| Molecular properties that are based upon Hermitian, one-electron, position-space projection operators have been developed. These projectors can partition either Hilbert or 3-dimensional space. In the latter, we have investigated various functions that define the atomic volume, as well as the hardness of the interatomic boundary. The local atomic spin properties S A that appear in the Heisenberg Hamiltonian were then defined using this partitioning. The quantities ⟨S A2⟩ and ⟨S A·SB⟩ are related in the single-determinant approximation to chemically relevant quantities such as the Wiberg-Mayer bond order and free valence. Moreover, these definitions have been extended to multi-determinant wave functions, where many properties remain undefined. The local spin quantities have been applied to wave functions that describe: (i) thermally- and photochemically-induced Bergman cyclization of organic enediynes as well as metalloenediynes; (ii) didehydrobenzenes... |
