J. Phys. Chem. 1993,97, 13403-13407
13403
Ab-Initio Studies of Radical Cations Derived from Hexa- 1,5-diene Systems: Semibullvalene Heinz D. Roth' and Prasad S. Lakkaraju Wright and Rieman Laboratories. Department of Chemistry, Rutgers University, New Brunswick, New Jersey 08855 Received: May 7, 1993'
The radical cation of semibullvalene has been investigated by ab-initio molecular orbital calculations; both a fully delocalized structure (3c, CZ,symmetry) and a species with two non-interacting allyl moieties (3a, C, symmetry) were considered. At the HF/6-31G* level of theory both species are minima (all positive vibrational frequencies); the C, species lies 2.5 kcal mol-' below the CZ, species. Single point calculations at the MP2/ 6-31G* level of theory reverse the relative stability, placing the CZ,species 14 kcal mol-' below the C, species. The interallyl distance is significant (232 pm for CZ,, 245 pm for C,);the interallyl interaction is correspondingly weak, as shown by very weak off-diagonal elements in the spin density matrix. An equation proposed by Whiffen (Whiffen, D. H. Mol. Phys. 1963,6,223) to calculate hyperfine coupling constants from spin densities at two adjacent carbons needs to be modified to include a normalization constant. The modified equation does not allow a differentiation between the cyclic conjugated structure and the time-average of two "localized" structures.
The structures of organic radical cations, particularly their relationship to the structures of the corresponding diamagnetic precursors, are of significant interest and have attracted much attention in recent years.'" Some of the most interesting radical cations are those derived from hexadiene systems.622 These species are related to the putative mechanistic extremes of the Cope rearrangement, which may proceed via one of three pathways: (a) addition precedes cleavage (associative mechanism); (b) cleavage precedes addition (dissociative mechanism); (c) additionand cleavage occur in coordinatedfashion (concerted mechanism). Extensive and elegant studies, both experimental^^ and theoretical,29-30 support the concerted mechanism, although the dissociative pathway may not have a much higher barrier.27c In some cases, Cope rearrangements can be induced by photoinduced electron transfer.&'O For example, a deuterium labeled dicyclopentadienewas found to rearrange upon irradiation of chloranil? and a similarly labeled 2,5-diphenylhexadiene rearranges upon electron transfer to photoexcited 9,lO-dicyanoanthracene.10 The structureof the intermediateradical cations may be assigned on the basis of CIDNP and/or ESR results. Thus, CIDNP results observed during the electron-transfer reaction of dicyclopentadiene require that one of the bonds linking the two cyclopentadiene units has been cleaved; two carbons have been rehybridized from sp3 to sp2, creating the doubly allylic cation 1. This ion can be viewed as an entity in which two allyl moieties are linked to a four-carbon "spacer" (a-b-c-d). Model considerationsindicate that the termini of the allyl functions are separated by 3-4 A, clearly precluding a significant bonding interaction between themeG9 On the other hand, a structure of type 2 has been suggested for the parent hexadiene system; the assignment rests on ESR spectral data observed at cryogenic temperatures.Mz2
The assignment of the unique structure, 1, raises the question, whether the dissociative structure type is generally preferred for substituted hexadiene systems or whether the separation of the *Abstract published in Aduonce ACS Absrrucrs. November 15, 1993.
0022-365419312097- 13403$04.00/0
two allyl groups is caused by the four-carbon spacer to which the allylic termini are linked. We have examined various spacers that might reduce the separationof the two units and, thus, increase the interaction between their termini. For example, in radical cation, 3, the two allylic moieties are connected via a two-carbon link. For this species, semibullvalene is conveniently available as a potential precursor. Semibullvalene: A Cyclic Conjugated Radical Cation? Radical cation 3 is perhaps the most intriguing species in the family of intermediates discussed here. Model considerations suggest that the two allylic moieties of these ions may be separated by slightly more than 2 A. The proposed species raise the interesting question, whether cyclic conjugation can be a significant factor at nonbonding distances of this magnitude. In essence, to identify the structure of 3, one needs to differentiate between a cyclic conjugated structure, e.g., 3c, a localized structure, e.g., 3a or 3b, and the time-average of two "localized" structures, e.g., 3a and 3b.
The structure of the semibullvalene radical cation was pursued by both the CIDNP and ESR techniques; both methods furnished interesting results pertinent to its structure. The CIDNP spectrum (Figure 1) shows strong emission for the "bridge" protons Hc (attached to C1,Cs), weaker enhanced absorption for the nuclei HB, equilibrating between olefinic and cyclopropane positions (Hz, H4, He, and HE),and negligible polarizationsfor the olefinic protons HA(H3, H7). These results are equally compatible with two different structure types, bearing electron spin density either in two allylic carbons (Cz, C4, structure 3a; or Cb. CE,structure 3b) or a cyclic conjugated 5r electron system with identical spin densities in all four "corner" carbons (structure &).I* Strictly, the CIDNP results do not allow a differentiation between the limiting structures for the radical cation 3. The semibullvaleneradical cation was investigated also by ESR spectroscopy in halocarbon matrices at cryogenic temperatures. Williamsandco-workers13J4andR h o d d s found that two protons are stronglycoupled (A = 36.2 G; Hc);four others are interacting to a lesser degree (A = 8.1 G; HB); the coupling of the remaining 0 1993 American Chemical Society
13404 The Journal of Physical Chemistry, Vol. 97,No. 50, 1993
Roth and Lakkaraju
TABLE I: Bond Lengths, Nonbonding Distances, Bond Anglea, and Mhedral Angles of SemibullValem Radical Cation Bond Lengths (A) ~~~
bond
C" 1.521 1.491 1.548 1.390 1.378
1.So0 1SO0 1.547 1.382 1.382
Nonbonding Distances (A) bond cfi8
(23x7 Crcr C648
C*
C,
2.449 3.152 2.296 2.229
2.317 3.512 2.225 2.255
Bond Angles (deg)
angle C&&I crc344 c64&8
C,
C2.
