We calculate the low-lying spectra of the zirconium isotopes (Z = 40) with neutron numbers from N = 52 to N = 60 using the 1p 1/2 0g 9/2 proton and 2s1d0g 7/2 0h 11/2 neutron sub-shells to define the model space. Effective proton-proton, neutron-neutron and proton-neutron interactions have been derived using 88 Sr as closed core and employing perturbative many-body techniques. The starting point is the nucleon-nucleon potential derived from modern meson exchange models. The comprehensive shell-model calculation performed in this work provides a qualitative reproduction of essential properties such as the sub-shell closures in 96 Zr and 98 Zr. PACS number(s): 21.60. Cs, 27.60.+j