We report accurate variational and diffusion quantum Monte Carlo calculations for the size dependence of the vibrational frequency shift of HF molecules embedded in helium clusters with up to n = 198 helium atoms,The frequency shift exhibits a strong initial size dependence and saturates at a redshift of about 2.7 +/- 0.1 cm(-1) for clusters with over 100 atoms, This value is in good agreement with our experimental redshift of 2.65 +/- 0.15 cm(-1) for clusters with over 1000 atoms, The helium cluster is found to undergo significant structural changes upon embedding of HF, The density in the nearest neighbor shell exceeds : the bulk helium density by a factor of two, A second nearest neighbor density maximum and a peripheral density plateau very close to the bulk helium value is found, In spite of the anisotropic interaction between HF and helium all clusters have almost perfectly spherical helium density profiles and indicate close to free rotor behavior of HF inside the cluster. The cluster size dependence of The redshift can be qualitatively described by an induced dipole model.