MCML: Combining physical constraints with experimental data for a multi‐purpose meta‐generalized gradient approximation

Abstract

The predictive power of density functional theory for materials properties can be improved without increasing the overall computational complexity by extending the generalized gradient approximation (GGA) for electronic exchange and correlation to density functionals depending on the electronic kinetic energy density in addition to the charge density and its gradient, resulting in a meta‐GGA. Here, we propose an empirical meta‐GGA model that is based both on physical constraints and on experimental and quantum chemistry reference data. The resulting optimized meta‐GGA MCML yields improved surface and gas phase reaction energetics without sacrificing the accuracy of bulk property predictions of existing meta‐GGA approaches.

Data-driven and constrained optimization of semi-local exchange and non-local correlation functionals for materials and surface chemistry

“…To compare the performance of the VCML-rVV10 functional, calculations were also performed with PBE 10 , MS2 31 , SCAN 12 , r 2 SCAN 13 (a regularized modification of SCAN with better numerical stability), SCAN-rVV10 25 , MCML 17 , and MCML-rVV10 (introduced in this work). For the error analysis, the mean error (ME) and mean absolute error (MAE) are computed…”

“…In the following, the meta-GGA as well as the vdW fitting procedure is presented. The procedure to obtain the meta-GGA functional form has been outlined in Brown et al 17 for the MCML functional. We will briefly discuss its main components here.…”

“…We extend the approach introduced in Brown et al 17 by including the vdW description via rVV10. The vdW description is optimized based on the functional form, after which our exchange functional is optimized based on a given vdW parameterization.…”

“…There are several approaches combining constraints and data for XC functionals. [17][18][19] Recently, our group has applied such a combined approach to construct a multi-purpose, constrained and machine learned (MCML) XC functional that shows improved predictions of surface and gas phase reactions without sacrificing the good description of bulk properties via previous approaches. 17 The MCML a) Electronic mail: ktrepte@slac.stanford.edu b) Electronic mail: vossj@slac.stanford.edu functional is a so-called semi-local functional, lacking an explicit description of non-local, i.e., van der Waals (vdW) type correlation.…”

“…[17][18][19] Recently, our group has applied such a combined approach to construct a multi-purpose, constrained and machine learned (MCML) XC functional that shows improved predictions of surface and gas phase reactions without sacrificing the good description of bulk properties via previous approaches. 17 The MCML a) Electronic mail: ktrepte@slac.stanford.edu b) Electronic mail: vossj@slac.stanford.edu functional is a so-called semi-local functional, lacking an explicit description of non-local, i.e., van der Waals (vdW) type correlation. Supplementing a semi-local functional with vdW correlation does not only affect the performance for vdW-dominated interaction energies, but the attractive dispersion forces can lead to even stronger overbinding in chemisorption systems than already present in some semi-local approximations.…”