108.8 111.4 107.9
101.8 109.4 109.4
Dihedral Angles (ded angle ~
cp
e
Figure 1. 'HCIDNPspectra (90 MHz)observedduringthephotoreaction of chloranil with semibullvalene (0.02 M each in acetonitrile-d3)during UV irradiation. The signals denoted A, B, and C represent, respectively,
the olefinic protons (attached to C3, C7), those equilibrating between olefinic and cyclopropane positions (H2, H4,Hs, and &), and the 'bridgehead" protons.
two protons (HA) is smaller than the line width (AHpp= 4 G). It is obvious that the same intermediate is responsible for the CIDNP data as well as the ESR results. The fact that four equivalent protons are found is incompatible with two localized structures (3a and 3b) separated by an appreciable barrier; it requires at least that the system undergo rapid electron exchange between the two allylic moieties on the EPR time scale. In fact, however, the spectrum was interpreted in terms of the cyclic conjugated structure (3c) with 5?r electrons in analogy to the previous assignment of a 5?r electron system to the barbaralane radicalcation.16 This assignment was basedon the large hyperfine coupling (hfc) of the bridgehead protons, which is characteristic for 8-IH nuclei in "flagpole" positions. For example, the endo protons of bicyclobutane cation have hfc = 77 G.31 These hfcs arise from the hyperconjugative interaction of a nucleus H1 with the 2p electron spin densities, ptj at the adjacent carbons, CtJ; the resulting hfc interaction was formulated by Whiffen as a function of p t ~the , dihedral angle, 0, between the Cl-HI bond and the 2p axes at Ct and C,; and the Heller-McConnell constant, 8 : 3 2
Ab-Initio Calculations on the SemibullvaleneRadical Cation We have attempted to elucidate the intriguing problem of the semibullvalene radical cation structure by ab-initio calculations for this species, both as a delocalized system, 3c (with imposed Cbsymmetry), and as a (localized) bifunctional species, 3a (with C, symmetry),and have examined the following: their geometries, especially the separation between the two allylic moieties, the flap angle, a, and the dihedral angles, 0, between the 2p axes at C2 and CB(Cd and c6) and the CI-H ( C r H ) bonds; the carbon spin densities; and the resulting hyperfine coupling parameters. Previously, restricted H F AM1 calculations have been carried
112.3 42.0
102.3 36.2
out for a localized as well as a delocalized semibullvaleneradical cation.33 However, only the total energies of these species were reported; neither geometries, nor hfcs, nor vibrational analyses were mentioned. The ab initio calculations34 reported here were carried out with the GAUSSIAN 88 series of electronicstructure programs.35 Molecular structures wereoptimized at theunrestricted HartreeFock level with the 6-31G* basis set (UHF/6-31G*//6-31G*); optimized C-C bond lengths, selected nonbonding distances, and some key angles are listed in Table I. Total energies including electron correlation contributions were obtained by single point calculations at the optimized geometries using Mdler-Plesset perturbation theory through second order (MP2/6-3 lG*//HF/ 6-31G*). In view of previous experience we expect this level of theory to be sufficient for elucidatingthe major structural features of this system.3We have previous performed calculations on various radical cations with unusual structures, including those derived from norbornadiene and q~adricyclane,'~ Dewar benzene" and prismane,3* bicyclobutane and b e n ~ v a l e n eand , ~ ~a series of methylsubstituted cyclopropanes.a These calculationsappear to provide reasonable geometries as well as spin densities, although no experimental data are available to compare directly with these results. Accordingly,we expect that the calculations on the radical cationic system 3 will provide reasonable values for the spin densities, p, at the key carbons, and for the dihedral angle, 0. More significantly, we have demonstrated in several systemsthat ab-initio calculations reproducepositive hfcs quite well. Positive splittings arise from hyperconjugative interactions between magnetic nuclei and the unpaired electron spin; they are proportional to the calculated Fermi contact terms (FCT) and are obtained simply by multiplicationwith a proportionality factor (hfc = 1600 FCT). For example, the positive hfcs calculated for several methyl-substitutedcyclopropaneradical cations reproduce the experimental values, assigned on the basis of ESR data,41#42 within 15%" The agreement is even better for rigid structures; thus, hfc = 76.9 G is calculated for the endo protons of bicyclobutane radical cation,39 compared with a measured value of 77.1 G.31 These results lead us to expect a reliable calculation for the.(positive) hfcs of the key protons H1,s. On the other hand, negative hfcs, which result from ?r,upolarization, are reproduced
Ab-Initio Study of Semibullvalene Radical Cation
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13405
TABLE II: Hyperfine CoupIing Constants (hfc) of Semibullvalene Radical Cation hfc (G) nucleus C* Cz, expt Hl,5 31.5 37.0 36.2 -36.5 -19.4 H2.4 ) (47.7 H6.8 -2.5 -19.4 H3 22.7 13.6
