6410
J. Phys. Chem. 1995,99, 6410-6416
Linear vs Angular Phenylenes: An Interplay of Aromaticity, Antiaromaticity, and Baeyer Strain in Fused Molecular Systems Z. B. MaksiC,*,i D. KovaEek, and M. Eckert-MaksiC Ruder BoZkoviC Institute, P.O.B. 1016, 41001 Zagreb, Croatia
M. Biickmann and M. Klessinger” Organisch-Chemisches Institut der Wesfalischen Wilhelms-Universitat, Corrensstrasse 40, 0-48149 Munster, Germany Received: May 18, 1994; In Final Form: February 9, 1995@
Geometric structure and electronic properties of some first [Nphenylenes, where N stands for the number of benzene fragments, are examined by the HF/6-3 lG* and MP2(fc)6-3 lG*//HF/6-3 1G* theoretical methods. It is found that angular isomers are slightly more stable than their linear counterparts. The difference increases with N . The fundamental importance of the biphenylene bonding pattern for the stability of higher [Nphenylenes is established. It appears, somewhat paradoxically, that the lower total energies of the angular [Nphenylenes are a consequence of the fact that the electronic structure is more localized in the angular than in the linear [Nphenylenes. A plausible explanation is given in terms of decreased antiaromatic character of the planar four-membered rings and by the synergism between (T and n electrons, in contrast to some antagonism in the linear [Nphenylenes. Simple indices of localization based on the CC bond distances and/or n-bond orders are introduced, which offer an interesting insight into aromaticity defects in particular benzene rings. Intrinsic destabilization energies Ed (generalized strain) are estimated by homodesmic chemical reactions. It is found that Ed values follow an approximate but simple additivity rule being determined by the number of cyclobutadiene moieties. The calculated structural parameters are in good agreement with the available experimental data. Both are in accordance with the significant Mills-Nixon effect in angular phenylenes.
1. Introduction
+
Fused planar molecules involving juxtaposed 4n and 4n 2 n-electron fragments represent an interesting class of the extended n-electron systems with competing destabilizing and stabilizing cycles (the [4n]annuleno[4n+2]annulenes). A particularly attractive subset of this class of compounds is provided by n = 1 implying the presence of the cyclobutadiene moiety, which in addition to the unfavorable 4n-electron configuration introduces considerable 0 angular strain. The interplay of the destabilizing angular strain and antiaromatic character of the four-membered rings and the stabilizing aromaticity of benzene ring yields compounds possessing a full scale of new unexpected properties, which represent a challenge for the theory of chemical bonding. The archetypal molecule of this kind is provided by biphenylene ( l ) ,but sequential cyclobutabenzoannelation offers a variety of linear and bent [NJphenylenes,where N stands for the number of benzene fragments while N - 1 is the number of four-membered antiaromatic rings. Synthetic routes to [NJphenylenes have been developed by Vollhardt and co-workers.’ It was pointed out that linear [NJphenylenesare good candidates for organic conductors, ferromagnets, etc. in view of the decreasing LUMO-HOMO gap as N increases.* There are a number of theoretical treatments of [Nphenylenes in the literature concomitant with their practical relevance and the raised conceptual problems. However, theory has been confined to some simple or even arbitrary constructs, which prevented unambiguous answers. Thus simple HMO calculations indicated that the bent [NJphenylenes were slight preferred thermodynamically over their linear counterpart^,^ whereas the + Also at the Faculty of Science and Mathematics, University of Zagreb, MaruliCev trg 19, 41001 Zagreb, Croatia. Abstract published in Advance ACS Abstracts, April 1, 1995. @
contrary was concluded by using “conjugated circuit theory”? PMO t h e ~ r yand , ~ the BORT (bond orbital resonance) theory)? Taking into account both the importance of the posed question and the controversial conclusion drawn so far, we deemed it worthwhile to examine some [NJphenylenes employing current methods of computational quantum chemistry. The studied systems are schematically depicted in Figure 1.
