Bounds on molecular properties of π systems: first-order properties

Wederive upper and lower bounds to first-order properties in the H¨uckel model: π charge, bond order, bond number, and matrices of higher spectral moments. Bounds that depend on the electronic configuration, and on the molecular graph alone are derived. A ladder of relations between higher and lower spectral moments leads to bounds via the Cauchy-Schwarz theorem. The old square-root degree bound on bond number implicit in the work of Coulson, Moffitt and Longuet-Higgins is sharpened. Key to this development is the distinction between core and core-forbidden vertices of a graph.