Using force-matching to reveal essential differences between density functionals in ab initio molecular dynamics simulations

The exchange-correlation (XC) functional and value of the electronic fictitious mass μ can be two major sources of systematic errors in ab initio Car-Parrinello Molecular Dynamics (CPMD) simulations, and have a significant impact on the structural and dynamic properties of condensed-phase systems. In this work, an attempt is made to identify the origin of differences in liquid water properties generated from CPMD simulations run with the BLYP and HCTH∕120 XC functionals and two different values of μ (representative of "small" and "large" limits) by analyzing the effective pairwise atom-atom interactions. The force-matching (FM) algorithm is used to map CPMD interactions into non-polarizable, empirical potentials defined by bonded interactions, pairwise short-ranged interactions in numerical form, and Coulombic interactions via atomic partial charges. The effective interaction models are derived for the BLYP XC functional with μ=340 a.u. and μ=1100 a.u. (BLYP-340 and BLYP-1100 simulations) and the HCTH∕120 XC functional with μ=340 a.u. (HCTH-340 simulation). The BLYP-340 simulation results in overstructured water with slow dynamics. In contrast, the BLYP-1100 and HCTH-340 simulations both produce radial distribution functions (indicative of structure) that are in reasonably good agreement with experiment. It is shown that the main difference between the BLYP-340 and HCTH-340 effective potentials arises in the short-ranged nonbonded interactions (in hydrogen bonding regions), while the difference between the BLYP-340 and BLYP-1100 interactions is mainly in the long-ranged electrostatic components. Collectively, these results demonstrate how the FM method can be used to further characterize various simulation ensembles (e.g., density-functional theory via CPMD). An analytical representation of each effective interaction water model, which is easy to implement, is presented.