We present the electronic and magnetic properties of the antiferromagnetic Cr8 molecular ring (i.e. [Cr8F8Piv16], where HPiv - pivalic acid, trimethyl acetic acid) found by means of density functional theory (DFT) simulation techniques. The all-electron linearized augmented plane wave method (LAPW) implemented in the Wien2k package is exploited. It is also used to calculate the electronic structure, to estimate the exchange coupling parameter and to analyse magnetic anisotropy of an infinite chain model systems corresponding to the Cr8 ring. We demonstrate that the chain models mimic with good approximation the electronic and magnetic properties of the original Cr8 molecule. They reduce substantially computational complexity and speed up extensive investigations of molecules belonging to the Cr-based molecular rings family.