2. Method Standard ab initio MO calculations have been performed employing the GAUSSIAN 92 computer program.’ The HF/ 6-3 lG* level in geometry optimization computations was selected for economic reasons. The use of the 6-31G* basis set was justified a posteriori by comparison with the available experimental data. Since the energetic properties are pivotal and the systems under investigation are highly delocalized involving mobile n electrons, single-point MP2/6-3IG*//HF/ 6-31G* calculations were performed in order to estimate correlation effects. The same theoretical model has proven very successful in reproducing the heat of formation of biphenylene and the geometric parameters of nonbenzenoid aromatics.* Results are interpreted in terms of local hybridization parameters and Coulson’s Jc-bond orders. Hybridization is one of the most important concepts of covalent bonding, and there are several recipes for extracting the hybridization parameters from the MO wave function^.^ Despite their widely different procedures, the resulting parameters are very similar, indicating that they do reflect something essential about redistribution of the atomic density in chemical environments. In this work we use the procedure due to Foster and Weinholdlo yielding the so-called natural bond orbitals (NBO) composed of natural hybrid orbitals (NHO). n-Bond orders and orbital populations were derived from the HF//6-31G* wave function by symmetric Lowdin
0022-3654/95/2099-6410$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 17, 199.5 6411
Linear versus Angular Phenylenes 4
5
5
1
4
2
5-6 A
6
9
10
1
2
10
11
3
12
1
4
11
5
2
Figure 1. Numbering of atoms in biphenylene (1) as well as linear and angular [Mphenylenes 2-5.
orthogonalization. I The atomic populations obtained from the NBO procedure,I0 from the Lowdin-orthogonalized orbital populations and from a Mulliken population analysisI2 are all very similar and exhibit the same trends. Therefore, only NBO and Lowdin charges are given in the tables, since they are determined by widely different procedures. The variations in the atomic densities are very small, but appear to be significant.
3. Results and Discussion Structural Features. We commence the discussion with biphenylene (1) as progenitor of the [Nlphenylene family, since its structural and electronic properties will enable a better understanding of the larger systems. Results presented in Table 1 show that the experimental g e ~ m e t r i e s ' ~ -are ' ~ well reproduced by the HF/6-31G* method in a semiquantitative sense. Since the experimental structures for [Nlphenylenes with N > 3 are not available, the forthcoming discussion is based on their HF/6-31G* geometries for the sake of consistency. In discussing structural details of these systems the fused or annelated bond will be referred to as an ipso bond, the adjacent as ortho, and the others as meta and para, respectively. From the data collected in Table 1 it appears that fusion of the four-membered ring causes substantial bond distance alternation around the benzene perimeter in the original MillsNixonI6 sense. The ipso bond in 1, as well as the meta bonds, e.g., C(l)-C(2), is considerably longer than in benzene, while the ortho and para bonds are s h ~ r t e r . ' ~ A ! ' ~plausible explanation, at the n-electron level only, is offered by the concept of stability of the aromatic sextet, its perturbation, and the avoidance of the unfavorable antiaromatic quartet. Consequently, as a compromise between the desired maximum in aromaticity of the six-membered rings and the minimum in antiaromaticity of the cyclobutadiene moieties, JZ density will be shifted from ipso to ortho bonds producing bond fixation as described above. This conjecture is corroborated by the Lowdin n-bond orders computed from the HF/6-31G* wave function. They are 0.52 and 0.72 for the ipso and the ortho bond,
respectively (Table 1). This is, however, only part of the story, because rehybridization at the carbon junction atoms is an important factor. For this purpose hybridization of the o orbitals should be considered too. In Table 1 NBO s characters calculated from the HF/6-31G* wave function are given. A salient feature is rehybridization of the carbon junction atom which shifts s character from ipso into ortho bonds. Hence, the former should be longer and the latter shorter than in the free benzene. The same change is required by the n-electron distribution, meaning that o and n electrons act in biphenylene (1) in a concerted and synergetic way, resulting in a rather strong alternation of bond distances in the benzene fragment. The value 0.21 of the n-bond order for the bridge bond C(4a)-C(4b) points to a small but nonzero delocalization between the two benzene fragments, which is important for understanding the geometry of the four-membered ring. The fused and bridge bonds have similar average s characters, but considerably different bond distances (1.414 vs 1.507 A), as is to be expected from the corresponding n-bond orders of 0.52 vs 0.21, respectively. The bridge bond, on the other hand, is significantly shorter than in a free cyclobutadiene with perfectly localized double bonds (1SO7 vs 1.565 A, respectively, at the HF16-3 1G* level), implying Considerably less pronounced antiaromatic character. Finally, it should be noted that bond angles obtained by the HF/6-3 lG* method are in fine agreement with experiment. A general feature is an enlarging of the ipsoortho bond angle C(4)-C(4a)-C(8b), with concomitant sharpening of the apical ortho-meta angle C(3)-C(4)-C(4a), as a consequence of rehybridization. Before proceeding further we would like to introduce a simple localization index Li based on the variation of bond distances within the benzene ring: benzene
where &C is the average bond length and & refers to the nth
MaksiC: et al.
