Understanding Molecular Orbital Wave Functions in Terms of Resonance Structures Padeleimon Karafiloglw Faculty of Chemistry, Aristotelian University of Thessalonlki, P.O.B. 135. Thessaloniki-54006 Greece Gilles Ohanessian Laboratoire de Chimie Theorique, Unlversite de Paris-Sud, bat. 490, 91405 Orsay Cedex, France Most quantum mechanical studies of molecular structure and reactivity are currently carried out using delocalized molecular orbital (MO) wave functions: these are by far the easiest to ohtain. On the other hand, most qualitative ratio- nales in organic chemistry (with thenotable exception of the Woodward-Hoffmann rules) use resonance structures (RS), which have a local character. It is an unfortunate state of affairs that both approaches seem to he mutually exclusive, for a simple hridge exists between them (I). It is the purpose of this paper to present a pedagogical construction of this bridge, thereby allowing one togo from the usual delocalized MO wave function to a totally local one, which is a linear combination of Slater determinants involving atomic orbi- tals (AO) only. We may then take advantage of both, and avoid their drawbacks: MO's are easy to obtain, and RS's are easy to understand (2). Let us consider the textbook example of the Hz molecule. The simple MO-Slater determinant of HZ can be decom- posed as follows into AO-Slater determinants: where II. is the bonding MO and 4, and 42 are the two H- centered AO's. The first two determinants in eq 1 represent situations in which one electron is on HI and the other on Hz, that is, the neutral (or covalent) RS HI-Hz. The plus sign between the two determinants denotes a singlet spin cou- pling. The last two terms clearly are the ionic Hl-Hz+ and HlfH2- RSs, respectively. In molecules other than H?. the analoeous decomoosition of a larger MO-determinant a more complicated prohlem, solved auite sometime ago bv .Moffitt (1). However, both the originaiderivation and <he formulation of the result involve a highly specific jargon; in this paper, we present an induc- tive hut simple derivation of what we call "Moffitt's theor- em", which has proved easy to understand by students who then enjoy "translating" MO wave functions into more fa- miliar RSs. An Elementary Derlvatlon 01 Moffltt's Theorem In what follows, we will make use of two properties of determinants. The first is that interchanging any two col- umns of a determinant reverses its sign. The second, multi- linearity, means that a Slater determinant, written in the usual diagonal form, can be developed as if it were a simple product. ~ h u s , for a six-electron six-AOsystem with~O';@, and MO's$, = C,,@, (in the following, letter indices will be reserved for AO's, end number indices for MO's) Volume 68 Number 7 July 1991 583