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, Annexe A Expression formelle d'un élément de matrice
9)) comment s'exprime un élément de matrice en fonction d'un nombre restreint d'intégrales à deux centres standards. Nous avons pris une fonction d de symétrie drz-rr. L'influence du champ cristallin; traité en perturbation ,
9) a pour expression formelle: r/(e, e) : (ôY,_n lïlôy"_u,> = eyd + C3d,"z-oz -v{ (za"'-n'$\l3d ,
r, '' I v#o + I ertn' (1d,, -u, 6) I yM (r) 13d ,
Expression formelle d'un éIément de matrice ,
Nous regroupons toutes les intégrales à deux centres qui interviennent comme des coefficients que l'on met en facteur pour une même dépendance en X, Y et Z. Pour alléger l'écriture nous adoptons les notations suivantes S(9, 9) = f rit, Cette expression fait intervenir des intégrales à deux centres de type recouvrement Isikn' (ld',-n (r)lvM(r)l3d, p.2 ,
, On se sert de la relation (A.1) de Slater-Koster pour réduire le nombre d'intégrales à deux centres
,
, Pour ne pas alourdir les calculs et par souci de clarté nous nous limitons à la contribution provenânt des intégrales à deux centres de type recouvrement, les contributions des autres types d'intégrales étant obtenue de façon tout à fait similaire
-sr(r)l3d,r-rr(r -R")) [mitée aux six ,