J. Org. Chem. 2001, 66, 3215-3219
Linear versus Y-Topology in Conjugated Polyene Dications: Questioning Y-Aromaticity† T. P. Radhakrishnan* School of Chemistry, University of Hyderabad, Hyderabad 500 046, India
Israel Agranat* Department of Organic Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
[email protected] Received October 19, 2000
The unique topology of trimethylenemethane bestows on its neutral and ionic states fascinating electronic structural characteristics.1 It has led to notions such as Y-aromaticity, which suggests that acyclic conjugated species with closed shell (4n + 2) π-electron configuration and branched (Y-shaped) delocalization possess “aromatic” stability. This concept2 was put forward by Gund on the basis of the special stability of the guanidinium ion and by Klein and co-workers, who observed the facile formation of the trimethylenemethane dianion. The essence of Y-aromaticity is the delocalization through the Y-center, cyclic delocalization being not necessary. Intuitively, the Hu¨ckel rule and the Hu¨ckel magic numbers, (4n + 2) and 4n, played an important role in the formulation and development of this concept. Guanidinium ion and trimethylenemethane dianion have six π-electrons each, and trimethylenemethane dication has two π-electrons, while neutral trimethylenemethane is a non-Kekule´ hydrocarbon, a diradical with four π-electrons.3 The original formulation of the (4n + 2) Hu¨ckel rule was based on the requirement of a closed shell electron configuration, i.e., an electron configuration consisting of doubly occupied orbitals, as a condition for stability.4 A broader interpretation of the Hu¨ckel rule requires the filling of all bonding MOs and vacancy of all nonbonding and antibonding MOs.4 Both trimethylenemethane dication and dianion are closed shell molecular systems. However, the requirement of vacancy of nonbonding and antibonding MOs is met only in the case of trimethylenemethane dication and not in the case of trimethylenemethane dianion. * Corresponding information for T.P.R.: Fax, 91-40-3012460; Email,
[email protected]. Fax for I.A.: Fax: 972-2-6511907. † This Note is dedicated to the memory of the late Professor Jozef Klein (1916-1998), an eminent scientist, a professors' professor, and a pioneer of Y-delocalization and charge alternation. (1) Berson, J. A. In Diradicals; Borden, W. T., Ed.; Wiley-Interscience: New York, 1982; p 151. (2) (a) Gund, P. J. Chem. Educ. 1972, 49, 100. (b) Finnegan, R. A. Ann. N. Y. Acad. Sci. 1969, 159, 242. (c) Klein, J.; Medlik, A. J. Chem. Soc., Chem. Commun. 1973, 275. (3) Borden, W. T.; Iwamura, H.; Berson, J. A. Acc. Chem. Res. 1994, 27, 109. (4) Minkin, V. I.; Glukhovtsev, M. N.; Simkin, B. Ya. Aromaticity and Antiaromaticity: Electronic and Structural Aspects; Wiley: New York, 1994; pp 117-118; see also the term Aromaticity in the “Glossary of Terms Used in Theoretical Organic Chemistry (IUPAC Recommendations 1999)” in Pure Appl. Chem. 1999, 71, 1919.
