@article{a1295b8303a447968ea604bc31d4007a,
title = "Electronic structure of high-nuclearity mixed-valence clusters",
abstract = "A general method is suggested for consideration of the electronic problem of high-nuclearity mixed-valence systems containing delocalized electronic pairs. A new approach based on the site symmetry concept with the electronic pairs is developed, and the magnetic properties of cluster metal oxides (heteropoly-blues) involving 12 and 18 metal sites are considered.",
author = "Borras-Almenar, {J. J.} and Clemente, {J. M.} and E. Coronado and R. Georges and Tsukerblat, {B. S.}",
note = "Funding Information: about 7 A). On the other hand, the fact that two adjacent octahedral sites share edges or corners, restrict the number of transfer processes to two: t (transfer through corners) and 1{\textquoteright} (transfer through edges). These transfer processes split the ground level only through the coupling with the excited states. When both t and t{\textquoteright} are non vanishing, the ground Ievel splits into four different levels ({\textquoteleft}A ,, 3Tz, IT* and [{\textquoteleft}E, 3T,D, as shown in Fig. 2(a). The ground state can be either the singlet IA, (P/t > 0) or the degerate level formed by the multiplets [{\textquoteleft}E and 3T1], (t/t < 0). The splitting scheme is not symmetric with respect to a sign change-of the f/t ratio. Indeed, its amplitude increases -& this ratio increases from 0 to I, and remains nearly constant for larger values. The behavior is rather similar for negative r{\textquoteright}/t, but with smaller amplitudes. With respect to the double-transfer processes we have found that only one process is able to split the ground group of levels. This combines the two types of single-electron transfers (actually it is proportional to the product t, t{\textquoteright}). If the associated P parameter is negative, the {\textquoteleft}A, singlet is stabilized, whereas the [{\textquoteleft}E, 3T,] mixture is stabilized if P is positive (Fig. 2b). The above discussion shows that in these mixed-valence clusters electron delocalization is able to stabilize a singlet ground spin state when both f and t{\textquoteright} have the same sign, or when P is negative. This last condition involves different signs for t and t{\textquoteright}, thus indicating that the two kinds of electronic transfer processes have opposite (competing) effects on the splitting of the levels. Although it is very difficult to determine in the present case which of the two processes is the leading one,the important conclusion is that these processes are operative even when the two moving electrons are widely separated in the structure in order to minimize the Coulomb repulsions. This makes completely irrelevant the possibility of spin pairing via a super~xchange pathway which involves the presence of strong antiferromagnetic interactions, In the previously examined system it remains possible, due to the simplifying assumptions, to list the various states belonging to each irreducible representation of the complete symmetry group (spin space and molecular symmetries), and to build the corresponding reduced hamiltonian matrices. For larger molecules, or for larger spins carried by the metals, or for larger moving electron numbers, etc., the problem becomes cumbersome and really intractable by Sand. Nevertheless, the basic processes are unchanged; they are merely used an exceedingly large number of times, As a consequence it was appealing to build a program able to organize and perform all the required elementary operations. Such a program has been developed. It allows us to treat any kind of molecular symmetry: it requires to be furnished with the corresponding multiplication table and irreducible representation basis. The amplitude of the localized spins, as well as their number and that of the moving electrons, are only limited by the available computer capacity. Any two-function transfer integral, as well as four-function Coulomb term, may be included in the computation. This program has been applied successfully to a four-site square molecule with arbitrary localized spin values and two moving electrons. Acknowledgements: This work was supported by the DGICYT (Grant PB91-0652 and sabbatical grant to BST) and the European Union (Network on Magnetic Molecular Materials and post-doctoral grant to JJBA). JMC thanks the Generalitat de Valencia for a pre-doctoral grant.",
year = "1995",
month = jan,
day = "1",
doi = "10.1016/0304-8853(94)01077-3",
language = "English",
volume = "140-144",
pages = "197--198",
journal = "Journal of Magnetism and Magnetic Materials",
issn = "0304-8853",
publisher = "Elsevier B.V.",
number = "PART 1",
}