A novel computational scheme for accurate and efficient evaluation of π-π and π-σ stacking

Stacking involving aromatic rings has a significant contribution to the structural stability of biological macromolecules. However, conventional calculations such as density functional theory (DFT) and molecular mechanics (MM) fail to estimate such stabilization energies, most of which are fundamentally derived from van der Waals interactions. For the accurate description, higher level ab initio calculations, such as CCSD(T), should be employed; however, their computational costs are huge. MM calculations provide better estimation of the interactions of the aromatic rings than DFT, but not sufficient. In this report, we propose a novel scheme to calculate the interaction energy at an accuracy compatible to CCSD(T) with the computational costs comparable to MM calculations. In our scheme, the electron density of the aromatic rings is represented by Gaussian-type functions, and the parameters involved in the functions are determined by an optimization scheme to reproduce the CCSD(T) results. Here, we employ model structures involving tryptophan and tyrosine rings, and successfully obtain the optimal parameter set. By using this type of representation of the stacking proposed, the computational time to calculate the interaction energy is dramatically reduced by 10(-10)-fold, compared with CCSD(T).