6412 J. Phys. Chem., Vol. 99, No. 17, 1995
TABLE 1: Biphenylene and Some Linear and Angular [NIPhenylenes. Structural Parameters, s Character, n-Bond Order as Calculated by the HF/6-31G* Method bondangle
distance/angle" 6-31G* exptl
Cl-C2 C2-C3 C4-C4a
1.417 1.373 1.357
1.423' [1.425]' 1.385 [1.392] 1.372 [1.376]
C1-H
1.075
Cl-C2-C3 C3-C4-C4a
121.9 115.7
121.6 [122.0] 115.5 [115.5]
Cl-C2 C2-C3 C4-C4a C4a-C4b
1.424 1.368 1.352 1.508
1.436d 1.397 1.359 1.512
C1-H C2-H
1.075 1.075
c 1-c2-c3 C 1-ClOb-C4a C3-C4-C4a C4a-C4b-C 10a
121.8 122.5 115.7 90.3
120.1 121.7 118.3
Cl-C2 C 1-C 10d C2-C3 c3-c4 C4-C4a C4a-C4b
1.409 1.363 1.379 1.409 1.363 1.502
1.400(3)d 1.365(3) 1.370(3) 1.404(3) 1.368(2) 1.505(2)
C1-H C2-H
1.075 1.076
c 1 -c2-c3 C 1-ClOd-C4a C3-C4-C4a C4a-C 10d-C 1Oc
121.8 122.5 115.7 90.6
s character NBO
rc-bond order
34.2-34.0 36.3-36.3 35.4-40.3
Biphenylene (1) 0.56 C4a-C4b 0.74 C4a-CSb 0.72
30.5
33.8-33.7 36.4-36.4 35.5-40.6 30.0-30.0 30.5 29.4
bondangle
122.4
122.4 [122.4]
1.417 1.383 1.402
1.397 1.385 1.407
Linear [3]Phenylene (2) 0.53 C4a-ClOb 0.76 C4b-C5 0.74 C4b-ClOa 0.16
1.074
C4a-Cl Ob-C 10a
89.7 112.0 124.0
112.0 124.0
1.410 1.345 1.449 1.451 1.498 1.335
1.413(2) 1.348(3) 1.449(2) 1.446(3) 1.503(2) 1.345(2)
1.075
C4b-C5-C6 C4b-ClOc-ClOb C4b-ClOc-ClOd C5-C4b-C10c
117.5 118.0 89.5 124.5
Cl-C2 C1-C12b C2-C3 C4a-C4b C4a-C 12b
1.427 1.350 1.366 1.509 1.419
CI-H C2-H
1.075 1.075
30.5 29.4
c 1 -c2-c3 C3-C4-C4a C4-C4a-C12b C4a-C4b-C 12a
121.8 115.7 122.5 90.5
Cl-C2 Cl-Cl2f C2-C3 c3-c4 C4-C4a C4a-C4b C4a-Cl2f C4b-C5 Cl-H C3-H
1.411 1.361 1.378 1.411 1.362 1.504 1.411 1.349 1.075 1.075
Cl-C2-C3 C 1-C 12f-C4a c 2 - c 1 -C12f C4a-C 12f-C 12e
122.0 122.5 115.7 90.4
Cl-C2 Cl-C7 C2-C3 C3-H C4-H
1.401 1.512 1.387 1.076 1.076
rc-bond order
30.2-30.2 29.3-29.3
0.21 0.52
29.0-29.0 34.3-29.1 30.6-30.6
29.6-29.4 41.3-36.5 27.5-28.1 33.0-33.0 30.1-31.6 40.7-40.7
124.6
C5-H
1.074
31.1
C4a-C 12b-C12a C4b-C5-C5a C4b-Cl2a-Cl2
89.5 112.0 124.0
o-Xylene (6) 0.62 C3-C4 0.19 C4-C5 0.65 C7-He
0.54 0.79 0.41 0.45 0.23 0.77
117.7 117.9
38.7-34.1 31.0-3 1.0 34.6-39.6 29.8-29.8 30.3-30.3
C4b-C5-C6 C4b-Cl2e-Cl2d C4b-C 12e-C 12f C5-C4b-C 12e
0.60
30.3
1.391 1.394 1.376 1.510 1.407
Angular [4]Phenylene (5) 34.3-34.1 0.58 C4b-CI2e 0.71 C5-C6 35.1-40.1 0.72 C6-C6a 36.0-36.0 34.4-34.1 0.58 C6a-CI2d 39.9-35.2 0.71 C12e-Cl2f 0.22 C12c-Cl2d 30.4-30.2 29.6-29.4 0.54 C12d-CI2e 0.78 41.1 -36.3 C5-H 30.5 29.4
0.50 0.64
31.1
C5-H
C5-H
s character NBO
29.5
C4-C4a-C4b
Linear [4]Phenylene (4) 33.8-33.7 0.52 C4b-C5 35.6-40.7 0.75 C4b-CI2a 36.5-36.5 0.77 C5-C5a 30.0-30.0 0.20 C5a-C5b 28.9-28.9 0.49 C5a-Cllb
34.3-34.3 31.3-23.7 34.7-35.4 29.0 29.6
1.514 [1.516] 1.426 [ 1.4291
1.075
Angular [3]Phenylene (3) 34.2-34.4 0.59 C4a-Clod 35.1-40.0 0.70 C4b-C5 35.9-35.9 0.71 C4b-ClOc 34.2-34.4 0.59 C5-C6 39.8-35.1 0.70 C10a-C10b 30.3-30.5 0.23 CIOb-ClOc
122.4 122.7 115.3
1.507 1.414
C2-H
C4b-C5-C5a C5-C5a-C9b
30.5 29.4
