Electrostatic Potential Derived Atomic Charges for Periodic Systems Using a Modified Error Functional

Abstract

A method to generate electrostatic potential (ESP) derived atomic charges in crystalline solids from periodic quantum mechanical calculations, termed the REPEAT method, is presented. Conventional ESP fitting procedures developed for molecular systems, in general, will not work for crystalline systems because the electrostatic potential in periodic systems is ill-defined up to a constant offset at each spatial position. In this work the problem is circumvented by introducing a new error functional which acts on the relative differences of the potential and not on its absolute values, as it is currently done with molecular ESP charge derivation methods. We formally demonstrate that the new functional reduces to the conventional error functional used in molecular ESP approaches when the simulation box of the periodic calculation becomes infinitely large. Several tests are presented to validate the new technique. For the periodic calculation of isolated molecules, the REPEAT charges are found to be in good agreement with those determined with established molecular ESP charge derivation methods. For siliceous sodalite, it is demonstrated that conventional molecular ESP approaches generate 'unphysical' charges, whereas the REPEAT method produces charges that are both chemically intuitive and consistent between different periodic electronic structure packages. The new approach is employed to generate partial atomic charges of various microporous materials and compared to both experimentally derived and molecular fragment ESP charges. This method can be used to generate partial atomic charges to be used in simulations of microporous and nanoporous materials, such as zeolites and metal organic framework materials.

Surface of glassyGeS2: A model based on a first-principles approach

“…This shows that the ESP-derived charges do not reflect the change in the bond chemistry as the local coordination around a Ge or S atom varies. The REPEAT method [72], which is a corrected version of the ESP method developed for periodic systems, was also tested but nonphysical partial charges were obtained for both Ge and S atoms; indeed we obtained negative charges for many Ge atoms and positive charges for many S atoms. The failure of the REPEAT method [72] for chalcogenide materials has been already reported [72].…”

“…The REPEAT method [72], which is a corrected version of the ESP method developed for periodic systems, was also tested but nonphysical partial charges were obtained for both Ge and S atoms; indeed we obtained negative charges for many Ge atoms and positive charges for many S atoms. The failure of the REPEAT method [72] for chalcogenide materials has been already reported [72]. This is due to the fact that the ESP methodology cannot reproduce the electrostatic potential for systems with high local atomic densities [72].…”

“…The failure of the REPEAT method [72] for chalcogenide materials has been already reported [72]. This is due to the fact that the ESP methodology cannot reproduce the electrostatic potential for systems with high local atomic densities [72]. The Bader method leads to absolute charges which increase with the atomic coordination.…”

On the inner workings of Monte Carlo codes

“…. Point charges: Parameters can be obtained by minimising the difference of the classical electrostatic potential and a QM electrostatic potential over many grid points (ChelPG methods) [16 -18]; REPEAT method [19,20]; partial equalisation of orbital electronegativity (PEOE) or the Gasteiger method [21] and charge equilibration methods. [22 -24] .…”

Computation of Charge Distribution and Electrostatic Potential in Silicates with the Use of Chemical Potential Equalization Models

“…70 The authors noted that in the correspondence between HI and ESP fitted charges was found for a set of organic molecules. 47 We suspect that this is a deficiency inherent to the Hirshfeld-I procedure when applied to (nearly) ionic systems.…”