Modeling the Electronic Behavior of $\mathit{\gamma }-{\mathrm{LiV}}_2{O}_5$: A Microscopic Study

We determine the electronic structure of the one-dimensional spin- $\frac{1}{2}$ Heisenberg compound $\gamma -{\mathrm{LiV}}_2{\mathrm{O}}_5$, which has two inequivalent vanadium ions, V(1) and V(2), via density-functional calculations. We find a relative V(1)-V(2) charge ordering of roughly 70:30. We discuss the influence of the charge ordering on the electronic structure and the magnetic behavior. We give estimates of the basic hopping matrix elements and compare with the most studied ${\alpha }^{\prime }-{\mathrm{NaV}}_2{\mathrm{O}}_5$.