distance/angle" 6-3 lG* exptl
1.442 1.444 1.349 1.445 1.499 1.491 1.339
27.8-28.4 33.2-33.2 41.1-36.3 27.9-28.2 30.1-31.5 31.4-31.4 40.4-40.4
1.075
30.3
0.61 0.63 0.67 0.19 0.58
0.44 0.47 0.77 0.43 0.22 0.24 0.76
117.6 117.9 89.7 124.5 1.387 1.381
35.3-35.0 35.2-35.2
1.OS3
24.1
0.64 0.66
J. Phys. Chem., Vol. 99, No. 17, 1995 6413
Linear versus Angular Phenylenes TABLE 1 (Continued) distancelangle” bond/ande
s character
NBO
exDtl
6-3 lG*
n-bond order bond/anele o-Xylene 6 ) (Continued) C2-Cl-C7 C3-C4-C5
distance/angle“ exptl
6-31G*
s character
NBO
Cl-C2-C3 C2-C3-C4
119.0 121.5
c-c
1.386
1.3971
35.1-35.1
0.66
C-H
1.076
1.084
29.6
c-c
1.527
1.5319
27.9-27.9
0.14
Ethane C-H
1.086
1.096
24.0
H-C-H
107.7
107.8
111.2
111.1
n-bond order
120.9 119.5
Benzene
H-C-C
Distances in angstroms, angles in degrees. Reference 9. Reference 10. Reference 2. e C-H bond denoted by asterisk lies in the plane of the molecule. fstoicheff, B. P. Can. J. Phys. 1954, 32, 339. 8 As cited in the following: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A b Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986; p 156. TABLE 2: Localization Indices Defined by the Bond Lengths and mBond Order@ molecule 1 2 3 4 5
-
benzene rings
dcc
Li(dcc)
central peripheral averageb central peripheral average central peripheral average central peripheral average central peripheral average
1.389 (1.404) 1.389 (1.404) 1.389 (1.392) 1.390 (1.397) 1.390(1.395) 1.396 (1.398) 1.389 (1.387) 1.391 (1.393) 1.389 1.390 1.390 1.394 1.389 1.392
0.16 (0.14) 0.16 (0.14) 0.05 (0.06) 0.19 (0.15) 0.14 (0.12) 0.32 (0.30) 0.12 (0.11) 0.19 (0.17) 0.05 0.21 0.13 0.30 0.13 0.22
ELH
UZCC) (6-31G*)
~ C C
0.637 0.637 0.627 0.633 0.630 0.603 0.638 0.621 0.628 0.633 0.631 0.608 0.640 0.624
0.46 0.46 0.11 0.68 0.39 1.08 0.39 0.74 0.17 0.74 0.46 0.97 0.44 0.71
0.36 0.31 0.35 0.28 0.32
n-Bond orders are calculated by the HF/6-31G* procedure employing Lowdin population analysis. Distances in angstroms; &~(6-31G*) denotes the energy difference between HOMO and LUMO in au. Average values are defined per benzene ring. (I
bond of the phenyl fragment. Analogously, one can define a localization index Li(ncc) employing n-bond orders: benzene
cc
JCCCI
n
Obviously, the localization indices (1) and ( 2 ) are 0 in the perfectly aromatic free benzene while for 1 values of Li(ncc) = 0.46 and Li(dcc) = 0.16 (0.14) are obtained (Table 2), the value in parentheses being from experimental bond distances. As L@c) or Li(ncc) increases, both the aromatic defect and bond fixation are higher. Hence it gives an interesting insight into the variation in bond distances in deformed benzene fragments, electronic localization and stability. The results discussed so far for the localization pattern characteristic for the bonding situation in biphenylene (l),which are due primarily to the concerted action of B and n electrons, can be nicely described in terms of the dominating VB structure
I.
