a triply degenerate T2 state and an A1 state. The difference in energy between each ionized state and the ground state would be ionization energy, which yields two values in agreement with experimental results. Localized vs canonical molecular orbitals Bonding orbitals formed from hybrid atomic orbitals may be considered as localized molecular orbitals, which can be formed from the delocalized orbitals of molecular orbital theory by an appropriate mathematical transformation. For molecules in the ground state, this transformation of the orbitals leaves the total many-electron wave function unchanged. The hybrid orbital description of the ground state is, therefore equivalent to the delocalized orbital description for ground state total energy and electron density, as well as the molecular geometry that corresponds to the minimum total energy value. Two localized representations Molecules with multiple bonds or multiple lone pairs can have orbitals represented in terms of sigma and pi symmetry or equivalent orbitals. Different valence bond methods use either of the two representations, which have mathematically equivalent total many-electron wave functions and are related by a unitary transformation of the set of occupied molecular orbitals. For multiple bonds, the sigma-pi representation is the predominant one compared to the equivalent orbital (bent bond) representation. In contrast, for multiple lone pairs, most textbooks use the equivalent orbital representation. However, the sigma-pi representation is also used, such as by Weinhold and Landis within the context of natural bond orbitals, a localized orbital theory containing modernized analogs of classical (valence bond/Lewis structure) bonding pairs and lone pairs. For the hydrogen fluoride molecule, for example, two F lone pairs are essentially unhybridized p orbitals, while the other is an spx hybrid orbital. An analogous consideration applies to water (one O lone pair is in a pure p orbital, another is in an spx hybrid orbital). See also Crystal field theory Isovalent hybridisation Ligand field theory Linear combination of atomic orbitals MO diagrams VALBOND References External links Covalent Bonds and Molecular Structure Hybridisation flash movie Hybrid orbital 3D preview program in OpenGL Understanding Concepts: Molecular Orbitals General Chemistry tutorial on orbital hybridization Chemical bonding Molecular geometry Stereochemistry Quantum chemistry