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The notion of Y-aromaticity has been the subject of extensive computational investigations.5 The latest papers in the series suggest the following: (i) the energy differences relevant to the discussion of Y-aromaticity are quite small, making alternate conclusions possible from further studies,5f and (ii) the stabilization of the Yconjugated system over its linear counterpart cannot be taken as a signature of aromaticity when compared to prototypes such as benzene.5h We report here the results of an ab initio computational study of a series of acyclic hydrocarbon dications with linear and branched π-conjugation. Previous computational studies on dications have focused on the stabilization of the trimethylenemethane system using heteroatoms6 and the energetics involved in the C-C bond rotations.7 In the latter paper, the stabilization of the planar Y-species over its linear counterpart was attributed to the pronounced Y-delocalization. Synthetic studies on substituted trimethylenemethane dications8 have however revealed no unusual stabilities. We have chosen to investigate the dications since they circumvent the problems associated with pyramidalization,5d effective theoretical description of the wave functions,5e and the role of counterions,5f which have complicated the issue in the case of dianions. Several of the dications we have studied are genuine energy minima in the planar geometry, diffuse functions are not required to describe the wave functions of dications, and counterions exert little influence on the relative energetics of the dications.9 In this study, we inquire whether the preference for Y-topology over the linear one is maintained in the higher homologous conjugated polyene dications; to the best of our knowledge, such an investigation has not been carried out earlier in connection with the question of Y-aromaticity. The computations show that in the higher homologues the preference is clearly for the linear systems, and there is no hint of any special stabilization for the (4n + 2) π-system with Y-topology. These points are argued on the basis of computed energies and homodesmotic reactions; the role of bond and charge alternation as well as the connectivity of allyl cation motifs are examined. The dications we have considered in this study are represented by their molecular graphs in Figure 1. Calculations were carried out using Gaussian 94.10 HF, MP2, and B3LYP Hamiltonians were used with a variety of basis sets in the case of the C4H62+ systems and 6-31G* and 6-311G** basis sets in the others. All isomers were fully geometry optimized and characterized as genuine (5) (a) Agranat, I.; Skancke, A. J. Am. Chem. Soc. 1985, 107, 867. (b) Wiberg, K. B. J. Am. Chem. Soc. 1990, 112, 4177. (c) Agranat, I.; Radhakrishnan, T. P.; Herndon, W. C.; Skancke, A. Chem. Phys. Lett. 1991, 181, 117. (d) Gobbi, A.; MacDougall, P. J.; Frenking, G. Angew. Chem., Int. Ed. Engl. 1991, 30, 1001. (e) Guerra, M. Chem. Phys. Lett. 1992, 197, 205. (f) Skancke, A. J. Phys. Chem. 1994, 98, 5234. (g) Kalcher, J.; Sax, A. F. Chem. Rev. 1994, 94, 2291. (h) Ohwada, T.; Kagawa, H.; Ichikawa, H. Bull. Chem. Soc. Jpn. 1997, 70, 2411. (6) Scho¨tz, K.; Clark, T.; Schaller, H.; Schleyer, P. v. R. J. Org. Chem. 1984, 49, 733. (7) Agranat, I.; Skancke, A. New J. Chem. 1988, 12, 87. (8) (a) Kawase, T.; Wei, C.; Ueno, N.; Oda, M. Chem. Lett. 1994, 1901. (b) Head, N. J.; Olah, G. A.; Surya Prakash, G. K. J. Am. Chem. Soc. 1995, 117, 11205. (9) (a) Koch, W.; Maquin, F.; Stahl, D.; Schwarz, H. Chimia 1985, 39, 376. (b) Koch, W.; Schwarz, H. In Structure/Reactivity and Thermochemistry of Ions; Ausloos, P., Lias, S. G., Eds.; D. Riedel: Dordrecht, 1987; p 413. (c) Pagni, R. M. Tetrahedron 1984, 40, 4161.
10.1021/jo0015016 CCC: $20.00 © 2001 American Chemical Society Published on Web 04/06/2001
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Notes
Figure 1. Molecular graphs (H atoms and double bonds not shown) of dications considered in this study and their labeling; all vertexes represent sp2 C atoms. Table 1. Calculated Energies (Corrected for Zero-Point Energies; Exceptions Noted) and Relative Energies of C4H62+ Ions calculation method/basis set
energy of 4-1a (hartrees)
energy of 4-2 [4-3] (hartrees)
E4-2 - E4-1 [E4-3 - E4-1] (kJ mol-1)
HF/STO-3G -152.228824 -152.200990b 73.1 HF/6-31G* -154.049035 -154.023391b [-154.008961]c 67.3 [105.2] b HF/6-311G** -154.085295 -154.059757 67.1 b HF/6-31++G** -154.062632 -154.036851 67.7 d e MP2/6-31G* -154.483090 -154.468826 [-154.458018] 37.5 [65.8] d MP2/6-311G** -154.564378 -154.550000 37.8 38.7 MP2/6-31++G** -154.529296 -154.514558d B3LYP/6-311G** -155.073419 -155.060372d [-155.050617]e 34.3 [59.9] MP4/6-31G** f -154.676210 -154.662248b 36.7 CISD/6-31G**f -154.597424 -154.576646b 54.6 b Point group symmetry C c Point group symmetry C d Point group symmetry C e Point group symmetry a Point group symmetry D 3h 2h 2 i C1; one force constant is negative. No structure could be located which is a true minimum. f Frequencies not checked; energies not corrected for ZPE
minima on the basis of calculated analytical frequencies; exceptions are noted. Symmetry was not imposed in the calculations; the symmetries reported are those observed in the optimized geometries. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, revision D.2; Gaussian, Inc.: Pittsburgh, PA, 1995.