I We shall focus now on the linear [3]phenylene (2). It is a planar molecule, although the X-ray structure reveals some puckering presumably due to the influence of the four peripheral
trimethylsilane substituents.* Nevertheless, the HH6-3 lG* bond lengths and angles are in good accordance with experiment. The observed longer terminal C(2)-C(3) bond is most likely a consequence of the repulsion between the bulky substituent groups. Inspection of both experimental and 6-31G* bond distances as well as the localization indices presented in Table 2 indicates that the terminal benzene rings in 2 are slightly more localized than in 1. On the other hand, the central benzene unit exhibits a highly pronounced delocalization as revealed by a very low value L,(dcc) = 0.05 (0.06), the experimental estimate being given in parentheses. This conjecture is further supported by the Lowdin n-bond orders, which are close to the free benzene value of 0.67 for the central ring (Table 1). It is interesting to observe that the n-bond order of 0.64 for the C(4b)-C(5) bond is the same as the average value of the C(3)-C(4) and C(4)-C(4a) bond orders in the parent biphenylene (l),as intuitively expected. The same holds for bond distances. Finally, in concluding comments on the structural properties of 2, one should mention the small value of 112” for the apical C(4b)-C(5)-C(5a) angle. Rehybridization at the carbon junction atoms increases the C(5)-C(5a)-C(9b) angle as observed already in 1. In the central ring in 2 this effect is doubled since two cyclobutadiene fragments are present in positions pura to each other. The picture of the angular [3]phenylene (3) indicated by the bond distances and the calculated n-bond orders is just the opposite to that in its linear counterpart: the central ring is more localized than in 1, whereas the terminal ones are slightly more delocalized than in the progenitor 1. It should be stressed that the double bond C( 10b)-C( 1Oc) bridging two €our-membered rings is the shortest and the most localized one in harmony with its highest average s character of 41%. Higher localization in the central benzene and a more pronounced delocalization in the peripheral phenyl rings as compared with the linear isomer 2 are nicely reproduced by the localization indices L, (Table 2). It is gratifying that Li(&) values calculated for the available experimental geometries are in fine agreement with the corresponding HF/6-3 lG* indices. Lowdin n-bond orders reflect the variation in bond lengths rather well. The structural features of molecules 4 and 5 are qualitatively similar to those found in the corresponding systems 2 and 3. Hence they do not have to be discussed in detail. The results given in Table 2 are self-evident. Bond distances in [Nphenylenes could also be interpreted in qualitative terms by considering the relevant VB structures. Important in determining the significance of the particular resonance structure is the presence of the biphenylene pattern of the dominant n-electron spin-pair coupling. The reason behind the important role of the biphenylene mode of bond localization is that it
Maksii et al.
6414 J. Phys. Chem., Vol. 99, No. 17, 1995 minimizes the antiaromaticity of the four-membered ring and that it is in harmony with the synergetic behavior of u and n electrons. In concluding this section it should be mentioned that there is a very good linear correlation between the Lowdin n-bond orders and the HF/6-31G* CC bond distances:
dcc = 1.563 - 0 . 2 7 4 (A) ~~~
(3)
The corresponding average absolute error and the coefficient of correlation are 0.006 A and 0.99, respectively. Despite a high correlativity there are some systematic and characteristic deficiencies. One of them is that ortho bonds are persistently longer than expected from eq 3, which is a consequence of the fact that this relation does not take into account the rehybridization effect which shortens bonds emanating from the fourmembered rings. Finally, a word about atomic electron densities is in order here. The calculated data are displayed in Table 3. A conspicuous feature of the results is neutrality of the carbon junction atoms. On the other hand, C atoms linked to a hydrogen possess an effective charge of --0.21e( as a consequence of the electron density transfer from hydrogen to carbon. It is noteworthy that n densities, related to 2pn and 3pn atomic populations, are lower than unity at the carbon junction atoms. This is indicative of the somewhat increased influence of d orbitals. Energetic Properties. Total molecular energies for the phenylenes 1-5 together with some molecules necessary for establishing relevant homodesmic reactionsI9are given in Table 3. A survey of these data shows that angular phenylenes are more stable than their linear counterparts for the same N , the difference being smaller at the MP2(fc)6-31G*//HF/6-3 lG* level. In order to get a deeper insight into the energetic preference of the angular isomers we shall make use of the hypothetical homodesmic reactions as exemplified by
+ 2(CH,-CH,) = 2(o-xylene) + I$’ 2 + 4(CH,-CH,) + benzene = 4(o-xylene) + g2’ 3 + 4(CH,-CH,) + benzene = 4(o-xylene) + g3’ 1
(4b) (4c)
Here Ed stands for the destabilization energy inherent in all [NIphenylenes. Analogous reactions can be easily deduced for molecules 4 and 5. It follows that the difference in energy E(2) - E(3) is equal to the difference in the corresponding destabilization energies, E(d2) The main contributions to the destabilization energies Ed come beyond doubt from the Baeyer strain and the antiaromatic cyclobutadienemoiety. Some fine contributions to Ed energies arise from the aromaticity defects caused by n-bond fixation within the benzene fragments and from the degree of incompatibility between u and n electrons. Destabilization energies Ed are collected in Table 4. The influence of the electron correlation makes the Ed values larger by a couple of kcaumol. A point of considerable interest is the fact that the destabilization energies are approximately additive with I.$w = ( N - l)I.$’), where E(dN) refers do [NIphenylene and I.$’’ is the corresponding energy for biphenylene. To put it in another way, the total destabilization energy is given roughly by the number of four-membered rings. If the additivity were to hold exactly, linear and angular [Nlphenylenes with the same N would have equal total energies and would therefore be of equal stability. Thus, in order to get
e’.
