The treatment of the spin coupling in the bonding of NO to the Ni-doped MgO (100) surface

The results are reported of density functional theory (DFT) and explicitly correlated wave-function (CASSCF and CASPT2) calculations on the bonding of NO with the Ni-doped MgO(100) surface. The surface is represented by means of a cluster of ions embedded in point charges. A comparison is made between unrestricted (spin polarized) and spin restricted approaches. While the geometry of the surface complex is described in quite an accurate way by a spin unrestricted DFT approach, e.g., using the B3LYP functional, the spin distribution does not correspond to that of the real physical situation. In fact, the spin polarized DFT treatment shows three unpaired electrons, two with spin up and one with spin down, while EPR experiments show clearly the existence of a single spin localized on an Ni 3d shell. A spin restricted B3LYP treatment, on the other hand, gives a correct spin distribution and geometry but fails in reproducing the adsorption energy. Other exchange-correlation functionals behave in a similar or even worse way. The CASPT2 results, by contrast, are in substantial agreement with the experiment, showing the importance of treating on the same footing the spin and electron correlation as well as the multi-configuration character of the wavefunction.     

Extension of the Virasoro and Neveu-Schwarz Algebras and Generalized Sturm-Liouville Operators

We consider the universal central extension of the Lie algebra Vect(S ¹) C(S ¹). The coadjoint representation of thisLie algebra has a natural geometric interpretation by matrix analogues ofthe Sturm –Liouville operators. This approach leads to new Liesuperalgebras generalizing the well-known Neveu –Schwarz algebra.