2 gives the VB bond orders between JC AOs. Since the interaction between the diagonal atoms is quite strong, we can conclude that the Dewar structures are important in the description of the benzene.
Cyclobutadiene As the archetype of aromatic molecules, cyclobutadiene is very unstable and can only be observed as a short-lived intermediate in The most intriguing problem is between the u frame and the JC electrons, which one should be responsible for the instability of cyclobutadiene? According to the Huckel MO theory, its JC electronic energy is twice that in ethylene, namely, 4 a 4p, thus the delocalization energy is equal to zero. In order to account for the antiaromacity, it is generally conceived that cyclobutadiene has a large negative RE. Breslow and his collaborator^^^ estimated the conjugative destabilization of cyclobutadiene experimentally as 12- 16 k c d mol. Theoretically, by the additivity rules of the bond energies, Dewar et ~ 1obtained . ~ the ~ value - 18 kcdmol while the RE of benzene was 20 kcaymol. Hehre and Popleu performed HFSCF calculations with 4-3 1G on the following isodesmic reactions
+
+ 6CH4 - 3C& + 3CH,=CH2 C,H4 + 4CH4 - 2C2H6+ 2CH2=CH2 C6H6
where the heats are 64 and -68 kcal/mol, respectively. However, part of these energies should be attributed to bond strain in the u systems. Many theoretical works have been dedicated to the structure and properties of cyclob~tadiene?~ and both GVB45dand SCVB23d345e have been used. Voter and G ~ d d a r dproved ~ ~ ~ that for square C4& there is 22 kcdmol of stability energy with two conformations
11-1-1 When a minimal basis set is used, cyclobutadiene and localized cyclobutadiene can be described by 20 and 9 resonance structures, respectively, while 336 and 100 CBTs are needed with the 6-31G basis set. It is well-established that the equilibrium nuclear configuration of C4H4 in the ground state is rectangular. Indeed we find that the square C4& is a
. I . Phys. Chem., Vol. 98, No. 40, 1994 10051
Theoretical Resonance Energies
SCHEME 2
TABLE 5: Optimized Bond Lengths and Energies of (aU)
&UnS-C&
S=l
.-i
butadieneo rigid localized C4H6 stable localized C4&
17.9kcal/mol
Id
u
4.0kcal/mol
s=o Rectangular
Square
Rectangular
TABLE 3: Optimized Bond Lengths and Energies of C4H4 (au) Rcc no. of molecular RE short long CBTs energy (au) (kcdmol) STO-6G cyclobutadiene" 1.369 1.538 20 -153.346 17 rigid localized C f i 1.369 1.538 9 -153.340 22 3.73 stable localized C4H4 1.355 1.555 9 -153.341 14 3.16 6-31G cyclobutadieneb 1.364 1.550 336 -153.653 08 rigid localized C f i 1.364 1.550 100 -153.642 86 6.41 stable localized C4H4 1.355 1.580 100 -153.644 04 5.67 "The SCF energy is -153.233 14 au. bThe SCF energy is -153.570 83 au.
TABLE 4: VB x Bond Orders in the Ground State of STO-6G 6-31G
B(Ci-C2) 1.4372 1.4960
B(Ci-C3) 0.0000 -0.0263
C4H4
B(C2-Cd 0.1778 0.1233
SCHEME 3 cyclobutadiene molecule
. ml B
rigid localized-C4H4
stable localized-C4H4
transition state, whose optimum C-C bond length is 1.453 8, with the STO-6G basis set. Scheme 2 presents the singlet and triplet energy curves for cyclobutadiene. More calculation results for C f i are listed in Tables 3 and 4, while Scheme 3 illustrates the relationship between the VRE and TRE of C f i . Our optimization shows that the short bond lengths in cyclobutadiene and stable localized C4H4 are rather similar and near to double bond length, while the long bond lengths are even longer than the CC single bond length in ethane. Our short and long bond lengths with 6-31G are 1.364 and 1.550 8, compared with 1.347 and 1.567 8, by means of GVB-CI-SD with the [3s2pld/2s] basis Both the TRE and VRE are positive, though the numerals are not big. These results indicate that the cyclic conjugation of 4 JC electrons is of benefit energetically. The compression energy from stable localized C f i to rigid localized C f i is negligible. Consequently it can be deduced that the binding energies in the long bonds are quite small and cyclobutadiene is easy to dissociate or react with other molecules. Moreover, the antiaromacity of cyclobutadiene maybe mainly resulted from its c7 component owing to the ring strain in the (5 frame. One feature of the calculated results is
butadieneb rigid localized C4H6 stable localized C4H.5
Rcc no. of short long CBTs STO-6G 1.351 1.486 20 1.351 1.486 9 1.344 1.524 9 6-31G 1.351 1.465 336 1.351 1.465 100 1.344 1.509 100
molecular RE energy (au) (kcavmol) -154.605 57 -154.591 74 -154.592 97
8.68 7.91
-154.92701 -154.912 08 -154.913 44
9.37 8.52
a The SCF energy is -154.516 47 au. The SCF energy is -154.862 01 au.
