Cooperativity in noncovalent interactions of biologically relevant molecules

Using a recently published benchmark MP2 database of nucleic acid base trimers, the three-body contribution to the interaction energy (TBE, also termed (non)cooperativity) as a function of base composition and complex geometry is studied. In 28 out of 141 cases (or 20%), the counterpoise-corrected MP2/TZV(2df,2pd) TBE exceeds 1 kcal mol−1. The TBE is below 1 kcal mol−1 for all trimers in the benchmark set consisting of U, T, and A, irrespective of the geometrical arrangement in the database. The largest MP2/TZV(2df,2pd) cooperativity of −9 kcal mol−1 is obtained for a hydrogen-bonded guanine trimer. The largest anti-cooperativity occurs for a protonated cytosine–guanine–cytosine trimer (6 kcal mol−1). Generally, the many-body non-additivity term is an order of magnitude smaller than the interaction energies (on average −33 kcal mol−1). Employing various density functionals (GGA, meta-GGA, and hybrid) and wave function methods up to third order perturbation theory, and using atomic-orbital basis sets of double-, triple-, and quadruple-ζ quality, we find that the non-additivity effects are almost independent of one particle basis set and method. To enable an interpretation of the TBE, the intermolecular interaction energy is subjected to an energy decomposition analysis (EDA) with a similar definition of the energy terms as the Morokuma decomposition scheme. We find that nonadditive effects are mainly due to the induction, while exchange repulsion, electrostatic, and dispersion contributions are essentially additive, the latter also beyond second order at the MP3/SV(d,p) level. The performance of dispersion-corrected density functional theory for the prediction of structures and binding energies is assessed. While an accurate reproduction of the MP2-optimized reference structures of the trimers can already be accomplished with modern density functionals, only the inclusion of the long-range (London) dispersion interaction provides a consistent picture for both structures and binding energies.