Following the first principles the analytic Born–Oppenheimer (BO) potential curve for the ground state X1Σ+ of the molecule ClF is proposed for whole range of internuclear distances R∈[0,∞). It is based on matching the perturbation theory at small internuclear distances R and multipole expansion at large distances R, it has the form of two-point Pade approximant and provides 3–4 figures in rovibrational energies. It supports 5719 rovibrational states with maximal vibrational number νmax=47 and maximal angular momentum Lmax=210 including 36 weakly-bound states close to threshold (to dissociation limit) with the energies ≲10-4hartree. The van der Waals constant C6(ClF)∼29.3a.u. is predicted.