Two families of molecular descriptors are proposed, based on new functions of the molecule spectrum derived from any molecular matrix M(w), calculated by any weighting scheme w. The first class of molecular descriptors, denoted as SpAD(M,w), is defined in terms of the absolute deviations of the eigenvalues and is a generalization of the concept of graph energy proposed by I. Gutman [1]. The second class, denoted as SpMAD(M,w), is defined in terms of mean absolute deviations of the eigenvalues and, unlike the first class, is size-independent. Some simple QSPR models were calculated, showing an encouraging capability of these descriptors to model physico-chemical properties of compounds.