A new shifted zeroth-order Hamiltonian is presented, which will be used in second-order multiconfigurational perturbation theory (CASPT2). The new approximation corrects for the systematic error of the original formulation, which led to an relative overestimate of the correlation energy for open shell system, resulting in too small dissociation and excitation energies. Errors in the D, values for 49 diatomic molecules have been reduced with more than 50%. Calculations on excited states of the N-2 and benzene molecules give a similar improvement. (C) 2004 Elsevier B.V. All rights reserved.