Electronic Substituent Effects in Bicyclo[1.1.1]pentane and [n]Staffane Derivatives: A Quantum Chemical Study Based on Structural Variation

The transmission of electronic substituent effects through one or more bicyclo[1.1.1]pentane units has been investigated by ascertaining how a variable substituent at a bridgehead position perturbs the geometry of a phenyl group at the opposite end of the molecule. We have analyzed the molecular structures of many bicyclo[1.1.1]pentane and [n]staffane derivatives of general formula Ph-[C(CH2)3C]n-X (n ) 1-5), as obtained from molecular orbital calculations at the HF/6-31G* and B3LYP/6-311++G** levels of theory. When n ) 1, the structural variation of the benzene ring is controlled primarily by the long-range polar effect of X, with significant contributions from electronegativity and π-transfer effects. The capability of the bicyclo[1.1.1]pentane framework to transmit these short-range effects originates from the rather high electron density inside the cage and the hyperconjugative interactions occurring between substituent and framework. A set of at least two bicyclo[1.1.1]pentane units appears to be necessary to remove most of the electronegativity and π-transfer effects. In higher [n]staffanes (n g 3), the very small variation of the benzene ring geometry is controlled entirely by the long-range polar effect of X. With charged groups and for n g 2, the potential energy of the ring deformation decreases linearly with n-3. In Ph-C(CH2)3C-X molecules, the relatively large deformation of the bicyclo[1.1.1]pentane cage is determined primarily by the electronegativity of X, similar to the electronegativity distortion of the benzene ring in Ph-X molecules. Transfer of π electrons from substituent to cage or vice versa also plays a role in determining the cage deformation.