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.