The effect of nonorthogonality in the broken symmetry approach to magnetic coupling has been explicitly considered for the first time in Hartree−Fock and a variety of DFT methods. On the basis of the results for three different systems, representative of a variety of physical situations it is shown that the most often quoted trend concerning the much larger degree of delocalization of magnetic orbitals obtained from DFT, as opposed to Hartree−Fock, is not fully justified. A new and simple way to relate the overlap integral entering into the calculation and the spin density is proposed and tested in a variety of model systems.

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Ab initio calculations including correlation energy are reported on a series of halogen-substituted carbenes and silylenes: CH 2, CHF, CF 2, CHC1, CC12, CHBr, CBr2, Sill2, SiHF, SiF2, using the difference-dedicated configuration interaction method. All these compounds with the exception of CH 2 have singlet ground states. The singlet-triplet energy differences are in very good agreement with experiment when available, as well as with other high level calculations. The singlet-triplet separation is also determined in trifluoromethyl carbenes, CHCF3, CFCF3, CCICF 3 and CBrCF 3. The CF 3 substituent has little influence on the energy gap since CHCF 3 like CH 2 has a triplet ground state, with a gap of 11"1 kcal mo1-1, and CFCF~, CCICF 3 and CBrCF 3 have singlet ground states, like CHF, CHCI and CHBr, with gaps of -17.6, -5"4, and -3"5 kcal mo1-1.

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The exchange coupling of Ullman's nitroxide biradicals, bis[2,2'-( 1-oxy-3-oxido-4,4,5,5-tetramethyldihydro-lH-imidazolyl)] (1) and bis[2,2'-( l-oxy-4,4,5,5-tetramethyldihydro-1H-imidazolyl)] (2), has been determined by performing ab initio calculations followed by a specific configuration interaction on model compounds where the methyl groups have been substituted by hydrogen atoms, C1 and C2, respectively. The analysis of the dependence of the coupling on the conformation angle between each nitroxide moiety shows that even in the perpendicular structure the singlet state is found below the triplet. The calculated singlet-triplet gaps for the experimental value of the twist angle, -364 cm-l for C1 and -175 cm-' for C2, are in very good agreement with recent experimental results for 1 and 2.

Ab initio DDCI2 (difference-dedicated configuration interaction) calculations are performed on the exchange coupling constant of the doubly-bridged Ni(II) complexes [Ni(en)(2)Cl](2)(2+) and [Ni(terpy)(N(3))](2)(2+), which are modeled by substituting the external ligands with ammonia groups. The variational CI space is selected on the grounds of the effective Hamiltonian theory and includes all the second-order contributions to the difference between the lowest quintet, triplet, and singlet states. Both complexes are found to be ferromagnetic, with coupling constants of 1.8 and 21.1 cm(-1), in good agreement with the experiment. A transformation of the molecular orbitals is also proposed for large systems, enabling the molecular orbital set to be significantly truncated-as well as the file of two-electron integrals and the DDCI2 space-with no loss of efficiency.

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Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF 3 , K 2 NiF 4 , NiO, and La 2 CuO 4 . Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved. ͓S0163-1829͑97͒04634-1͔The proper and accurate description of magnetic interactions in systems with localized magnetic moments, i.e., ionic solids, is of importance not only from the point of view of basic knowledge but also to understand the electronic structure and magnetic behavior of superconductor parent compounds. 1 The experimental and theoretical study of the magnetic coupling in ionic solids is often based on the use of the Heisenberg Hamiltonian which may be written aswhere the ͗i, j͘ symbol means that the summation is restricted to nearest-neighbor i and j magnetic centers with total spin moment S. The question addressed in this work concerns whether J contains two-body interactions only or if it is better regarded as an effective two-body parameter containing collective effects from the whole solid. We must point out that existence of collective effects in J is claimed mainly from intuition and has not been theoretically or experimentally proven. Because ionic solids are extended systems, it is customary to investigate their electronic structure by using a solid-state approach, usually exploiting translational symmetry. Notice, that this approach cannot provide an answer to the above question because there is no way to separate the collective effects from the two-body interactions. From a purely ab initio, or first-principles, point of view of the theory of the electronic structure, these solid-state approaches are often based on modifications 2-6 of the local-density approach ͑LDA͒. Without these modifications the LDA fails to describe the antiferromagnetic order of many compounds such as NiO or La 2 CuO 4 . 7 More recently, the periodic HartreeFock, in its unrestricted or spin-polarized version, has been applied to a variety of antiferromagnetic systems with, on first sight, a rather good agreement with experiment. 8,9 An alternative approach, different albeit complimentary, is one based on the use of cluster models. [10][11][12][13][14][15][16][17][18] By construction, the cluster model permits one to investigate the importance of the collective effects. From a technical point of view, the main difference between periodic and local approaches lies in the way to estimate the instantaneous electron-electron interactions. Hence, while the former are constrained to the use of more or less approximate correlation ͑or exchangecorrelation͒ functionals, the latter permits the use of more accurate comput...