For the HF dimer we calculate the fundamental HF stretching vibration frequencies, and the fundamental and overtone frequencies of the intermolecular (HF-HF) stretching vibration, using an ab initio potential energy surface and the previously developed semirigid bender Hamiltonian. The ab initio surface used involves the addition of 459 nuclear geometry points to the 1061 reported in our earlier work. These extra points have been chosen to give more information on those parts of the surface that involve distortions of the HF bond lengths. We have fitted these 1520 points to an analytic expression, slightly modified from our previous work, that involves 39 adjustable parameters and one constrained parameter; the weighted standard deviation of the fit is 29.3 cm-1. To calculate the vibrational frequencies, and the tunneling splittings in these vibrationally excited states, we use the semirigid bender Hamiltonian to average over the trans-tunneling path. We also calculate from the ab initio surface the effect of the adiabatic corrections, for the HF stretching states, that arise from the separation of the tunneling mode. In the adiabatically corrected calculation we obtain v1 = 3926 cm -1, and v2 = 3875 cm-1, which are in good agreement with the experimental results (3930.9 and 3868.1 cm-1 respectively). We also predict v4 = 146 cm-1, 2v 4 = 280 cm-1, and 3v4 = 405 cm-1. The value obtained for v4 enables us to explain the observed perturbation of the lower tunneling component of the K = 4 ground state level as being due to interaction with the lower tunneling component of the v 4 = 1, K = 3 level.