The atomic orbitals of the topological atom

The effective atomic orbitals have been realized in the framework of Bader’s atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure

Spin-coupled description of aromaticity in the retro Diels−Alder reaction of norbornene

The electronic rearrangements along the lowest-energy path for the gas-phase retro Diels−Alder reaction of norbornene are monitored using spin-coupled theory. We find that the most dramatic changes to the electronic structure occur in a relatively narrow interval in which the system passes through a geometry at which it can be considered to be significantly aromatic. We provide an estimate of the vertical resonance energy. Our results are consistent with the anticipated synchronous “aromatic” nature of this reaction, but we find that the key changes occur a little before the actual transition state is reached