Ab initio calculations are carried out, at various levels of treatment of correlation forces, for the orientation and distance dependence of the interaction between a helium atom and the structure of the ionic core found earlier in protonated He cluster studies, i.e. the linear (HeHHe)(+) triatomic molecular ion. Several aspects of the potential energy surface are discussed and specific details of the stable configuration analysed. The final energy surface is spline-fitted for further use in the stochastic calculations for the ground vibrational states of the small protonated clusters presented in a following paper. (C) 2000 Elsevier Science B.V. All rights reserved.