The equilibrium structure and potential-energy surface of calcium difluoride, CaF2, have been determined from large-scale ab initio calculations using the coupled-cluster method, CCSD(T), in conjunction with basis sets of quadruple- and quintuple-zeta quality. The CaF2 molecule was found to be quasilinear, with an equilibrium FCaF anale of 154.3degrees and barrier to linearity of 54 cm(-1). The vibrational-rotational energy levels of the C, (CaF2)-Ca-40 and (CaF2)-Ca-44 isotopomers were predicted using the variational method. In particular, the FCaF bending fundamental (the v(2) mode) was determined to be very low at only 9 cm(-1). The calculated spectroscopic constants could be used to guide future high-resolution spectroscopic experiments on calcium difluoride.