AbstractsThe explicit forms of the spin density matrix variations which are responsible for the external instability in the restricted Hartree-Fock (RHF) method are found. The R H F open shell instability matrix which guarantees the distorted wave function to belong to the same space as the initial one is derived for arbitrary spin.On prtsente des formes explicites des variations de la matrice densit6 de spin, auxquelles sont dues I'instabilit6 externe dans la m6thode Hartree-Fock restreinte (RHF). La matrice d'instabilit6 dans le proc6dt R t i F i couches ouvertes, qui garantit que la fonction d'onde dtformte appartient au meme espace que la fonction initiale, est obtenue pour un spin arbitraire.Die fur die aussere lnstabilitat in der beschrankten Hartree-Fock Methode (RHF) verantwortlichen expliziten Formen fur die Variationen in der Spindichtematrix werden vorgelegt. Die RHF-tnstabilitatsmatrix im Falle mit offenen Schalen, die garantiert, dass die verzerrte Wellenfunktion demselben Raum als die ursprungliche Funktion gehort, wird fur willkiirliche Spins hergeleitet.

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Different methods of averaging of energy over the states of electronic configurations yN (nr = I , 2, 3 and N = 1, 2 , . . . , 2n, -1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (vcc) in energy functionals for various states as well as for average values of energy are presented.It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations tN (N = 2-4) and e z there exist states for which vcc are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such "non-Roothaan" terms and peculiarities of its calculation by the restricted Hartree-Fock method are discussed.

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AbstractsAll the second-order density matrix spin components for the spin-extended HartreeFock method are obtained. The coefficients in the final formulae are only w s M , wsMfl, o,l(f*2 , where o,M are the weights of pure states of spin s in the initial unprojected determinant with spin projection M . The eigenvalue problem for the best electron density natural orbitals in the spin-extended method is formulated. All the second-order transition density matrix spin components between pure spin basis functions built of orthogonal orbitals and distinguished by different core choice are also found. This basis may be used on GI calculations.Toutes les composantes de spin pour la matrice densitt du second ordre ont t t t ohtenues dans la gtntralisation du point de vue du spin de la mtthode Hartree-Fock. Les formules finale ne contiennent que O,M , w , M *~ I , w s~+ 2 , oh U,M sont les poids des ttats pures avec spin s dans le dtterminant initial nonprojett avec la projection de spin M . Pour les orbitales naturelles on a formult le problkme stculaire de la mtthode gtntraliske. De m&me toutes les composantes de spin pour les matrices densitt de transition de second ordre ont t t t trouvtes entre les fonctions de spin pures se formtes par des orbitales orthogonales et se distinguant par les choix difftrents du coeur.