Determination of noncovalent intermolecular interaction energy from electron densities

Noncovalent intermolecular interactions, widely found in molecular clusters and bio-molecules, play a key role in many important processes, such as phase changes, folding of proteins and molecular recognition. However, accurate calculation of interaction energies is a very difficult task because the interactions are normally very weak. Rigorous expressions for the electrostatic and polarization interaction energies between two molecules A and B, in term of the electronic densities, have been programmed: E es=AB ZAZB R&ar;A-R&ar; B-A ZAr 0Br&ar; BR&ar; A-r&ar;B dr&ar;B- BZBr 0Ar&ar; AR&ar; B-r&ar;A dr&ar;A + r0A r&ar;A r0B r&ar;B r&ar;A- r&ar;B dr&ar;Adr&ar; B1 Epol=- AZAD rpolB r&ar;B R&ar;A- r&ar;B dr&ar;B- BZBDr polAr&ar; AR&ar; B-r&ar;A dr&ar;A+ r0 Ar&ar; ADrpol Br&ar; Br&ar; A-r&ar;B dr&ar;Ad r&ar;B + r0B r&ar;B DrpolA r&ar;A r&ar;A -r&ar;B dr&ar;Ad r&ar;B+ DrpolA r&ar;A DrpolB r&ar;B r&ar;A -r&ar;B dr&ar;Ad r&ar;B 2 Z is atomic charge, rho0 is the electron density of the isolated molecule and Deltarhoind is the electron density change of the molecule caused by polarization. With some approximations, procedures for electrostatic and polarization energy calculations were developed that involve numerical integration. Electrostatic and polarization energies for several bimolecular systems, some of which are hydrogen bonded, were calculated and the results were compared to other theoretical and experimental data.; A second method for the computing of intermolecular interaction energies has also been developed. It involves a "supermolecule" calculation for the entire system, followed by a partitioning of the overall electric density into the two interacting components and then application of eq. (1) to find the interaction energy. In this approach, according to Feynman's explanation to intermolecular interactions, all contributions are treated in a unified manner. The advantages of this method are that it avoids treating the supersystem and subsystems separately and no basis set superposition error (BSSE) correction is needed. Interaction energies for several hydrogen-bonded systems are calculated by this method. Compared with the result from experiment and high level ab initio calculation, the results are quite reliable.