  We present a systematic derivation of a minimal five-band tight-binding model
for the description of the electronic structure of the recently discovered
quasi one-dimensional superconductor K2Cr3As3. Taking as a reference the
density-functional theory (DFT) calculation, we use the outcome of a Lowdin
procedure to refine a Wannier projection and fully exploit the predominant
weight at the Fermi level of the states having the same symmetry of the crystal
structure. Such states are described in terms of five atomic-like d orbitals:
four planar orbitals, two dxy and two dx2-y2, and a single out-of-plane one,
dz2 . We show that this minimal model reproduces with great accuracy the DFT
band structure in a broad energy window around the Fermi energy. Moreover, we
derive an explicit simplified analytical expression of such model, which
includes three nearest-neighbor hopping terms along the z direction and one
nearest-neighbor term within the xy plane. This model captures very efficiently
the energy spectrum of the system and, consequently, can be used to study
transport properties, superconductivity and dynamical effects in this novel
class of superconductors.
