Comparing momenta and π-electron energy of benzenoid molecules

Let G be a graph associated with the hexagonal system of a benzenoid hydrocarbon. Let λ1⩽⋯⩽λn be the set of eigenvalues of the adjacency matrix of G and consider the momenta Mk=∑i=1nλik for k even. We show the lower bound Mq2(MrMs)-1/2⩽Eπ(G) for the total π-electron energy of G, where q,r,s are even integers with 4q=r+s+2. Particular cases of this bound improve the well-known McClelland's inequalities.