Spin-coupled calculations are performed for the lowest 3B1, 1A1 and 1B1 states of CH2. The orbital picture for the 1A1 state is very different from that from molecular-orbital theory. This has important consequences for the stereospecificity of the cycloaddition reaction with ethene to form cyclopropane, for which we consider two paths on the potential surface. Spin-coupled valence-bond (non-orthogonal CI) calculations are also reported for the 3B1 and 1A1 states. We use the same list of 202 spatial configurations for both states and obtain a singlet–triplet splitting of 12.11 kcal mol–1, which compares favourably with a recent full CI value (11.97 kcal mol–1) in the same basis set. The same list of structures with a more extended basis set gives a value of 9.6 kcal mol–1, which is in very good agreement with experiment. The spin-coupled valence bond approach provides a clear and coherent description of the low-lying states of methylene and of its addition reaction with ethene.