Table 1 provides the energies and relative energies of the C4H62+ ions from calculations at various levels. The D3h symmetry Y-shaped 4-1 is found to be the stablest in all cases; at B3LYP/6-311G** level, it is found to be stabler than 4-2 and 4-3 by 34.3 and 59.9 kJ mol-1 respectively. The Z-isomer 4-3 is a transition state with one negative force constant even at the lowest symmetry of C1; at higher symmetries it was found to be a higher order saddle point. The results of the calculations on the C6H82+ ions are presented in Table 2. All of the energies reported are for genuine energy minima, except in the case of 6-10. Only selected systems are computed at the
Notes
J. Org. Chem., Vol. 66, No. 9, 2001 3217
Table 2. Calculated Energies (Corrected for Zero-Point Energy) and Relative Energies, ∆E with Respect to 6-1 of Different C6H82+; All Structures Are Genuine Energy Minima except 6-10 MP2/6-31G*
B3LYP/6-311G**
no.
symmetry
energy (hartrees)
∆E (kJ mol-1)
energy (hartrees)
6-1 6-2 6-3 6-4 6-5 6-6 6-7 6-8 6-9 6-10 6-11
C2h C1 Cs C1 C1 C1 C1 C2v C1 Csa D2
-231.682487 -231.672364 -231.663631 -231.678763 -231.668294 -231.674335 -231.661464 -231.624490 -231.624254 -231.615040 -231.664428
0.0 26.6 49.6 9.8 37.3 21.4 55.2 152.3 152.9 177.1 47.4
-232.559389
0.0
-232.555175
11.1
-232.551069
21.8
-232.505743
140.8
-232.537722
56.9
∆E (kJ mol-1)
a
One force constant is negative; this coordinate leads to a closed ring structure which is a genuine energy minimum with an energy of -231.692243 hartrees. Table 3. Calculated Energies (Corrected for Zero-Point Energy; Exceptions Noted) and Relative Energies, ∆E with Respect to 8-1 of Different C8H102+; Structures 8-1 to 8-6 Are Genuine Minima MP2/6-31G*
B3LYP/6-311G**
no.
symmetry
energy (hartrees)
∆E (kJ mol-1)
energy (hartrees)
∆E (kJ mol-1)
8-1 8-2 8-3 8-4 8-5 8-6 8-7a 8-8a 8-9a
C2h C1 Cs C2v C1 C1 Cs Cs Cs
-308.859314 -308.840267 -308.800809 -308.839960 -308.816041 -308.822679 -308.907738 -308.919834 -308.929396
0.0 50.0 153.6 50.8 113.6 96.2 280.7 249.0 223.9
-310.023470 -310.002614 -309.968117 -310.003869 -309.973566 -309.982288
0.0 54.8 145.3 51.5 131.0 108.1
a Frequency calculations not carried out; energies not corrected for ZPE.
B3LYP/6-311G** level since the energy trends are identical with the trends seen in the MP2/6-31G* energies. The linear system 6-1 is found to be the stablest. The lowest energy Y-structure 6-6 is found to be less stable than 6-1 by 21.4 and 21.8 kJ mol-1, respectively, at the two levels of computation. The C8H102+ ions were also computed at the same two levels, and all except the high energy species were characterized as genuine energy minima (Table 3). Once again, the linear system 8-1 is the stablest; it is more stable than the branched ions 8-2 and 8-4 by 50.0 and 50.8 kJ mol-1, respectively, at the MP2/ 6-31G* level and by 54.8 and 51.5 kJ mol-1, respectively, at the B3LYP/6-311G** level. The ion 8-1 is stabler than the doubly branched 8-6 by 96.2 and 108.1 kJ mol-1, respectively, at the two computational levels. The three C10H122+ ions were also studied at the two levels; the frequencies were computed to confirm the local minimum status at the B3LYP/6-311G** level. The linear 10-1 is found to be stabler than the singly branched 10-2 and the doubly branched 10-3 by 75.4 and 167.7 kJ mol-1, respectively, at the MP2/6-31G* level and by 80.7 and 181.5 kJ mol-1, respectively, at the B3LYP/6-311G** level (ZPE included). Except in the 4-carbon series, the linear [n]-polyene dications are found to be consistently and significantly more stable than the isomeric Y-shaped 2-methylene-[n - 1]-polyene and 2,(n - 3)-dimethylene-[n - 2]-polyene
dications. Moreover, the two relative energies
