17 research outputs found
Prendersi cura della generatività ,genitorialità e cogenitorialità con gli operatori socio-sanitari per una profilassi psicoeducativa
From Kohn–Sham to many-electron energies via step structures in the exchange-correlation potential
Accurately describing excited states within Kohn–Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems
How Interatomic Steps in the Exact Kohn–Sham Potential Relate to Derivative Discontinuities of the Energy
Accurate
density functional calculations hinge on reliable approximations
to the unknown exchange-correlation (xc) potential. The most popular
approximations usually lack features of the exact xc potential that
are important for an accurate prediction of the fundamental gap and
the distribution of charge in complex systems. Two principal features
in this regard are the spatially uniform shift in the potential, as
the number of electrons infinitesimally surpasses an integer, and
the spatial steps that form, for example, between the atoms of stretched
molecules. Although both aforementioned concepts are well known, the
exact relationship between them remained unclear. Here we establish
this relationship via an analytical derivation. We support our result
by numerically solving the many-electron Schrödinger equation
to extract the exact Kohn–Sham potential and directly observe
its features. Spatial steps in the exact xc potential of a full configuration-interaction
(FCI) calculation of a molecule are presented in three dimensions
Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density-functional theory using the ensemble-generalization approach
Density functional theory calculations of continuum lowering in strongly coupled plasmas
Assessment of tuning methods for enfacing approximate energy linearity in range-separated hybrid functionals
A range of tuning methods, for enforcing approximate energy linearity through a system-by-system optimization of a range-separated hybrid functional, are assessed. For a series of atoms, the accuracy of the frontier orbital energies, ionization potentials, electron affinities, and orbital energy gaps is quantified, and particular attention is paid to the extent to which approximate energy linearity is actually achieved. The tuning methods can yield significantly improved orbital energies and orbital energy gaps, compared to those from conventional functionals. For systems with integer M electrons, optimal results are obtained using a tuning norm based on the highest occupied orbital energy of the M and M + 1 electron systems, with deviations of just 0.1–0.2 eV in these quantities, compared to exact values. However, detailed examination for the carbon atom illustrates a subtle cancellation between errors arising from nonlinearity and errors in the computed ionization potentials and electron affinities used in the tuning