AbstractsFollowing Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh-Ritz method in thereplacement of the usual kinetic energy operators T ( p ) with operators T ( p ) = T ( p ) + I ( p ) , where I(p) generates contributions from surfaces of nonsmooth behavior. If one uses the VT . VV way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of VT and the change of T across surfaces of discontinuity. Various calculations are carried out for the hydrogen molecule-ion and the hydrogen molecule. It is shown that a6 initio calculations on molecules can be carried out quite generally with a basis of atomic orbitals exactly obeying the zero-differential overlap (ZDO) condition, and a firm basis is thereby provided for theories of molecular electronic structure invoking the ZOO approximation. It is demonstrated that a valence bond theory employing orbitals exactly obeying ZDO can provide an adequate account of chemical bonding, and several suggestions are made regarding molecular orbital methods. Si la forme V q . VV est utiliste, il faut aussi tenir compte de certaines integrales de surface.Divers calculs ont Ctt faits pour l'ion de la molicule d'hydrogkne et la molecule d'hydrogkne. II est demontrt que des calculs de type ab initio peuvent $tre effectuts d'une faGon gtnirale avec un jeu de base d'orbitales atomiques, qui satisfont exactement la condition de recouvrement difftrentiel zero, ce qui fourmit une base solide pour les thtories de la structure electronique moleculaire, qui se fondent sur I'approximation ZDO. Une theorie de type mtsomtrie avec des orbitales satisfaisant exactement I'approximation zDO peut fournir une description adequate de la liaison chimique. Verschiedene Berechnungen werden fur das Wasserstoffmolekulion und das Wasserstoffmolekul ausgefuhrt. Es wird gezeigt, dass ab-initio-Berechnungen fur Molekule ganz allgemein gemacht werden konnen mit einem Atomorbitalbasissatz, der exakt der Bedingung "Differentialuberlappung Null" (ZDO) genugt. Es wird weiter gezeigt, dass eine Valenzbindungsstheorie, die solche Orbitale verwendet, die exakt der zDo-Bedingung genugen, eine angemessene Beschreibung der chemischen Bindung geben kann.