The zero-field splitting of the copper acetate monohydrate complex is studied using wave function based calculations. The anisotropy parameters extracted from highly correlated methods are in excellent agreement with the most accurate experimental results; in particular, the negative sign of the axial anisotropy parameter D is reproduced. During several decades, the interpretation of experimental data based on an analytical expression derived from perturbation theory led to a positive D-value. Although the validity of this expression is confirmed, it is explained that the incorrect attribution of a positive D is related to the assumption of an antiferromagnetic coupling between excited states. We have found in the present work that this coupling is actually ferromagnetic. The analysis of the various contributions to the anisotropy parameters shows that both spin-spin and spin orbit couplings participate in the magnetic anisotropy of this complex. Although the anisotropy arising from the spin spin coupling is essentially independent of the level of calculation, the zero-field-splitting parameters resulting from the spin orbit coupling are strongly sensitive to the effects of dynamic correlation. This works provides important new insights into the physical origin of the zero-field-splitting parameters in copper dimers.