A new method is introduced that provides a definitive analysis of the nature and the extent of the valence anti-bonding and Rydberg character of excited orbitals involved in excitations from core levels to unoccupied bound states. These excitations are observed in X-ray absorption and related spectroscopies. The new method depends on defining pure valence anti-bonding orbitals using, literally, a linear combination of atomic orbitals. Application to the O K-edge excited states of H2O is presented. This analysis is important since Rydberg and valence anti-bonding orbitals will behave differently when a molecule is placed in a condensed environment. (c) 2006 Elsevier B.V. All rights reserved.