The completely renormalized (CR) CCSD(T) method has been used to calculate the entire ground-state potential I energy surface (PES) for the Be + HF reaction on a grid of nuclear geometries consisting of similar to3000 points. The cc-pVTZ and cc-pVQZ basis sets have been employed. In addition to the case of the Be atom approaching the HF molecule from the fluorine side and the case of the Be atom approaching HF from the hydrogen side, several values of the Be-F-H angle and the insertion of the Be atom between the H and F atoms of HF have been examined. The CR-CCSD(T) results have been compared with the results of CCSD(T) and multireference configuration interaction (MRCI) calculations. It has been demonstrated that the ground-state PES of the BeFH system obtained from the single-reference "black-box" CR-CCSD(T) calculations is in excellent agreement with the PES obtained from the expensive MRCI calculations, whereas the PES resulting from the standard CCSD(T) calculations is qualitatively incorrect and characterized by large errors relative to MRCI on the order of several electronvolts.