X.alpha.-SW calculations of the electronic structure and magnetic properties of weakly coupled transition-metal clusters. The [Cu2Cl6]2- dimers.

The self consistent field multiple scattering Xa model has been used to calculate the electronic structure and the magnetic coupling constant, J , of planar and pseudotetrahedral [ C U ~ C I ~ ] ~ complexes with the aim of exploiting the actual possibilities of the model to describe the spectral (electronic and EPR) and magnetic properties of transition-metal polynuclear complexes. The observed variation of J with the degree of tetrahedral distortion has been quantitatively reproduced. The 19 000-cm-' feature characteristic of the electronic spectra of hexachlorodicuprate(l1) complexes is computed in the present calculations as a chlorine-to-metal charge transfer. The exchange interactions between transition-metal ions in orbitally nondegenerate states have been extensively studied in oligonuclear and polynuclear c~mplexes . l -~ These interactions generate manifolds of closely spaced levels which give the molecule unusual magnetic properties and have attracted the interest of both theoreticians and experimentalists. Two types of interactions can occur. To the first type belong the magnetic interactions which involve the ground states of the ions in the cluster. These are usually the strongest ones and isotropic in space. To the second type belong the interactions involving the excited states of the ions. These are usually less than I cm-I and highly anisotropic. A number of experimental techniques, ranging from the measurement of the temperature dependence of magnetic susceptibility to optical spectroscopy and magnetic resonance techniques, have been employed to measure also very weak interactions involving both the ground and the excited electronic Many studies have been devoted to the correlation of the isotopic exchange interaction with the electronic structure and geometry of the c o m p l e x e ~ . ~ The effect of this interaction on the energy levels of the cluster is generally represented by using a spin Hamiltonian approach through the operator where the sum runs all the neighboring paramagnetic metal atoms with total spin S,, and Jab is the exchange coupling constant between atoms a and b, which is evaluated experimentally. The Jab values are commonly related to the electronic structure of the polynuclear molecule by using semiempirical methods based on the Anderson theory of superexchangelo*" or using orbital models which relate the Jab values to overlap and energy differences between molecular orbitals evaluated within Ligand Field1* or extended Huckel formali~ms.l~'~ The use of these models allowed the rationahation of the magnetic properties of series of structurally related complexes, but they did not give any quantitative estimate of the S s. The actual calculation of the J a b values with more rigorous M O methods is hampered by the necessity of computing energy differences of the order of 10'-102 cm-l which are largely affected by electron correlation. In order to overcome this problem, whose solution requires extensive configuration interactions, a perturbation approach has recently been suggested to calculate Jab with an a b initio approach. Calculations have been performed on copper(l1) acetate,I6 oxalate," and di-pchloro bridged1* dimers. The agreement between the experimental and the computed J values was generally satisfactory. By using a b initio models, however, it is not a simple task to compute other physical observables such as electronic transitions and EPR parameters, which *Address correspondence to this author at the Institute per lo Studio della Stereochimica ed Energetica dei Composti di Coordinazione del C.N.R. 0002-7863/86/1508-5763$0l .SO10 constitute a severe test of the applicability of the model to the description of the electronic structure of transition metal clusters. A more approximate method than a b initio but still retaining enough flexibility in the radial wave functions is needed in order to make the problem computationally tractable. In recent years density functional methods have been shown to give an accurate description of the properties of open-shell transition-metal c o m p l e ~ e s . ' ~ In particular the Slater-Johnson Xa-SW has been applied with some success to calculate the electronic structure of several transition-metal complexes.22-2x ( I ) Martin, R. L. In New Pathways in Inorganic Chemistry; Ebsworth, E. A. V., Maddock, A. G.; Sharpe, A. G., Eds.; Cambridge University Press: 1968. ( 2 ) Hodgson, D. J . Progr. Inorg. Chem. 1975, 19, 173. (3) Ginsberg, A. P. Inorg. Chim. Acta, Re[. 1971, 5, 45. (4) Kokoszka, G. F.; Gordon, G. I n Transition Meral Chemistry; Carlin, R. L., Ed.; Marcel Dekker: New York, 1969; Vol. 5, p 181. ( 5 ) Carlin, R. L.: Duyneveldt, A. J . Magnetic Properties o/ Transition Metal Compounds; Springer-Verlag: New York, 1977. ( 6 ) O'Connor, C. J . Progr. Inorg. Chem. 1982, 29, 203. (7) Day, P. Acc. Chem. Res. 1979, 12, 236. ( 8 ) Gatteschi, D. In The Coordination Chemistry oJ Metalloenzynies; Bertioi, I., Drago, R . S., Luchinat, C., Eds.: D. Reidel: Dordrecht, 1983: p 215. (9) Magneto Structural Correlations in Exchange Coupled Sysfems; Willett, R. D., Gatteschi, D., Kahn, O., Eds.; D. Reidel: Dordrecht, 1985. ( I O ) Anderson, P. W. Phys. Rec. 1959, 115, 2. ( 1 1 ) Anderson, P. W. In Magnetism; Rado, G. T.. Suhl, E. H., Eds.; (12) Bencini, A.; Gatteschi, D. Inorg. Chim. Acta 1978, 31, 1 I . (13) Hay, P. J . ; Thibeault, J . C.; Hoffman, R. J . Ant. Chem. Soc. 1975, (14) Kahn, 0.; Briat, B. J . Chem. Soc., Faraday Trans. 2 1976, 72, 268. (15) Kahn, 0.; Briat, B. J . Chem. Soc., Faraday Trans. 2 1976, 72, 1441. (16) De Loth, P.; Cassoux, P.; Daudey, J. P.; Malrieu, J . P. J . A m . Chem (17) Chariot, M. F.; Verdaguer, M.; Journaux, Y . ; De Loth, P.; Daudey. (18) Bencini, A.; Daudey, J . P.; Gatteschi. D., to be published. (19) Computational Methods f o r Large Molecules and Localized States in Solids; Herman, F., McLean, A. D., and Nesbet, R. K., Eds.; Plenum: New York, 1979. Academic Press: 1963.