TABLE 6: VB x Bond Orders in the Ground State of &UnS-C4H6
STO-6G 6-31G
B(Cl-C2) 1.3617 1.3053
B(Cl-C3) 0.0206 0.0194
B(C1-C4) 0.1721 0.1915
B(CZ-C~) 0.1223 0.1524
that the long bond lengths and the RESare sensitive to the basis sets, and the minimal basis sets may be not suitable to describe cyclobutadiene. From Table 4, the JC bond order between the diagonal atoms is slightly negative with 6-31G, which indicates that n electrons tend to destabilize these diagonal bonds in view of Mayer's theory .46 Butadiene Since linear polyenes are the best models for the understanding of conjugation in organic chemistry, butadiene has been extensively s t ~ d i e d . ' ~Though , ~ ~ butadiene is strongly localized, the poor conjugation has a significant effect on the central bond, and the shortening of the central bond (1.463 compared with the Csp3-Csp3 bond (1.532 8,) in alkanes49was classically attributed to the weak JC conjugation between the double bonds as well as the difference in hybridization. Many authors50 believed that the above two reasons can be separately assessed with the full geometry optimizations for planar and perpendicular conformations of butadiene. However, Daudey et al. l 5 pointed out that the hyperconjugation effect stabilizes the perpendicular form and tends to compensate the loss of direct JC conjugation. Furthermore, they investigated the JC conjugation in butadiene by replacing the two SCF JC MOs with two ethylenic JC MOs and obtained the Csp2-Csp2 single bond length, 1.521 8,, and the conjugation energy, 10.4 kcal/mol. In the present paper, we optimized the CC bond lengths with the STO-6G and 6-3 1G basis sets while other parameters were taken from ref 47a. Results are listed in Tables 5 and 6. Like C4H4, regardless of whether there is resonance between two double bonds or not, the short bond lengths are rather close to the bond length in ethylene. On the other hand, the long bond length changes remarkably. For the stable localized C4H6 where no strain exists, the long bond length represents the Csp2Csp2 single bond length, which is not directly available in the nonempirical MO methods. We find that the Csp2-Csp2 single bond is somewhat longer than generally assumed and near the value obtained for ethane with the same basis set (1.534 8, with STO-3G and 1.530 8, with 6-31G). In light of these values, we estimate that about 70% of the central bond length shortening would be specifically due to JC conjugation, while the remainder would be due to a hybridization change from Csp3 to Csp2. Our results are in good agreement with those obtained by Daudey et aZ.15 Though experimentally there is no direct proof for the above findings, with respect to experimental data, the Csp3-H
Mo et al.
