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

Abstract

New parameters for the electronegativity equalization model (EEM) and the split-charge equilibration (SQE) model are calibrated for silicate materials, based on an extensive training set of representative isolated systems. In total, four calibrations are carried out, two for each model, either using iterative Hirshfeld (HI) charges or ESP grid data computed with Density Functional Theory (DFT) as a reference. Both the static (ground state) reference quantities and their responses to uniform electric fields are included in the fitting procedure. The EEM model fails to describe the response data, while the SQE model quantitatively reproduces all the training data. For the ESP-based parameters, we found that the reference ESP data are only useful at those grid points where the electron density is lower than 10 −3 a.u. The density value correlates with a distance criterion used for selecting grid points in common ESP fitting schemes.All parameters are validated with DFT computations on an independent set of isolated systems (similar to the training set), and on a set of periodic systems including dense and microporous crystalline silica structures, zirconia, and zirconium silicate. Although the transferability of the parameters to new isolated systems poses no difficulties, the atomic hardness parameters in the HI-based models must be corrected to obtain accurate results for periodic systems. The SQE/ESP model permits the calculation of the ESP with similar accuracy in both isolated and periodic systems.

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

“…A recent calibration of EEM and SQE parameters for silicates revealed that Hirshfeld-I charges systematically overestimate (in absolute value) the MEP of silica clusters. 12 Similar observations were made during the development of a forcefield for MIL-53(AL). 119 It is clear that there is still room for improved partitioning schemes that enhance the trade off between the sphericity and locality of the AIMs.…”

“…This result can be seen as a generalization of the expressions proposed by Itskowitz et al 79 Conventionally, EEM parameters are obtained through daunting least-squares fits, in which correlations between chemical potential and hardness parameters are practically unavoidable. 8,12,77 The spherical atom EEM provides an alternative for these cumbersome calibration procedures. In analogy with the seminal paper of Mortier, 4 we also observe that the intrinsic chemical potential and hardness of an atom in a molecule must be corrected for the molecular environment.…”

“…Later, Nistor et al proposed the split-charge equilibration (SQE), 66 which has EEM and AACT as limiting cases. SQE parameters were calibrated for organic 28 and inorganic 12,66 systems, and were found to be transferable to other molecules not included in the training set. The transferability indicates that the bond hardness parameter must have some physical interpretation.…”

“…Due to the large number of EEM parameters, these calibrations are afflicted by statistical correlations. 8,12,77 The more advanced the model, the more parameters it contains and the harder it becomes to determine the parameters. Keeping in mind that extended EEM models will be even more parameter-laden, one urgently needs an alternative to the conventional calibration of parameters.…”

The conformational sensitivity of iterative stockholder partitioning schemes

“…This is a distinct advantage of HI over QTAIM and implies that HI charges are both useful for a direct chemical interpretation as well as for the development of force field models. Unfortunately, a recent study revealed that HI charges severely overestimate molecular dipoles of isolated inorganic clusters [16], showing that the accurate reproduction of the molecular ESP is not a universal property of the HI scheme. Because of this deficiency, it is clear that the Hirshfeld-I scheme can be improved.…”