We have theoretically analyzed mimics of Watson-Crick adenine-thymine (AT) and guanine-cytosine (GC) base pairs in which N-H⋯O and N⋯H-N hydrogen bonds are replaced by N-H⋯F and N⋯H-C, respectively, by using the generalized gradient approximation of density functional theory at BP86/TZ2P. The general effect of the above substitutions is an elongation and weakening of the hydrogen bonds that hold together the base pairs. However, the precise effects depend on how many and, in particular, on which hydrogen bonds are substituted in AT and GC. Another purpose of this work is to clarify the relative importance of electrostatic attraction versus orbital interaction in the weak hydrogen bonds involved in the mimics, by using a quantitative bond-energy decomposition scheme. At variance with widespread believe, the orbital interaction component in these weak hydrogen bonds is found to contribute 34-42% of the attractive interactions and is thus of the same order of magnitude as the electrostatic component, which provides the remaining attraction component.