QTAIM Investigation of the Electronic Structure and Large Raman Scattering Intensity of Bicyclo-[1.1.1]-pentane

Our previous studies of the variation of Raman scattering intensities in saturated hydrocarbons have identified a number of structural descriptors that correlate with calculated polarizability derivatives for particular bond displacements: ring strain, steric hindrance, and alignment and location of a C-H group within the molecular framework (e.g., endo-/exo-, axial/equatorial, in-plane/out-of-plane). The bridgehead C-H bond intensities in bicyclo-[1.1.1]-pentane appear to be extraordinarily large, given its size and structure. Molecular polarizability and derivatives are analyzed here for bicyclo-[1.1.1]-pentane and propane, with HF, MP2, CCSD, B3LYP, M06, and M062X levels of theory and the Dunning AVTZ basis set. Analyses of calculated electronic charge densities were performed with two implementations of QTAIM, including an origin-dependent method and an implementation with origin-independent atomic moments. Numerically accurate atomic partitioning of mean molecular polarizabilities is achievable with either; however, accurate partitioning of polarizability derivatives places stringent requirements on the numerical integration, more so for this highly strained bicyclic structure. QTAIM reveals that most of the polarizability (~90%) can be attributed to charge transfer between atomic basins. Calculated Raman intensities are in accord with our experimental data, notably in the prediction of large trace scattering intensities for stretching of the bridgehead CH in bicyclo-[1.1.1]-pentane and for the methyl in-plane C-H in propane. Density difference plots illustrate the effects of bond displacements on the electron densities and the resultant changes in polarizability. Stretching of the bridgehead C-H bond in bicyclo-[1.1.1]-pentane produces electron density changes that are similar to those encountered upon stretching the methyl in-plane C-H of propane.