The energy-differences based exact criterion for testing approximations to the functional for the kinetic energy of non-interacting electrons

Abstract

Gradient-dependent approximations to the functional of the kinetic energy of non-interacting electrons (T s [ρ]), which reflect various properties of the exact functional, are considered. For specially constructed pairs of electron densities, for which the analytic expression for the differences of T s [ρ] is known, it is shown that the accuracy of the quantities derivable from a given approximation to T s [ρ]: energy differences and their functional derivatives, does not reflect that of T s [ρ] itself. The comparisons between the exact values of the kinetic energy in such cases are proposed as an independent condition/criterion for appraisal of approximations to T s [ρ].

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

“…To quantify these errors, the integral of the absolute value of the difference densities 47,48,79 ͑referred to as absolute errors in the following͒, ⌬ abs = ͉͐ err ͑r͉͒d 3 r, are given in Table I. When applying the reconstructed potential the error in the electron density is approximately one order of magnitude smaller than for the sum of the fragment electron densities, about six times smaller than for FDE͑s͒, and half of the error when comparing to FDE͑s͒ with freeze-and-thaw cycles.…”

The electronic spectrum of CUONg4 (Ng = Ne, Ar, Kr, Xe): New insights in the interaction of the CUO molecule with noble gas matrices

“…84) functional and the zero-overlap correction of Jacob and Visscher 78 that eliminate such problems. We used the error measures defined by Bernard et al: 104 integrated absolute errors in the electron density, the integrated root mean square errors in the electron density, and the magnitude of the errors in the dipole moment. While the former two strictly depend on the absolute size of the error in the electron density, the latter also provides information on its spatial redistribution.…”

Orbital-Free Embedding Effective Potential in Analytically Solvable Cases

“…It [18,[20][21][22] showed that this assumption is not founded at least for the most common approximants. A more refined strategy relies on the direct analysis of the quality of electron density obtained from a given approxi- [18,[20][21][22] rather than on the performance of the parent approximant to T s [n].…”

“…A more refined strategy relies on the direct analysis of the quality of electron density obtained from a given approxi- [18,[20][21][22] rather than on the performance of the parent approximant to T s [n]. Note that in calculations based on the Wesolowski-Warshel embedding formalism the absolute values of T s [n] obtained from an approximant to this functional are not needed.…”