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Resonance weights derived from the Natural Resonance Theory Ž . NRT , introduced in the preceding paper are used to calculate ‘‘natural bond order,’’ ‘‘natural atomic valency,’’ and other atomic and bond indices reflecting the resonance composition of the wave function. These indices are found to give Ž significantly better agreement with observed properties empirical valency, . bond lengths than do corresponding MO-based indices. A characteristic feature of the NRT treatment is the description of bond polarity by a ‘‘bond ionicity’’ Ž . index resonance-averaged NBO polarization ratio , which replaces the ‘‘covalent-ionic resonance’’ of Pauling-Wheland theory and explicity exhibits the complementary relationship of covalency and electrovalency that underlies empirical assignments of atomic valency. We present ab initio NRT applications Ž . to prototype saturated and unsaturated molecules methylamine, butadiene , Ž . Ž polar compounds fluoromethanes , and open-shell species: hydroxymethyl . radical to demonstrate the numerical stability, convergence, and chemical reasonableness of the NRT bond indices in comparison to other measures of valency and bond order in current usage. Q 1998 John Wiley & Sons, Inc. J Comput Chem 19: 610]627, 1998

Natural resonance theory: II. Natural bond order and valency