In this paper, we use an analytic linear response to develop efficient expressions for calculating a first-order energy response using the multi-reference Hilbert space coupled-cluster (HSMRCC) theory. Equations for the first-order response are derived and their diagrammatic evaluation is outlined. The Z-vector formalism used in SRCC to eliminate the explicit presence of a cluster amplitude response in favor of a de-excitation operator is generalized to HSMRCC and applied here. We also discuss several aspects of the Z-vector and outline different ways of introducing the technique and appropriateness of these in various circumstances. Efficient expressions for the energy response in terms of state-dependent effective CC density matrices are presented. We also compare our approach with Szalay's approach based on the generalized Hellmann-Feynmann theorem and discuss the advantages of our approach. (C) 2001 American Institute of Physics.