Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

Abstract

An accurate semianalytic wavefunction is proposed for the Hookium and two‐electron atoms for varying strength of αVee(0≤α≤1) where α is the strength parameter and Vee is coulomb interaction between two electrons. The wavefunction leads to energies that are as accurate as those from the Coupled cluster singles and doubles (CCSD) calculations. Using this wavefunction, we construct the external potential vextα such that the density of the system remains unchanged as α is varied. The work thus gives a unified picture of adiabatic connection for these systems based on an easy to use wavefunction and complements the past investigations done in this direction. Using the potential obtained, we explicitly calculate the energy of the corresponding positive ions and show that the chemical potential—calculated as the difference between the energies of the two‐electron system and its positive ion—is equal to the experimental ionization energy and remains unchanged as α is varied. Furthermore, using total energies E(α) of these systems as a function of α, we provide a new perspective into a variety of hybrid functionals.

Investigation of structural, magneto‐electronic, and thermoelectric response of ductile SnAlO3 from high‐throughput DFT calculations

“…However, the thermoelectric performance can be enhanced by reducing the thermal conductivity or by doping various elements in different concentrations and via band engineering or switching to nanostructures. [32][33][34] At the same time, the exhibition of high electrical conductivity at room temperature than experimentally reported electrode material SrRuO 3 and the many more related properties including analogous electronic structure, paramagnetism, and metallicity in the other theoretically reported electrode materials, [6][7][8][9] the cubic SnAlO 3 oxide emerges as a new and efficient electrode material.…”

A study of accurate exchange-correlation functionals through adiabatic connection

“…These energies have been calculated from the near exact semi analytic densities 55,57 for H − and He and the exact density 42,56 for the Hookium atom. We note that SCAN functional has also been studied 58 for Hooke's atom recently.…”

“…(4) to obtain W α xc curves for the functionals being studied and compare them with the exact curves 57 . Since the exact part W α x of it is a constant equal to the exchange energy, we display only W Table II.…”

A general penalty method for density‐to‐potential inversion

“…This is known as the ZMP method and has been implemented [47][48][49][50][51][52][53][54][55] successfully over the years. The method above is a penalty-based method as λ is the penalty parameter imposed if the functional of Equation 11is nonzero.…”

“…In actual calculations, v ext ( r ) and v H ( r ) are fixed, and therefore v xc ( r ) is varied to achieve the maximum. The method has been applied to obtain both the exchange‐correlation potential v xc ( r ) and the external potential [ 15,55 ] for scaled electron‐electron interaction. Like the ZMP method, this approach is also related to finding the universal functional F [ ρ ], defined by Lieb as where E [ v ] is the energy corresponding to N electrons moving in potential v ( r ).…”