10052 J. Phys. Chem., Vol. 98, No. 40, 1994
and Csp2-H bond lengths are 1.096 and 1.085 8,, re~pectively,~~ thus we can reasonably estimate that the Csp*-Csp2 single bond is about 0.022 8, shorter than the Csp3-Csp3 bond, which is accordance with our calculated results. Our calculated RESfor butadiene changed only slightly with the variation of basis set, but the TRE is higher than the ERE by 3.5 kcal/mol, which is understandable from the following process
Science Foundation of China. We thank the referees for their very detailed and helpful instructions to update this paper. References and Notes
(1) George, P. Chem. Rev. 1975, 75, 85. (2) For a recent summary, see the following: Janoschek, R. J . Mol. Struct. (THEOCHEM) 1991, 229, 197. (3) Hiickel, E. Z. Elektrochem. 1937, 752, 827. (4) Wheland, G. W. Resonance in Organic Chemistry; Wiley: New York, 1955. (5) Streitwieser, A. Molecular Orbital Theory for Organic Chemists; csp3-csp3 csp2-csp2 2csp2-csp3 Wiley: New York, 1961. (6) (a) Garratt, P. J. Aromaticity; Wiley: New York, 1986; p 35. (b) Since the bond lengths in are different from those in C a 6 , Epiotis, N. D. Nouv. J . Chim. 1984,8, 411; Lecture Notes Chem. 1983, 34, the energy change of the above process is incomparable with 358-371; Pure Appl. Chem. 1983,35,229. (c) Shaik, S. S.; Bar, R. Nouv. J . Chim. 1984,8,411. (d) Shaik, S. S.; Hiberty, P. C. J . Am. Chem. SOC. the value for The study of the torsional potential function 1985,107,3089. (e) Shaik, S. S.; Hiberty, P. C.; Lefour, J.-M.; Ohanessian, of 1,3-butadieneutilizing Raman spectrophotometry and a highG. J . Am. Chem. SOC. 1987, 109, 363. (0 Hiberty, P. C.; Shaik, S. S.; intensity argon ion laser source gives the energy difference Lefour, J.-M.; Ohanessian, G. J. Org. Chem. 1985,50,4657. (9) Hiberty, P. C.; Shaik, S. S.; Lefour, J.-M.; Ohanessian, G. J . Org. Chem. 1985, 51, 3908. truns-l,3-butadiene 90" - 1,3-butadiene (7) (a) Maddox, J. Nature 1987,329,481. (b) Cooper, D. L.; Gerratt, J.; Raimondi, M. Nature 1986, 323, 699. (c) McWeeny, R. Nature 1986, as 7.16 kcal/m01,~~ which is in good agreement with our results. 323,666. (d) Harcourt, R. D. Nature 1987,329,491. (e) Messmer, R. P.; Schultz, P. A. Nafure 1987,329,492. (0Gerratt, J.; Raimondi, M.; Cooper, Since the n bond order between the two terminal atoms in D. L. Nature 1987, 329, 492. butadiene is 0.17-0.20, the resonance structure (l),where the (8) Pauling, L.; Wheland, G. W. J . Chem. Phys. 1933, I , 362. dashed line represents a formal bond, has some contribution to (9) Mulliken, R. S.; Parr, R. G. J. Chem. Phys. 1951, 19, 1271. the description of the butadiene. (10) Schultz, P. A,; Messmer, R. P. Phys. Rev. Lett. 1987, 58, 2416. (11) (a) Dewar, M. J. S.; Gleicher, G. J. J . Am. Chem. SOC.1965, 87, 685, 692. (b) Dewar, M. J. S.; de Llano, C. J . Am. Chem. SOC. 1969, 91, 789. (12) (a) Hess, B. A., Jr.; Schaad, L. J. J . Am. Chem. SOC. 1971, 93, 305; 1972, 94, 3068. (b) Schaad, L. J.; Hess, B. A., Jr. J . Chem. Educ. 1974,51,640. (c) Hess, B. A., Jr.; Schaad, L. J.; Agranat, I. J. Am. Chem. SOC. 1978, 100, 5268. (13) Lo, D. H.; Whitehead, M. A. Can. J . Chem. 1968,46,2027,2041. The n order of the long bond of C4H6 is surprisingly similar (14) Kao, J.; Allinger, N. L. J. Am. Chem. SOC. 1977, 99, 975. to that of C f i , which indicates that the degree of delocalization (15) Daudey, J. P.; Trinquier, G.; Barthelat, J. C.; Malrieu, J. P. Tetrahedron 1980, 36, 3399. is of the same order for these two molecules. (16) Kollmar, H. J . Am. Chem. SOC. 1979, 101, 4832. (17) Boys, S. F. Rev. Mod. Phys. 1960, 32, 296. Conclusions (18) (a) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. Theor. Chim. Acta 1975, 38, 121. (b) George, P.; Trachtman, M.; Bock, C. W.; We have shown that the VB theory is a quite convenient and Brett, A. M. J . Chem. Soc., Perkin Trans. 