TABLE 3: Biphenylene and Some Linear and Angular [NJPhenylenes. Atomic Population as Calculated by the HF/6-31G* Method population atom
NBO
Lowdin (total)
Lowdin (nelectron)”
c1 c2 C4a
6.22 6.22 6.02
Biphenylene (1) 6.17 6.16 6.00
c1 c2 C4a C4b c5
6.23 6.22 6.01 6.01 6.22
Linear [3]Phenylene (2) 6.17 6.16 6.00 6.00 6.17
c1 c2 c3 c4 C4a C4b c5 ClOa ClOb
6.22 6.22 6.22 6.22 6.02 6.01 6.22 6.02 6.02
Angular [3]Phenylene (3) 6.16 6.16 6.16 6.17 6.00 6.00 6.17 6.00 6.02
c1 c2 C4a C4b c5 C5a
6.23 6.22 6.01 6.01 6.22 6.00
Linear [4]Phenylene (4) 6.18 6.17 6.00 6.00 6.17
6.00
1.oo 0.99 0.95
1.oo 0.99 0.95 0.95 1.00 0.99
0.99 0.98 0.99 0.95 0.96 1.01 0.96 0.97 1.01 0.99 0.95 0.95 1.01 0.95
c1 c2 c3 c4 C4a C4b c5 C6 C6a C12d C12e C12f
6.21 6.22 6.22 6.22 6.02 6.22 6.22 6.22 6.01 6.02 6.01 6.02
Angular [4]Phenylene ( 5 ) 6.16 6.16 6.16 6.17 6.00 6.00 6.17 6.17 6.00 6.02 6.01 6.01
c2 c3 c4 c7
6.03 6.22 6.23 6.64
o-Xylene (6) 6.02 6.17 6.17 6.43
0.96 1.oo 0.99 1.13
C
6.23
Benzene 6.16
0.98
6.64
Ethane 6.44
C
0.99 0.99 0.98 0.99 0.95 0.96 1.oo 1.oo 0.96 0.98 0.96 0.96
a Atomic ~ tdensities . given here are related to (2p), and ( 3 ~orbital ) ~ population only.
some deeper insight into the distinct properties of linear and angular [Nlphenylenes,the difference in destabilization energies E(dhit for these two classes of compounds has to be analyzed in some detail. The similarity in bond hybridization parameters within the four-membered ring and the corresponding n-bond orders explains the approximate additive increase in the destabilization energy &(N), the latter being a simple multiple of the basic entity to be associated with a single cyclobutadiene pattern in both series of phenylenes. This fact provides a plausible explanation for the most surprising result that the ab initio energies of linear and angular [Nlphenylenes are nearly identiCal.20
J. Phys. Chem., Vol. 99, No. 17, 1995 6415
Linear versus Angular Phenylenes TABLE 4: Total Molecular Ab Initio Energies (in au) for IMPhenylenes, Ethane, Benzene, and o-Xylene (6) molecule €IF/6-3lG* MP2(fc)//HF/6-31G* CH3-CH3
benzene 1 2 3 4 5 6
-19.228 -230.703 -459.014 -681.325 -687.331 -915.636 -915.646 -308.776
76 14 59 85 32 00 36 22
-19.494 51 -23 1.456 48 -460.523 70 -689.594 24 -689.596 19 -918.664 66 -918.667 15 -309.791 98
TABLE 5: Intrinsic Destabilization Energy (in kcaymol) in [NJPhenylenesEstimated via the Homodesmic Chemical Reactions Employing Various ab Initio Model@ destabilization energy E‘,” molecule
HF/6-31G*
MP2(fc)// HF/6-31G*
E(2) - E(3) E(4) - E(5)
50.4 100.9 97.5 152.2 145.7. 3.4 6.5
52.2 102.4 101.2 152.6 150.7 1.2 1.9
1
2 3 4 5
(additivity) MP2(fc)// HF/6-31G* HF/6-31G* 100.8 100.8 151.2 151.2
104.4 104.4 156.6 156.6
Relative stabilities of angular vs linear phenylenes are given at the bottom. The average delocalization is larger in the linear phenylenes 2 and 4, being particularly pronounced in the central rings that are almost aromatic. The role of their aromatic stabilization is substantiated by the MP2 calculations, which describe n-electron delocalization better than the HF model. Hence, it is not surprising that MP2 model leads to a decrease in the energy difference between the corresponding linear and angular phenylenes (Table 5). Nevertheless, in spite of the increased aromaticity within the benzene rings, linear phenylenes are less stable because of the increased antiaromaticity in the cyclobutadiene rings and the less orchestrated behavior of u and n electrons. Their counteraction is particularly present in the fused bonds of the central benzene rings. The slightly lower energies of the angular [Nlphenylenes show up in the larger difference of % 3(N - 2 ) kcal/mol for angular [Nlphenylenes between the destabilization energies obtained from the additivity rule and the calculated MP2 values compared with &? rc 2(N - 2) kcaYmol for linear [Nlphenylenes. For a rationalization of this difference it is important to remember the good preservation of the biphenylene bonding pattern and the concomitant increased synaction of u and n electrons in the central rings of angular phenylenes. As a consequence, the antiaromatic character of the cyclobutadiene ring is diminished, as is evident also from the fact that the n-bond orders of the annelated bonds are significantly lower in the angular phenylenes than