A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representingcovalent, ionic, and total bond indices are derived. The eigenstatesof these operators come in pairs, and can be consideredas bonding, anti-bonding and lone-pair orbitals. The form ofthese operators is derived by generalising the rule that thebond order be defined as the net number of bonding electronpairs. The percentage of covalency and ionicity of achemical bond may be obtained, and bond indices can alsobe defined between groups of atoms. The calculation of thebond indices depends only on the electron density operator,and certain projection operators used to represent each atomin the molecule. Bond indices are presented for a series offirst and second row hydrides and fluorides, hydrocarbons,a metal complex, a Diels–Alder reaction and a dissociativereaction. In general the agreement between the bond indicesis in accord with chemical intuition. The bond indices areshown to be stable to basis set expansion.