A highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) calculations over generally contracted spherical harmonic Gaussian-type spinors (GTSs) is presented. Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M-2 (M=Cu, Ag, and Au), by the Dirac-Hartree-Fock (DHF) method were performed with a new four-component relativistic ab initio MO program package oriented toward contracted GTSs. The relativistic electron repulsion integrals (ERIs), the major bottleneck in routine DHF calculations, are calculated efficiently employing the fast ERI routine SPHERICA, exploiting the general contraction scheme, and the accompanying coordinate expansion method developed by Ishida. Illustrative calculations clearly show the efficiency of our computational scheme.