∆E1 ) E2-methylene-[n-1]-polyene2+ - E[n]-polyene2+ ∆E2 ) E2,(n-3)-dimethylene-[n-2]-polyene2+ E2-methylene-[n-1]-polyene2+ are found to progressively increase with n. For n ) 4, 6, 8, and 10, the values of ∆E1 are -34.3, +21.8, +54.8, and +80.7 kJ mol-1, respectively, at the B3LYP/6-311G** level. For n ) 6, 8, and 10, the values of ∆E2 are +35.1, +76.2, and +100.8 kJ mol-1, respectively. These results suggest that the branching makes the dication energetically less favored and a second branching worsens it further. Preference for linear conjugation over Y-conjugation is clearly manifested in all of the systems with the exception of the C4H62+ ions. We have considered the following homodesmotic reactions to examine possible significance of the π-electron count:
8-1 + 4-2 f 6-1 + 6-1
∆E ) -91.7 kJ mol-1
8-2 + 4-1 f 6-6 + 6-6
∆E ) -68.5 kJ mol-1
10-1 + 6-1 f 8-1 + 8-1
∆E ) -51.8 kJ mol-1
10-2 + 6-6 f 8-2 + 8-2
∆E ) -44.8 kJ mol-1
The ∆E values are calculated using the B3LYP/6311G** energies. This sample of reactions suggests that the energy stabilization is driven by the extent of π-electron delocalization rather than the number of π-electrons (4n or 4n + 2) in the reactants and products. An examination of the simple Hu¨ckel energies of the dications having different connectivity patterns in the various series reveals the following trends: 4-1 < 4-2; 6-6 < 6-1 < 6-11 < 6-8; 8-4 < 8-1 < 8-2 < 8-6 < 8-3 < 8-8 < 8-5 < 8-9 < 8-7; 10-1 < 10-2 < 10-3.11 The Hu¨ckel energies do not reflect the significant stability of the linear dications in the 6-n and 8-n series. However, it is interesting to note that the energetic preference of the branched isomer over the nearest linear one continuously reduces from the 4-n to the 10-n series. The trends agree with the results of the ab initio calculations in the 4-n and 10-n series. Beyond these generalizations, simple Hu¨ckel calculations cannot address the impact of important factors such as diastereomerism, conformations, bond alternation effects, and charge alternation effects. Bond and charge alternations are often discussed in connection with the relative stabilities of dianions and dications. However, there are no unique definitions for these quantities.12,13 In the molecular graphs of the dications (Figure 1) if the number of C atoms connected to two or three other C atoms are denoted as (11) The Hu¨ckel energies of the various dications in units of β are 4-1 (-3.464); 4-2 (-3.236); 6-1 (-6.098); 6-6 (-6.156); 6-8 (-5.864); 6-11 (-6.000); 8-1 (-8.822); 8-2 (-8.764); 8-3 (-8.576); 8-4 (-8.828); 8-5 (-8.472); 8-6 (-8.646); 8-7 (-8.378); 8-8 (-8.564); 8-9 (-8.424); 10-1 (-11.486); 10-2 (-11.344); 10-3 (-10.988). (12) Scott, A. P.; Agranat, I.; Biedermann, P. U.; Riggs, N. V.; Radom, L. J. Org. Chem. 1997, 62, 2026. (13) (a) Klein, J. Tetrahedron 1983, 39, 2733. (b) Klein, J. Tetrahedron 1988, 44, 503.
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Notes
Figure 2. C-C bond lengths (in Å) in MP2/6-31G* optimized geometries of selected dications.
n2 and n3 respectively, we define the bond alternation (BA) as
BA )
1
n2
n3
1
{|rij - rik| + |rij ∑{|rij - rik|} + 3n ∑ i)1
n2 i)1
3
ril| + |rik - ril|} where rab is the bond length between atoms a and b, and j, k, l are atoms attached to i; | | denote absolute values.
This definition circumvents the ambiguity associated with some of the previous definitions of BA in the choice of single and double bonds in borderline cases. If the number of bonds in the molecular graph is m and qi1 and qi2 represent the charges on the two atoms connected by bond i, an obvious definition of CA would be
CA )
1
m
∑{|qi1 - qi2|} m i)1
Notes
J. Org. Chem., Vol. 66, No. 9, 2001 3219
Table 4. Bond (BA) and Charge (CA) Alternation (See Text for Definition) in the Various Dications Calculated on the Basis of Their MP2/6-31G* Optimized Geometries and Computed Natural Charges; Dications of the Same Size Are Sorted According to Increasing Energies no.
