Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization

Abstract

This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron−electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron−electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn−Sham reference system, and employs a formally exact density functional to model the remaining electron−electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew−Burke−Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core−electron binding energies of second-period elements Li−Ne and third-period elements Na−Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations

“…40 Core-projected hybrids, including a uniform 70% core-projected exact exchange, give MAD 4 eV (1 eV) for these CEBE. 68 The present work extends this approach to core-electron excitations.…”

“…Our initial study of core ionization found that a uniform 70% core exact exchange admixture provided accurate core 1s ionization potentials for second- and third-period elements Li–Ar . However, Figure suggests that core-valence excitation energies will show a more complex interplay of core and valence exact exchange admixtures.…”

“…This section summarizes the implementation of core-projected hybrids in linear response TDDFT. Ref provides a detailed derivation of the SCF implementation. We consider a system of N σ , σ = ↑,↓ electrons in an external potential.…”

“…Ref presented a derivation of core-projected hybrids and an initial application predicting core-electron binding energies (CEBE) from ground-state orbital energies CEBE = −ϵ 1s . − Standard DFAs designed for valence properties give mean absolute deviations (MAD) ∼20 eV (∼50 eV) for first-period element Li–Ne (second-period element Na–Ar) CEBE computed from orbital energies . Core-projected hybrids, including a uniform 70% core-projected exact exchange, give MAD 4 eV (1 eV) for these CEBE .…”

Synthesis of 1-(4-Bromobenzoyl)-1,3-dicyclohexylurea and Its Arylation via Readily Available Palladium Catalyst─Their Electronic, Spectroscopic, and Nonlinear Optical Studies via a Computational Approach

“…The computational studies of the synthesis compounds ( 3 , 5a – g ) were also performed by using the DFT technique to calculate thermodynamic and chemical properties. All the calculations were also performed with a hybrid version of Adamo’s Perdew, Burke, and Ernzerhof functional (PBE0) along with the application of Grimme’s empirical dispersion correction (D3) with Becke–Johnson damping (D3BJ) . The solvent used for all the calculations was 1,4-dioxane induced through the polarizable continuum model (PCM) with the solvent model density (SMD) parameter set by Truhlar .…”