Abstract A potential energy surface for the FCN linear molecule is obtained by nonlinear least-squares fit to the pure ( l = 0 ) vibrational terms observed spectroscopically. The potential surface is expressed as a Morse-cosine expansion in valence coordinates, and the vibrational energy levels needed to carry out the fit are calculated variationally using a system of optimal generalized internal coordinates expressly determined for such a purpose. The quality of the potential energy surface fitted is checked by computing the vibrational terms G v and the rotational constants B v of the FCN molecule and its isotopologs 19 F 13 C 14 N and 19 F 12 C 15 N using a normal hyperspherical coordinate system which facilitates the assignments of normal modes quantum numbers to the vibrational energy levels and the subsequent comparison with the observed values. The spectroscopic FCN potential energy surface obtained is shown to reproduce the vibrational terms of the three molecular species well, and above all their rotational constants, thus endorsing the use of the potential to identify and characterize unobserved infrared bands of these species.