BA (Å)
CA
4-1 4-2 4-3
0.000 0.058 0.041
0.837 0.739 0.688
6-1 6-4 6-6 6-2 6-5 6-11 6-3 6-7 6-8 6-9 6-10
0.046 0.050 0.053 0.040 0.047 0.077 0.034 0.052 0.024 0.023 0.018
0.816 0.872 0.873 0.828 0.924 0.604 0.821 0.910 0.724 0.765 0.782
8-1 8-2 8-4 8-6 8-5 8-3 8-9 8-8 8-7
0.037 0.058 0.044 0.069 0.077 0.027 0.083 0.063 0.081
0.841 0.815 0.914 0.720 0.574 0.681 0.571 0.700 0.596
10-1 10-2 10-3
0.035 0.057 0.073
0.835 0.768 0.540
The values of BA and CA computed for the dications using the optimized bond lengths and computed natural charges on atoms from MP2/6-31G* calculations are provided in Table 4. In the table, the dications in each family are sorted based on their energies. There is no extended correlation between the energies of the dications and their BA or CA values. However some interesting trends can be discerned. If one considers the lowest energy isomer in the linear and single or multiple branched systems in each family, the branched ones have enhanced BA values and the values increase with the branching; 4-1 is an exception, where as a result of symmetry BA is zero. Thus the BA values increase as 6-1 < 6-6 < 6-11, 8-1 < 8-2 < 8-6 < 8-9 and 10-1 < 10-2 < 10-3. Within these sets including 4-1 and 4-2, the energies correlate well with the BA values. The CA values appear quite random when the full group of dications is considered. However, in the selected sets considered above, the CA values are found to show a steady decrease with increasing energy; the only exception is the case of 6-6 which has a higher value of CA than 6-1. Thus there appears to be a gross relation between lower BA and higher CA values and energy
stabilization of the dications. It is also observed that the Z-conformers are energetically disfavored. The series 6-1 to 6-5 provides a good illustration; the order of stability is 6-1 (E,E,E) > 6-4 (E,Z,E) > 6-2 (Z,E,E) > 6-5 (E,Z,Z) > 6-3 (Z,E,Z). The bond lengths from MP2/6-31G* optimizations of selected dications are provided in Figure 2. Except in 4-1 and 4-2 where symmetry forbids it, allyl cation motifs are clearly visible in most of the other structures. The energy trends in a particular set of isomers can be correlated to the following: (i) spatially separated allyl cation motifs connected at their end C atoms are favored most, and (ii) the energy increases with the number of instances of allyl cation motifs connected to the rest of the molecular framework at the middle C atom (recall that the allyl cation has a node passing through the central C atom). The isomers in which symmetry forbids the formation of allyl cation motifs generally possess higher energy. The 8-n series in Figure 2 provides a good test set; 8-1 with allyl motifs separated by three bonds and each one connected at the end C atoms is the stablest, while 8-2 with one allyl motif connected at the middle C and 8-4 having two bonds separating the allyl cation motifs come next. 8-6 with one allyl cation motif connected at the middle C and one connected at the end C is stabler than 8-5 having both allyl cation motifs connected at the middle C atom. 8-9 is similar to 8-5 in terms of allyl motif connectivity but has shorter separation between the two. The set of isomers 10-1, 10-2, and 10-3 also clearly demonstrates the significance of the connectivity of the allyl cation motifs. Thus a qualitative explanation of the relative energy trends and special stabilization of the linear dications is provided by the location and connectivity of the allyl cation motifs present in these structures. In conclusion, the stabilization of the Y-shaped C4H62+ (4-1) relative to the linear 4-2 is an exception rather than the rule. In the higher polyene dications, the linear topology is favored over the respective Y-topologies in energy stabilization and apparently in bond delocalization and charge alternation. This preference is attributed to the spatially separated and appropriately connected allyl cation motifs, which are best realized in linear CnHn+22+ with n g 6, but not in the parent 4-2. In C4H62+ systems where such separated allyl cation motifs are impossible, the favorable BA and CA associated with the D3h symmetry of the trimethylenemethane dication lead to the exceptional stabilization.
Acknowledgment. T.P.R. thanks the Department of Science and Technology, New Delhi, for financial support (Swarnajayanti Fellowship). JO0015016
