C8H8: A density functional theory study of molecular geometries introducing the localised bond density

In this paper we use density functional theory with all the common exchange-correlation functionals to investigate the structures of three isomers of C8H8 found in F. A. Cotton's text, barrelene, cyclooctatetraene, tetramethylenecyclobutane and also ethane and ethene. All calculations were performed with TZ2P basis sets and large quadrature. The results are compared with experiment and those obtained with Hartree-Fock theory. Delocalisation in the three molecules is discussed. A localised bond density is introduced to explain the transferability of the trends in the predictions of the functionals between different molecules. Three-parameter adiabatic connection functionals are examined and their usefulness in geometry prediction questioned. Finally a physical picture of the correlation as modelled by density functional theory is presented and used to explain trends in the overestimation or underestimation of bond lengths.