Graphical and color‐pairing symmetries

Symmetries are considered for a class of Hamiltonian models with one (spin‐free) orbital per site. The models include common types of Parisier‐Parr‐Pople and valence‐bond Hamiltonians, defined over a continuous range of parametrizations. The symmetries investigated are linear canonical transformations and include the common point‐group and alternancy symmetries. We find “graphical” symmetries extending the usual point‐group symmetries and novel “color‐pairing” symmetries which involve hybrids of point‐group–like and alternancy symmetries of relevance for certain heteroatomic species. The occurence of recolorpairing transformations relating the eigensolutions of models for different molecules is also noted.