The conditions required for the existence of a stable bond-stretched singlet isomer of hetero derivatives of bicyclo[2.1.0]pentane (which is a cyclopentane-1,3-diyl derivative) are discussed. Such species are non-Lewis systems with a ruptured C-C bond (formally diradicals), in which two electrons occupy the nonbonding orbital. A high-level calculation shows that in contrast with the carbon substituted compounds, in which the open form is a transition state between two classical-bonded closed bicyclic forms, in the heterosubstituted molecules, the open form is calculated to be a stable minimum. The ionization potentials of the open forms are considerably lower than those of their bicyclic isomers and also of regular organic radicals/diradicals. Nitrogen atoms are found to be more effective than oxygen or sulfur in stabilizing the open isomer. In this case, the open isomer is calculated to be a little more stable than the bicyclic compound, and a barrier of approximately 40 kcal/mol is computed for the ring closing reaction. Thus, the open isomer is both thermodynamically and kinetically stable. This result rationalizes some experimental observations that indicated the existence of non-Lewis singlet species.