Orbitals, Walsh

The choice of degenerate orbitals is not unique it is also possible to construct Walsh orbitals for cyclohutane. These are precisely the 3E and 4EU pairs of 111.82. 

By now the reader will already have been alerted to an important geometrical consequence of the hyperconjugative stabilization of B. Bond 12 should shorten, due to a decreased electron density in the (12 antibonding) Walsh orbital. 

Conjugated chains, 14, 46 Correlation diagrams, 44, 50 Cyclobutadiene, 171 Cyclobutane, 47, 222 orbital ordering, 26 through-space interactions, 26 Walsh orbitals, 27 Cyclobutene, 200 Cyclohexane, 278 Cyclohexene (half-boat), 274 Cyclopen tadiene, 225 Cvclopen tadienone, 269 Cyclopentadienyl anion, 237 Cyclopentane, 254 Cyclopen ten e, 241 Cyclopropane, 41, 47, 153 construction of orbitals, 19, 22 Walsh orbitals, 22, 36, 37 Cyclopropanone, 48, 197 bond lengths, 38 Cyclopropen e, 49, 132 reactivity, 40... 

In the present case, the Walsh orbital will overlap with the k orbital of the carbonyl group more efficiently than the (3-o orbitals because of agreement of orbital symmetry and the efficient overlapping. This out-of-phase motif (13) is consistent with retardation of syn addition with respect to the cyclopropyl group, that is, anti preference. 

This notion is also snpported by the following experimental observations. Because substitution of a cyano gronp on the cyclopropane ring lowers the energy of the Walsh orbital of the cyclopropyl group, the resultant attennation of the interaction of the olefin orbital with the Walsh orbital, if this interaction is indispensable, would reduce the facial selectivity. However, substitution of a cyano gronp on the cyclopropyl group, as in ejco-cyano 59c and endo-cymo 59d, essentially does not modify the syn-preference in dihydroxylation and epoxidation, but even increases the syn preference (59c (98 2) and 59d (>99 <1)) in the case of dihydroxylation. 

Semi-empirical molecular orbital calculations have been carried out on the model phosphorane HaPiCHa. Besides the expected transfer of charge, the inclusion of the phosphorus 2>d orbitals showed a significant hyperconjugative interaction between the CHg orbitals and a 2>d orbital of appropriate symmetry on phosphorus. Calculations on cyclopropylidene-phosphorane revealed a similar interaction between the Walsh orbitals of the ring and an in-plane phosphorus 2>d orbital. 

Fig. 1. a) The highest occupied and lowest unoccupied Walsh orbitals of cyclopropane, b) Ground configuration (left) and excited configuration (right) of cyclopropane, and level shifts upon increase of a. 

In terms of MO theory the stabilization is described by a linear combination of a two-electron filled antisymmetric 3c-2e-Walsh orbital of the cyclopropane ring with the vacant p-orbital at the C +-carbon atom (Fig. 5). 

Fig. 5 Schematic representation of the linear combination of the filled antisymmetric Walsh orbital of a a-cyclopropyl ring and the vacant p2-orbital of the C + -carbon of a carbocation leading to delocalization of the positive charge in a 4c-2e MO.

More intriguing, however, is the effect on 7-anti-positioned carbon atoms, which are shifted downfield considerably. The values given for 252 (202), 253 (371), 254 (372), 255 (374), 256 (374), 257 (375), and 258 (376) in Scheme 62 are calculated by comparison with the corresponding parent compounds (nor-bomane, noibomene, adamantane, diamantane, and benzohomoadamantene, respectively). A plausible explanation for this effect was given by Christl and co-workers (203,204,377), who invoked an interaction between an unoccupied Walsh orbital and the HOMOs of the C(2)-C(3) and C(3)-C(4) bonds (259). 

Strong shielding of the 0=0 carbon atom in 280 by endo-cyclopropane annelation was reported by Kessler and co-workers (362) and rationalized in terms of an interaction between a Walsh orbital and the n-orbital of the carbonyl oxygen via the intervening C-C bonds (281) an alternative explanation—spatial interference with the rr c—o orbital (282)—was mentioned as well (362). The double bond in 283 is polarized (A = 17.9) when 283 is transformed into 284... 

Christl and Lang (390) noticed an upheld signal shift of about 10 ppm when they compared the methine carbon atoms in bicyclo[1.1.0]butane (287) (391) and octavalene (288). On the other hand, in benzvalene (289), the corresponding shielding is +48.3 (203), because in this molecule back-donation from the Walsh orbitals to the ir -orbital of the olefinic group (290) is conceivable. Such an interaction is not possible in 288, because the ir -orbital of the diene chromophore is of different symmetry (390). 

Scheme 17. Tetramethyleneethane radical cation 94+ formed from bicyclopropylidene (1) and bonding linear combinations of the Walsh orbitals for 1 [78-80]...

Theoretical calculations predict that the highest occupied Walsh orbital of the cyclopropene ring in 1 should stabilize a positive charge at C2, ° and this prediction was experimentally confirmed. Appearance energy measurements for the loss of Br from ionized 2-bromobenzocyclopropene (202 X = Br) suggest that the benzo-cyclopropen-2-ylium ion 291 is stabilized by more than 27.6 kcal/mol over the phenyl cation 292. Calculations (3-2IG ) give a stabilization energy of 23 and 22 kcal/mol of 291 over 292 and over the m-isomer 293, respectively. ... 

No discussion about strained-ring radical cations would be complete without the valence isomers quadricyclane (15 +) and norbornadiene, (16 +) 15 features two adjacent rigidly held cyclopropane rings, whereas 16 contains two ethene n systems well suited to probe through-space interactions.Molecular orbital considerations suggest the antisymmetric combination of the ethene n orbitals (16) or cyclopropane Walsh orbitals (15) as respective HOMOs of the two parent molecules. The radical ions have different state symmetries and their SOMOs have different orbital symmetries. 

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