(98)00228-0 This phenomenon may be related to the fact that the gap between the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) tends to decrease when the size of the system increases, as long as the system does not present important bond-length alternation. In HF methods, the symmetry breaking takes place at smaller sizes than it does in DFT treatments. Large conjugated hydrocarbons with equal numbers of atoms of both colors, hence supposed to be singlet in their ground state, may exhibit spin instability of the mean-field descriptions, either Hartree-Fock (HF) or Kohn-Sham density functional theory (DFT). The singlet-to-triplet excitation energy is expected to be significant when the graph accepts a complete electron pairing on double bonds-in other words when one may write a Lewis or Kekulé formula. This rule claims that conjugated hydrocarbons presenting the same number of atoms of both colors are expected to be of singlet ground state. The spin polarization of the σ bonds plays in the same direction as the antiferromagnetic coupling between adjacent sites, and this rule is valid for non-planar geometries. Even disjoint diradicals such as tetra-methylene-ethylene (TME), which may be seen as two radicals connected by the nodes of their singly occupied Molecular Orbitals (MOs) (SOMOs) and presenting a small energy difference between the singlet and triplet states, obey the Ovchinnikov’s rule, thanks to the spin polarization of the other MOs. ![]() Up to now Ovchinnikov’s conclusion has never been contradicted. Guihèry, in Challenges in Computational Chemical Physics: Applications of Topological Methods in Molecular Chemistry, edited by R. It is possible to reach the same result for finite structures, whatever this ratio. Lieb has established the same result for periodic lattices from the Hubbard Hamiltonian, whatever the | t/ U| ratio (delocalization/electronic repulsion). These systems are usually seen as highly delocalized but it is perfectly possible to study their low-energy states from a magnetic approach. This demonstration was based on a magnetic description of the π electronic system. Ovchinnikov has formulated a general statement saying that in bipartite lattices, the spin multiplicity of the ground state is given by the difference between the numbers of atom of the two colors 1 1. Only the non-alternant hydrocarbons exhibit odd-membered rings. Alternant conjugated hydrocarbons are bipartite lattices, in the sense that one may give one of two colors to each carbon atom in such a way that the first neighbor atoms of an atom of one color are of the other color.
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