By R. K. Nesbet, R. Colle (auth.)

These volumes acquire thirty-eight chosen papers from the clinical contributions provided on the Fourth ecu Workshop on Quantum structures in Chemistry and Physics (QSCP-IV), held in Marly-le-Roi (France) in April 22-27, 1999, a complete ofone hundred and fifteen scientists attended the workshop, ninety nine from Europe and sixteen from the remainder ofthe global. They mentioned the cutting-edge, new tendencies, and destiny evolution of the equipment and functions. The workshop used to be held within the outdated city of Marly-le-Roi, which lies to the West of Paris among the ancient centres of Saint-Germain-en-Laye and Versailles. members have been housed on the nationwide adolescence Institute, the place over sixty lectures got by means of l- ding contributors ofthe clinical neighborhood; furthermore, over sixty posters have been awarded in very lively classes. we're thankful to the oral audio system and to the poster p- senters for making the workshop such an stimulating adventure. The social programme used to be additionally memorable - and notjust for the last ceremonial dinner, which used to be held on the French Senate apartment. we're certain that members will lengthy have in mind their stopover at to the 'Musée des Antiquités Nationales': created by means of Napoleon III on the birthplace ofLouis XIV, this museum boasts one ofthe international most interesting collections ofarcheological artifacts. The Marly-le-Roi workshop the structure validated on the 3 past conferences, geared up through Prof.

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15] (Ec); b) long dashed line: calculated up to second order in full space (E(2)); c) short dashed line: calculated up to second order in the space of orbitals with negative energies (E (2) (ε < 0)); d) dotted line: calculated with a configuration interaction in 1s,2s,2p subspace (Ec, q ) ; e) dashed dotted line: calculated up to second order in 1s,2s,2p subspace (Eq(2)) . CORRELATION ENERGY CONTRIBUTIONS 37 lations assuming that one can define a local gap (|∇ n|/n)2 (where n is the electron density of the system considered) which asymptotically is equal to the ionization potential [28].

DELCHEV ET AL. are not linearly independent. fR ) that produce linearly dependent sets, for which the Grammian is → → → equal to zero: (26) and The groups reduced in this manner are mutual isomor R → R Let us fix a normalized set of R linearly independent orbitals {ϕi (x)} i=1 ∈L1 (we restore the spin variables in the notation). The manifold of all orbital sets - Eqn (25) - forms an orbit: {ψi }i=R 1 induced by the operators (27) R where {ϕi(x)} i= 1 is the orbit-generating set. For this orbit ∂[{ϕi}Ri=1 ] ≡ ∂ϕR , holds the inclusion relation Hence ∂Rϕ is that manifold in L 1 which consists R induced by the eleof all sets of linearly independent orbitals {Ψi([fi (r)];x)}i=1 ments of the group Let R = N and (28) → N N be the N-particle product for a chosen spin-orbital set {ϕi(x)} i=1 ∈ L 1 Antisymmetrizing the expression (28) yields the corresponding Slater determinant: (29) where AN is the antisymmetrizer, LN the antisymmetric N-particle Hilbert space, and SN the subclass of single Slater determinants in LN .

Dobson, J. F. ) Nalewajski, R. Springer-Verlag, Heidelberg, vol. 181. p. 81 (1996). Casida, M. , in Recent advances in the density functional methods, (Recent Advances in Computational Chemistry) (ed) Chong, D. 155 (1996); Casida, M. , Jamorski, Casida, K. C. and Salahub, D. , J. Chem. Phys. 108, 5134 (1998). Harbola, M. K. , Phys. Rev. Lett. 182. 1 (1996). Sen, K. , Chem. Phys. Lett. and Deb, B. , Proc. Indian Acad. Sci. 106, 1321 (1994); J. Mol. Struc. Theochem 361, 33 (1996); J. Chem. Phys.