Electron Delocalization and Electrostatic Repulsion at the Origin of the Strong Spin Coupling in Mixed‐Valence Keggin Polyoxometalates: Ab Initio Calculations of the One‐ and Two‐Electron Processes

Abstract

We present here a general theoretical procedure to treat the problem of electron delocalization and magnetic interactions in high-nuclearity mixed valence clusters based on polyoxometalates. The main interactions between the delocalized electrons of mixed-valence polyoxometalate anions are extracted from valence spectroscopy ab initio calculations on embedded fragments. Electron transfer, magnetic coupling and exchange transfer parameters between nearest and next-nearest-neighbor metal ions, as well as the value of the electrostatic repulsion between pairs of metal ions are determined. These parameters are introduced in a model Hamiltonian that considers the whole anion. It thus provides macroscopic properties that should be compared with the experimental data. This method is applied to a two-electron-reduced polyoxowolframate Keggin anion. The results demonstrate that the electron transfer processes, combined with the Coulombic repulsion between the "extra" electrons, induce a strong antiferromagnetic coupling between the two delocalized spins providing a definite explanation of the diamagnetic properties of these high nuclearity mixed-valence clusters.

MVPACK: A package to calculate energy levels and magnetic properties of high nuclearity mixed valence clusters

“…This is a well known result for the 2e reduced polyoxoanion. 18,19,40,41 Present calculation shows that the spin pairing resulting in the diamagnetic ground state is rather common phenomenon in polyoxoanion species with different numbers of delocalized electrons. The case of four delocalized electrons represents an exception from this general trend because in this case the spin triplet state proves to be the ground one.…”

“…This result was initially attributed to a very strong antiferromagnetic coupling via a multiroute superexchange mechanism, 39 but more recently it was suggested [17][18][19] that the electron delocalization can stabilize the diamagnetic ground state and it was proved 18,19,40,41 (see also review 2 ) that a combination of Coulomb repulsion between the electrons and electron delocalization is an efficient mechanism of a spin pairing in the ground state. The cited works 18,19,40,41 dealt with the case of 2e-reduced polyoxoanion containing delocalized electronic pair. Here we present the calculations of the energy patterns for a series of polyoxoanions with Keggin structure containing different even numbers P 5 2, 4, 6, 8, 10, 12 of itinerant electrons.…”

“…In these calculations we use the set of parameters obtained from the ab initio study of the double reduced polyoxoanion with delocalized electronic pair. 40,41 The set of parameters includes the three one-electron transfer integrals t 5 2530 meV, t The energy patterns calculated with MVPACK are shown in Figure 14. One can see that for all even numbers P except P 5 4 the ground state proves to be diamagnetic.…”

Effect of on-site Coulomb repulsion termUon the band-gap states of the reduced rutile (110)TiO2surface

“…This procedure makes use of the effective Hamiltonian theory, and it has been previously used in the study of magnetic systems, as well as the evaluation of hopping integrals in mixed-valence systems. [29][30][31][32][33][34][35][36][37][38][39][40][41] A detailed description of the method can be found in Ref. 41, and a summary enlightening the most striking points will be provided here.…”

“…This strategy has been extensively used in the recent past, especially in the evaluation of magnetic coupling constants as well as the determination of hopping integrals in numerous systems. [29][30][31][32][33][34][35][36][37][38][39][40][41]46,48,49,61,62 The whole procedure can be summarized as follows. ͑1͒ A fragment of the bulk structure of TiO 2 has been chosen, containing two neighbor Ti centers, and the ten oxygen atoms around them, as shown in Fig.…”