in their linear counterparts. The importance of the cyclobutadiene moiety is easily seen by comparing its n-electron destabilization of -55 kcal/mol with the aromatic resonance energy of benzene taking a value of 23.4 kcal/mol.21 Hence, it appears that four-membered rings dominate structure and energetics in phenylenes firstly through the angular strain and secondly via the unfavorable n-electron distribution in the inserted four-membered rings, leading inevitably to antiaromatic interactions. It should be mentioned that our interpretation is independent of the controversial discussion regarding the dominant driving force leading to the aromatic and perfectly symmetric benzene. According to one group of researcher^,^^^^^ aromaticity of benzene is determined by u electrons, whereas x electrons prefer
bond fixation. A more traditional viewpoint on stability and delocalization of the n-electron sextets was recently reinforced by Wiberg et al.24and Glendening et al.25 Taking into account that stability of phenylenes is determined by a subtle balance between several types of intramolecular interactions, it is not surprising that oversimplified methods like BORT6 or the graph-theoretical “conjugated circuit” approach4 fail in the case of phenylenes. The same holds for the simple form of the PMO the01-y.~The role of the u framework cannot be simply ignored in fused systems involving small angularly strained rings. Finally, a word on the HOMO-LUMO splitting is in order. It rapidly decreases along the series of linear [Nlphenylenes (Table 2). The HOMO-LUMO gap diminishes in angular [Nlphenylenes, too, but it is larger than in the corresponding linear counterparts. This feature might be important for the electrical (supra) conductivity properties of these remarkable compounds which deserve to be better explored.
4. Conclusion It is found that preservation of the biphenylene bonding pattern is important for understanding the energetic properties of [Nlphenylenes. In particular, angular phenylenes are more stable than their linear counterparts for the same N , the difference in stability increases with N . Intrinsic destabilization energies Ed in [Nlphenylenes are roughly additive as estimated by the homodesmic reaction. They describe what may be termed the generalized strain, since Ed values involve the angular strain, the aromaticity defect, and some antagonistic interactions between u and n electrons. Smaller destabilization energies in angular phenylenes than predicted by the additivity nile are largely a consequence of a decrease in antiaromaticity of the involved four-membered rings and of a better synaction of u and n electrons. Hence, cyclobutadiene appears to be the leading structural motif exerting a dominant influence on the electronic interactions and electron density distributions in compounds considered here, whose properties are determined by the delicate interplay between contributions from aromaticity, antiaromaticity, and angular strain to the total energies. Paradoxically enough, the more stable angular phenylenes are more localized at the same time. Variation in structural parameters within their benzene rings is indicative of the presence of a substantial Mills-Nixon effect.I6 The same holds for the peripheral benzenes in linear phenylenes, while the central sixmember ring(s) in the latter molecules exhibit a more uniform distribution of CC bond distances. Finally, the LUMO-HOMO gap attenuates along the series rather quickly, being smaller in the linear [Nlphenylenes. Acknowledgment. Services and computer time of HLRZ Julich are gratefully acknowledged. Part of this work was performed during a stay by two of us (M.E.-M. and Z.B.M.) at the Organisch-Chemisches Institut der Universitat Miinster, Germany. M.E.-M. would therefore like to thank the Alexander von Humboldt-Stiftung for the fellowship. Z.B.M. thanks the International Office of the “Kernforschungsanlage Jiilich” for financial support. References and Notes (1) Vollhardt, K. P. C. Pure Appl. Chem. 1993,65, 153 and references cited therein. (2) Bems, B. C.; Hovakeemian, G. H.; Lai, Y. H.; Mestdagh, H.; Vollhardt, K. P. C. J . Am. Chem. SOC. 1985, 107, 5670. (3) (a) Barron, T. H. K.; Barton, J. W.; Johnson, J. D. Tetrahedron 1966, 22, 2609. (b) Barton, J. W.; Rowe, D. J. Tetrahedron 1985, 41,
1323.
