  A very accurate, (HF)$_2$ potential energy surface (PES) is constructed based
on \ai\ calculations performed using the MOLPRO package at the CCSD(T) level of
theory with an aug-cc-pvQz-F12 basis set at about 161~000 points. a higher
correlation correction is computed at CCSDT(Q) level for 2000 points and is
considered alongside other more minor corrections due to relativity,
core-valence correlation and Born-Oppenheimer failure. The analytical surface
constructed uses 500 constants to reproduce the \ai\ points with a standard
deviation of 0.3 \cm. Vibration-rotation-inversion energy levels of the HF
dimer are computed for this PES by variational solution of the nuclear-motion
Schr\"{o}dinger using program WAVR4. Calculations over an extended range of
rotationally excited states show very good agreement with the experimental
data. In particular the known empirical rotational constants $B$ for the ground
vibrational states are predicted to better than about 2 MHz. $B$ constants for
excited vibrational states are reproduced several times more accurately than by
previous calculations. The experimental dissociation energy of the HF dimer is
reproduced \ai\ within the experimental accuracy of about 1 \cm\ for the first
time. This level of accuracy is shown to extend to higher excited
inter-molecular vibrational states $v$ and higher excited rotational quantum
numbers $(J,K_a)$.
