We present ab initio calculations of atomic and molecular systems containing the first-, second-, and third-row post-d elements (Ga-Br, In-I, and Tl-At) using several methods including variational and diffusion Monte Carlo. In the quantum Monte Carlo calculations, we used the recent scalar-relativistic energy-consistent Hartree-Fock pseudopotentials [M. Burkatzki , J. Chem. Phys. 126, 234105 (2007)], which are nonsingular at the origin. For the first- and second-row elements, the calculated ionization energies and electron affinities are in excellent agreement with those obtained using CCSD(T) with large basis sets and with experiment after correcting approximately for spin-orbit effects. For the third-row elements, where relativistic effects cannot be adequately included by a simple j-averaging, the results are in excellent agreement with CCSD(T) energies obtained with a large (5-zeta) basis set. Benchmark calculations of the dissociation energies, vibration frequencies, and equilibrium bond lengths of several diatomic molecules including As-2, Br-2, Sb-2, and I-2 as well as the hydrides XH (X=Ga, Br, In, I, and At) are presented.