Correcting for dispersion interaction and beyond in density functional theory through force matching.

The force matching method is used to improve density functional theory (DFT) by designing a supplemental potential to capture the difference in atomic forces between a DFT functional and a high-quality post Hartree-Fock method. The supplemental potential has two-body terms designed to correct for dispersion and hydrogen bond interactions. The potential also has one-body terms to improve the description of the intramolecular potential energy surface. Our procedure is tested by providing corrections to the Becke-Lee-Yang-Parr exchange-correlation functional for water and is found to perform significantly better than the standard DFT-D approach, giving QCISD quality predictions for relative cluster energies, atomic forces, and molecular structures. It is found that a simple Lennard-Jones term does a good job at correcting for van der Waals interactions and possibly also providing corrections to exchange repulsion. The one-body corrections, while contributing only slightly to improving relative cluster energies, significantly reduce the errors in binding energies and atomic forces for the systems studied.