Molecular properties, equilibrium bond lengths, dissociation energies, and vibrational frequencies of the ground state, of diatomic molecules formed from alkali metal (Li, Na, K) and noble transition metal (Cu, Ag, An) have been calculated using density functional theory (DFT) with eight different density functionals. In addition, ab initio wave function based Hartree-Fock (HF) and coupled cluster singles doubles with triple excitations added perturbatively (CCSD(T)) methods are also included for comparisons. The pure density functionals PW91 and BP86 predict well the dissociation energies and harmonic vibrational frequencies but underestimate the bond lengths. CCSD(T) predicts the geometry well but underestimates the dissociation energies and vibrational frequencies. The hybrid HF/DFT B3P86 and B3LYP provide reasonable estimates for all the spectroscopic parameters. From the discrepancy between the computed and experimental bond length of KAg and the vibrational frequency of LiCu, we suggest a reanalysis or reexamination of the experimental spectrum of these two molecules. With only medium sized basis sets and small core relativistic effective core potentials, calculations using DFT functionals often give comparable or even superior results to ab initio wave function based methods in this mixed metal system.