Abstract Upper and lower bounds for the total π‐electron energy of conjugated hydrocarbons are found in terms of the number of carbon atoms, number of carboncarbon bonds, and the determinant of the adjacency matrix of the molecular graph. From these results and the application of some theorems concerning inequalities, we have been able to express those bounds in terms of spectral moments, up to the fourth. In the particular case of benzenoids, the bounds can be expressed solely in terms of the number of vertices and edges of the graph. It is shown that the upper bounds found are better than those of McClelland and those recently reported by Koolen et al. (Chem Phys Lett 2000, 320, 213). © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002