Any-Particle Molecular Orbital/Hartree-Fock (APMO/HF) calculations are performed for a variety of atoms and simple diatomic molecular systems containing one and two negative muons (mu). In these calculations electrons and muons are described quantum mechanically whereas nuclei are treated as point charges. Our results for atoms containing n = 1,2 negative muons reveal that electronic properties such as electronic densities and ionization potentials shift to those of all-electron atoms with atomic numbers Z - n. In the case of diatomic molecules these muonic effects are more diverse ranging from transmutation of atomic properties to drastic changes in equilibrium geometries and energies. (c) 2013 Elsevier B.V. All rights reserved.