2 1976, 1222. (c) George, P.; direct way to study conjugation. In addition, our results also Trachtman, M.; Bock, C. W.; Brett, A. M. Tetrahedron 1976, 32, 1357. (19) Hehre, W. H.; Ditchfield, R.; Radom, L.; Pople, J. A. J . Am. Chem. confirmed that the method in the frame of MO t h e ~ r y , ' ~ , ' ~ SOC.1970, 92, 4796. namely, that the n MOs in the SCF wave function are replaced (20) Pauling, L. The Nature of the Chemical Bond; Comell: Ithaca, NY, by nonresonating localized n MOs obtained by a calculation of 1960. ethylene in the same basis or by a Boys's localization method, (21) Slater, J. C. Phys. Rev. 1931, 38, 1109. (22) Gerratt, J.; Orville-Thomas, Eds.; Advance in Valence Bond Theory is rather efficient to treat conjugated systems. Since the Csp2(Special Issue); J . Mol. Struct. (THEOCHEM) 1991, 222. Csp2 single bond length is only about 0.021 8, (result for C4H6 (23) (a) Cooper, D. L.; Gerratt, J.; Raimondi, M. Adv. Chem. Phys. 1987, with 6-31G) shorter than the Csp3-Csp3 bond and consequently 69, 319. (b) Cooper, D. L.; Gerratt, J.; Raimondi, M. Chem. Rev. 1991, 91, 929. (c) Cooper, D. L.; Wright, S. C.; Gerratt, J.; Raimondi, M. J . the averaging of bonds in conjugated systems is mainly caused Chem. Soc., Perkin Trans. 2 1989,255,263,719. (d) Cooper, D. L.; Wright, by n electronic delocalization, we really conclude that the S. C.; Gerratt, J.; Raimondi, M. J . Chem. Soc., Chem. Commun.1989,675, delocalization is a driving force in chemistry, which is contrary 1489. to the viewpoint of Shaik et a1.& If the VRE can compensate (24) (a) Kursanov, D. N.; Gonikberg, M. G.; Dubinin, B. M.; Kabachnik, M. I.; Kaverzneva, E. D.; Prilezhaeva, E. N.; Sokolov, N. D.; Freidlina, R. the energy needed by the shortening of some Csp2-Csp2 bonds, Kh. J . Chem. Educ. 1952, 29, 2. (b) Tatevskii, V. M.; Shakhparanov, M. the system will prefer a regular geometry with uniform C-C I. J . Chem. Educ. 1954, 32, 13. bond lengths, otherwise the system will be stable toward an (25) (a) Pauling, L. Proc. Natl. Acad. Sci. USA. 1932, 18, 293. (b) Pauling, L.; Sherman, J. J . Chem. Phys. 1933, I , 606. altemate geometry where delocalization is also important. (26) (a) Zhang, Q.; Li, X. J . Mol. Struct. (THEOCHEM) 1989, 198, Indeed we agree that the u frame strongly prefers a regular 413. (b) Li, X.; Zhang, Q. Int. J. Quantum Chem. 1990, 36, 599. (c) Li, geometry, however, the bond lengths should be equal to the X.; Zhang, Q. Sci. China 1990, 33, 276. Csp2-Csp2 single bond, around 1.509 8, (deduced from c4H6 (27) (a) McWeeny, R. Int. J . Quantum Chem. 1988, 34, 25. (b) McWeeny, R. Theor. Chim. Acta 1988, 73, 115. with the 6-31G basis set). The long bond length of cyclobuta(28) Wu, W.; Mo, Y.; Zhang, Q. J . Mol. Struct. (THEOCHEM) 1993, diene is even longer than the CC bond in ethane, and this result 283, 227. is consistent with the concept of bent bonds. (29) (a) Bobrowicz, F. W.; Goddard, W. A,, III. In Methods of Electronic Structure Theory; Schaefer, H. F., III, Ed.; Plenum Press: New York, 1980. By comparing C4& and we conclude that the n (b) Li, X.; Paldus, J. J . Mol. Struct. (THEOCHEM) 1991, 229, 249. electronic delocalization is mainly related to bond lengths no (30) Rumer, G. Nachr. Ges. Wiss. Gotfingen 1932, 337. matter if the molecule is cyclic or not. Thus we believe the (31) Lykos, P. G.; Parr, R. G. J . Chem. Phys. 1956,24,1166; 25, 1301. antiaromacity is a direct result of the o frame's ring strain. The (32) McWeeny, R.; Ohno, K. A. Proc. R. SOC. London 1960, A255,367. (33) Mo, Y.; Wu, W.; Li, J.; Zhang, Q.Chin. Sci. Bull. 1992, 37, 948. conjugation of n electrons is always of benefit energetically. (34) Wu, W.; Zhang, Q.Chem. J . Chin. Univ. 1991, 12, 1517. (35) Binkley, J. S.; Whiteside, R. F.; Krishnan, R.; Schlegel, H. B.; Acknowledgment. This work is a State Major Key Project Seeger, R.; DeFrees, D. J.; Pople, J. A,, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Indiana. for Basic Researches and also supported by the National Natural
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