Magnetic exchange interactions in LiV2O5

V₂O₅ is a van der Waals bonded layered oxide with a unique structure exhibiting a mixture of 1D and 2D properties. Intercalation with Li in the van der Waals gap results in the formation of magnetic moments and a variety of interesting magnetic phenomena. A key question is whether the doping by 1 electron per Li results in charge disproportionation of V⁴⁺ an V⁵⁺ or in a magnetic moment residing in a molecular type state related to the V-O-V rungs in this ladder compound and how this affects the magnetic exchange interactions. Here we use quasiparticle self-consistent (QS) GW calculations to study the electronic band structure of both a charge disproportionationed P_{2_1mn} structure and a non-disproportionated P_mmn based structure both with ferromagnetic and antiferromagnetic ordering along the zig-zag chain direction. We use the transverse susceptibility response in a rigid spin per sphere averaged model to extract Heisenberg-like exchange directions and the corresponding mean field transition temperatures. The antiferromagnetic ordering along the chains is obtained in both cases but the nearest neighbor exchange interactions are different and in the disproportionated case are more isolated 1D like in nature whereas frustration between neighboring chains occurs in the other case.