An Extended Charge Equilibration Method.

We present a method for estimating partial atomic charges that uses all of the measured ionization energies (first, second, third, etc.) for every atom in the periodic table. We build on the charge equilibration (Qeq) method of Rappé and Goddard (which used only the first ionization energies) but reduce the number of ad hoc parameters from at least one for every type of atom to just two global parameters: a dielectric strength and a modified parameter for hydrogen atoms. Periodic electrostatic interactions are calculated via Ewald sums, and the partial charges are determined by simultaneously solving a system of linear equations; no iteration is required. We compare the predicted partial atomic charges of this extended charge equilibration (EQeq) scheme against plane-wave density-functional theory derived charges determined via the REPEAT method for 12 diverse metal-organic frameworks (MOFs). We also compare EQeq charges against ChelpG charges calculated using nonperiodic MOF fragments, as well as against Qeq charges as implemented in Accelrys Materials Studio. We demonstrate that for the purpose of ranking MOFs from best to worst for carbon capture applications, EQeq charges perform as well as charges derived from electrostatic potentials, but EQeq requires only a tiny fraction of the computational cost (seconds vs days for the MOFs studied). The source code for the EQeq algorithm is provided.