6416 J. Phys. Chem., Vol. 99, No. 17, 1995 (4) RandiC, M. J . Am. Chem. SOC. 1977, 99, 444; Tetrahedron 1977, 33, 1905. (5) Dewar, M. J. S.; Dogherty, R. C. The PMO Theory of Organic Chemistry; Plenum Press: New York, 1975. (6) TrinajstiC, N.; Schmalz, T. G.; ZivkoviC, T. P.; NikoliC, S.; Hite, G. E.; Klein, D. J.; Seitz, W. A. New J. Chem. 1991, 15, 27. (7) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. F.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replodge, E. S.; Gomperts, G.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Abker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision A; Gaussian Inc.: Pittsburgh, PA, 1992. (8) Schulman, J. M.; Disch, R. L. J. Mol. Struct. (THEOCHEM) 1992, 259, 173. (9) MaksiC, Z. B. In Theoretical Models of Chemical Bonding; MaksiC, Z. B., Ed.; Springer Verlag: Berlin, 1990; Vol. 2, p 137. (10) Foster, J. P.; Weinhold, F. J. Am. Chem. SOC. 1980, 102, 7211. Reed, A. E.; Curtiss, L. A,; Weinhold, F. Chem. Rev. 1988, 88, 899 and references cited therein. (11) Lowdin, P. 0. J . Chem. Phys. 1950, 18, 63. (12) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833, 1997, 2343. (13) Fawcett, J. K.; Trotter, J. Acta Crystallogr. 1966, 20, 87. (14) Boese, R. Private communication (1994). We thank Prof. Boese for sending us results prior to publication. (15) Diercks, R.; Vollhardt, K. P. C. Angew. Chem., lnt. Ed. Engl. 1986, 25, 266.
MaksiC. et al. (16) Mills, W. H.; Nixon, I. G. J . Chem. SOC.1930, 2510. (17) Stanger, A.; Vollhardt, K. P. C. J . Am. Chem. SOC.1988,53,4889. (18) MaksiC, Z. B.; Eckert-MaksiC, M.; KovaEek, D.; MargetiC, D. J . Mol. Struct. (THEOCHEM) 1992, 260, 241. (19) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. Tetrahedron 1976, 32, 317; J . Chem. SOC.,Perkin Trans. 2 1976, 1222. George, P.; Trachtman, M.; Brett, A. M.; Bock, C. W. J. Chem. SOC., Perkin Trans. 2 1977, 1036. (20) Zero-point energies (ZPE) hardly affect these results. At the HF/ 6-31G* level, calculated ZPE values for 2 and 3 are 145.43 kcal/mol and 145.81 kcal/mol, respectively. (21) Hess, B. A., Jr.; Schaad, L. J. J . Am. Chem. SOC. 1983,105,7500. (22) Hiberty, P. C.; Ohanessian, G.; Shaik, S. S.; Flament, J. P. Pure Appl. Chem. 1993, 65, 35 and references cited therein. (23) Jug, K.; Koster, A. M. J. Am. Chem. SOC. 1990, 112, 6772. Jug, K.; Matuschewski, M. Znt. J . Quantum Chem. 1994, 49, 197. Ou, M. C.; Chu, S. Y . J . Phys. Chem. 1994, 98, 1087. (24) Wiberg, K. B.; Nakaji, D.; Breneman, C. M. J . Am. Chem. SOC. 1989, 1 1 1 , 4178. (25) Glendening, E. D.; Faust, R.; Streitwieser, A.; Vollhardt,'K. P. C.; Weinhold, F. J . Am. Chem. SOC. 1993, 115, 10952.
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