A new X-ray diffraction study of the one-dimensional spin-Peierls compound α ′ -NaV2O5 reveals a centrosymmetric (Pmmn) crystal structure with one type of V site, contrary to the previously postulated non-centrosymmetric P21mn structure with two types of V sites (V +4 and V +5 ). Density functional calculations indicate that NaV2O5 is a quarter-filled ladder compound with the spins carried by V-O-V molecular orbitals on the rungs of the ladder. Estimates of the chargetransfer gap and the exchange coupling agree well with experiment and explain the insulating behavior of NaV2O5 and its magnetic properties. . A spin-Peierls system undergoes a lattice instability at T SP and for T < T SP the system dimerizes and a spin-gap opens. Here we propose that the spin-Peierls compound NaV 2 O 5 is at the same time a quarter-filled ladder system, in contrast to the previous notion which assumed NaV 2 O 5 to be made up of weakly coupled pairs of V +4 and V +5 chains [4,6]. Our proposition is based on a re-determination of the crystal structure of NaV 2 O 5 by X-ray diffraction and on density-functional calculations. Mapping of the density functional results on Hubbard and Heisenberg models yields values for the model parameters which explain readily the insulating behavior of NaV 2 O 5 and its the magnetic properties. Our results also show that NaV 2 O 5 and CaV 2 O 5 are isostructural and consequently establish CaV 2 O 5 as a half-filled ladder system.Crystal structure The crystal structure of α ′ -NaV 2 O 5 consists of double chains of edge-sharing distorted tetragonal VO 5 -pyramids running along the orthorhombic baxis, which are linked together via common corners of the pyramids to form sheets. These in turn are stacked

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~ ~~~~~~~The organometallic salt [Cp,Zr(N=C-CH,)

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