  The automated development of a new ab initio full-dimensional potential
energy surface (PES) is reported for the CH$_4\cdot$F$^-$ complex using the
ROBOSURFER program package. The new potential provides a near-spectroscopic
quality description over a broad configuration range including the methane-ion
dissociation, as well as isolated methane vibrations. In particular, it
improves upon the earlier [Czak\'o, Braams, Bowman (2008)] PES over
intermediate methane-fluoride distances. Full-dimensional (12D) variational
vibrational computations using the new PES and the GENIUSH-Smolyak algorithm
show that tunneling splittings larger than 0.1 cm$^{-1}$ appear below the top
of the interconversion barrier of the four equivalent minima of the complex.
