Empirical Correction to Molecular Interaction Energies in Density Functional Theory (DFT) for Methane Hydrate Simulation.

A general and empirical method is proposed for correction of London dispersion and other deficiencies in density functional theory (DFT). This method is based on the existing Lennard-Jones (L-J) equation and van der Waals parameters. The benchmark of energy correction is set as the energy difference between DFT and more accurate methods, for example CCSD(T). The energy correction includes all differences between CCSD(T) and DFT, dispersion energy, configuration interaction, induction interaction, residual correlation, and other effects. The energy correction is expressed as a linear combination of van der Waals potentials of nonbonded atomic pairs. The combination coefficients are determined using a least-squares approach in a training set of molecular pairs. The coefficients then can be used for the energy corrections in DFT calculations in a molecular family. Three correction equations of molecular pair interaction energy, water-water, water-methane, and methane-methane, are derived for methane hydrate simulation. The correction equation of the water-water pair is applied in the DFT calculation of water pentamer, yielding good intermolecular potential energy surfaces (PES), very close to the results of CCSD(T) over the active interaction range from 2.1 Å to 8.0 Å.