Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules

Abstract

We visualize the Kohn-Sham kinetic energy density (KED) and the ingredients--the electron density, its gradient, and Laplacian--used to construct orbital-free models of it, for the AE6 test set of molecules. These are compared to related quantities used in metaGGA's, to characterize two important limits--the gradient expansion and the localized-electron limit typified by the covalent bond. We find the second-order gradient expansion of the KED to be a surprisingly successful predictor of the exact KED, particularly at low densities where this approximation fails for exchange. This contradicts the conjointness conjecture that the optimal enhancement factors for orbital-free kinetic and exchange energy functionals are closely similar in form. In addition we find significant problems with a recent metaGGA-level orbital-free KED, especially for regions of strong electron localization. We define an orbital-free description of electron localization and a revised metaGGA that improves upon atomization energies significantly.

Visualisation and orbital-free parametrisation of the large-Z scaling of the kinetic energy density of atoms

“…In order to impose the von Weizsäcker bound in the limit of strong electron localization, it interpolates between this functional and the von Weizsäcker form using a nonanalytic but smooth function of the difference between the enhancement factors z = F GE4−M −F vW S . Despite an attractive design philosophy, the mGGA has deficiencies as a practical tool for OFDFT [10,41,47]. However, it is of value as a an approach for thinking about OFDFT -building from the basis of the kinetic energy density which is an important tool for visualization and quantitative modeling of electronic structure.…”

“…Secondly the form of interpolator between slowlyvarying and von Weizsäcker limits obeys a constraint that τ is greater than both τ GEA and τ vW while the mGGA interpolates in between the two limits. This difference proves to be helpful for modeling the KED of covalent bonds [47]. The factor α is used to control the rate at which the interpolating function switches between GEA and vW, with the leading correction to F vW…”

The Role of the Reduced Laplacian Renormalization in the Kinetic Energy Functional Development

“…More recently, the class of Laplacian-level meta-GGA (LLMGGA) KE functionals, in which the Laplacian of the density (∇ 2 ρ) is used as an additional ingredient, has attracted strong interest [11,[23][24][25][26][27][28][29]. The incorporation of the latter is especially important because it allows for distinguishing different density regions (e.g., the nuclear and the bonding region), which are out of reach for all present day GGAs.…”

Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals

“…Cancio and Redd 44 noticed some odd behavior of the PC mGGA for regions of small p and negative q which led them to suggest their CR mGGA 43,44 . (Remark: Cancio and Redd's p variable is not the same as the one defined at Eq.…”