Three-dimensional structures of a representative set of more than 30 hydrogen-bonded nucleic acids pairs have been studied by reliable ab initio quantum mechanical methods. We show that many hydrogen-bonded nucleic acid base pairs are intrinsically nonplanar, mainly due to the partial sp3 hybridization of nitrogen atoms of their amino groups and secondary electrostatic interactions. This finding extends the variability of intermolecular interactions of DNA bases in that i) flexibility of the base pairs is larger than has been assumed before, and ii) attractive proton-proton acceptor interactions oriented out of the base pair plane are allowed. For example, all four G-A mismatch base pairs are propeller twisted, and the energy preferences for the nonplanar structures range from less than 0.1 kcal/mol to 1.8 kcal/mol. We predict that nonplanarity of the amino group of guanine in the G(anti)...A(anti) pair of the ApG step of the d(CCAAGATTGG)2 crystal structure is an important stabilizing factor that improves the energy of this structure by almost 3 kcal/mol. Currently used empirical potentials are not accurate enough to properly cover the interactions associated with amino-group and base-pair nonplanarity.