Two-dimensional hückel molecular orbital theory

The conventional Hückel molecular orbital (HMO) theory is extended to include hydrocarbons with sp-hybridized C atoms in addition to the sp²-hybridization. MOs are constructed as linear combinations of 2p-orbitals in two dimensions perpendicular to each other. The resulting two parts of the π system (viz. π′ and π″) are assumed to be independent. The total π-bond order is assumed to be obtained by the addition of contributions from π′ and π″. The two-dimensional HMO theory covers hydrocarbons with acetylenic (CC) bonds and cumulated CC bonds. The theory is applied to vinylacetylene, diacetylene, allene, butatriene and divinylacetylene. CC bond lengths calculated from the theoretical π-bond orders are compared with experimental data. Agreements between calculated and observed bond lengths within ±0.03 Å are found.