A new procedure for evaluating energy gradients in a singularity-free manner is presented for use in the SAC/SAC-C1 program in which computational dimensions are reduced by the perturbation selection method. The singularity in the energy gradients stemming from a breakdown of the unitary invariance is effectively removed by the minimum orbital-deformation (MOD) method proposed in the previous study. All calculations can be done analytically via new two sets of linear equations combined with the coupled-perturbed Hartree-Fock method. Geometry optimizations for malonaldehyde in the ground and lowest singlet excited states are performed by the new method. (C) 2002 Published by Elsevier Science B.V.