Analysis of the inadequacies of some semi‐empirical MO methods as theories of structure and reactivity

Essential defects of present‐day semiempirical methods ( CNDO /2, CNDO /S, MINDO /3, MNDO ) can be identified on two levels. First, the formalism shared by nearly all these methods treats parametric expressions, supposed to refer to Löwdin orthogonalized orbitals, as transferable. At best, this idea is approximately valid for the β functions for strong bonds. Second, the expressions used for these approximately transferable functions are based on inadequate arguments. As a result, the errors in many terms of the energy expression amount to several electron volts. The mechanism of error compensation through the parametrization is investigated in detail and shown to be surprisingly flexible, at least for some combinations of errors. Some cases of systematic absence of compensation are identified, and for weak interactions, e.g., those responsible for the water dimer, the semiemperical expressions appear to be so irrelevant that a detailed analysis of the causes of their failure is no longer possible. Minimal requirements for a correct semiempirical approach are given in the MORBIT rules. The two‐center one‐electron integral β is to be replaced by a function introduced by Mulliken; an efficient approximation for this expression is proposed.