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The adsorption of benzene, pyridine, and two nucleobases on the Au(111) surface has been investigated using a fully relaxed, self-consistent meta-generalized gradient approximation (meta-GGA) density functional theory setup with the M06-L functional. The meta-GGA based molecule-surface separations are shortened and the adsorption bond strengths of the molecules are greatly improved over the virtually non-interacting results obtained when using a plain GGA exchange-correlation functional. The nucleobases containing oxygen atoms show higher corrugation with adsorption site and orientation than the other aromatic molecules considered. The adsorption of pentacene is studied on Au, Ag, and Cu surfaces. In agreement with experiment, the adsorption energies are found to increase with decreasing nobleness, but the dependency is underestimated. We point out how the kinetic energy density can discriminate between covalent and non-covalent bonding regions of orbital overlap