  We study the tight-binding dispersion of the recently discovered
superconductor K2Cr3As3, obtained from Wannier projection of Density Functional
Theory (DFT) results. In order to establish quantitatively the actual degree of
quasi-one dimensionality of this compound, we analyze the electronic band
structure for two reduced sets of hopping parameters: one restricted to the
Cr-As tubes and another one retaining a minimal number of in-plane hoppings.
The corresponding total and local density of states of the compound are also
computed with the aim of assessing the tight-binding results with respect to
the DFT ones. We find a quite good agreement with the DFT results for the more
extended set of hopping parameters, especially for what concerns the orbitals
that dominate at the Fermi level. Accordingly, we conclude that one cannot
avoid taking into account in-plane hoppings up to the next-nearest-neighbors
cells even only to describe correctly the Fermi surface cuts and the
populations along the kz direction. Such a choice of a minimal number of
hopping parameters directly reflects in the possibility of correctly describing
correlations and magnetic interactions.
