An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in real space. Indeed, we show that the series convergence is exponential as a function of the number of annulled multipolar moments in the unit cell. The method proposed in this work reaches such an exponential convergence rate. Its efficiency is comparable to the Ewald's method, however unlike the latter, it uses only simple algebraic functions.

We used quantum chemical ab initio methods to determine the effective parameters of Hubbard and t-J models for the Na(x)CoO(2) compounds (x = 0 and 0.5). As for the superconducting compound we found the a(1g) cobalt orbitals above the e'(g) ones by a few hundreds of meV due to the e'(g)-e(g) hybridization of the cobalt 3d orbitals. The correlation strength was found to increase with the sodium content x, whereas the in-plane AFM coupling decreases. The less correlated system was found to be the pure CoO(2), however it is still strongly correlated and very close to the Mott transition. Indeed we found U/t ∼ 15, which is the critical value for the Mott transition in a triangular lattice. Finally, we found the magnetic exchanges in the CoO(2) layers to be strongly dependent on the weak local structural distortions.

In this paper, we report on the magnetic properties of Ba 2 CoS 3 , a spin-chain compound recently found to be the first Co 2+ containing one-dimensional sulphide to show metallic-like conductivity and negative magnetoresistance. We carried out an in-depth experimental investigation of the local structure of the cobalt atoms, and ab-initio calculations of the resulting electronic configuration of Co 2+ . From theoretical considerations, the intra-chain coupling was predicted to be antiferromagnetic. Experimentally, several estimates of this magnetic coupling were derived by analysing the temperature dependence of the magnetic susceptibility. Magnetic and heat capacity measurements also provided evidence of a threedimensional antiferromagnetic ordering, a feature indicative of a noticeable inter-chain coupling in this quasi-1D system.We confirmed that Ba 2 CoS 3 is isostructural with Ba 2 FeS 34 as well as Ba 2 ZnS 3 ,7 , 13 K 2 CuCl 3 , , Cs 2 AgCl 3 , Cs 2 AgI 3 , (NH 4 ) 2 CuBr 3 and CuPbBiS 3 . 14 The unit cell is orthorhombic and the cell parameters are a = 12.000(1) Å, b = 12.470(1) Å and c = 4.205(2) Å. The Ba 2+ cations occupy two distinct crystallographic sites, both coordinated by S 2in a prismatic fashion. One Ba 2+ is surrounded by six S 2ions at corners of a trigonal prism and an additional S 2is approximately centred above one rectangular face. Seven S 2ions surround the other Ba 2+ forming a distorted trigonal prism with one face capped. Co 2+ is tetrahedrally coordinated by S 2and neighbouring Co-S tetrahedra are connected via corners, forming infinite chains. The Co-S tetrahedra are distorted, as the two Co-S bridging bonds are stretched along the chain direction. Those bonds are 2.427(2) Å, which is significantly longer than the two terminal Co-S bonds, 2.330(3) Å and 2.317(3) Å. The bonding angles of S-Co-S deviate from 109.5º by up to several degrees. A similar tetrahedral distortion is also observed in Ba 2 ZnS 3 .7 , 13The distance between Co 2+ cations within each chain (intra-chain) is 4.205(1) Å, whereas the distances between Co 2+ cations in two neighbouring chains (inter-chain) are 6.153(3) Å and 6.582(3) Å. Neighbouring chains of Co-S tetrahedra are inter-layered by Ba-S blocks. This confers one-dimensional character to the Co-S chains (Figure 1).4