Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory

Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian

This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.

Rydberg electron stabilizes the charge localized state of the diamine cation

A previous controversial discussion regarding the interpretation of Rydberg spectra of gaseous dimethylpiperazine (DMP) as showing the co-existence of a localized and delocalized mixed-valent DMP+ radical cation is revisited. Here we show by high-level quantum-chemical calculations that an apparent barrier separating localized and delocalized DMP+ minima in previous multi-reference configuration-interaction (MRCI) calculations and in some other previous computations were due to unphysical curve crossings of the reference wave functions. These discontinuities on the surface are removed in state-averaged MRCI calculations and with some other, orthogonal high-level approaches, which do not provide a barrier and thus no localized minimum. We then proceed to show that in the actually observed Rydberg state of neutral DMP the 3s-type Rydberg electron binds more strongly to a localized positive charge distribution, generating a localized DMP* Rydberg-state minimum, which is absent for the DMP+ cation. This work presents a case where interactions of a Rydberg electron with the underlying cationic core alter molecular structure in a fundamental way.

Reimagining the Wave Function in Density Functional Theory: Exploring Strongly Correlated States in Pancake-Bonded Radical Dimers

Pancake bonding between π-conjugated radicals challenges conventional electronic structure approximations, due to the presence of both dispersion (van der Waals) interactions and "strong" electron correlation. Here we use a reimagined wave function-in-density functional theory (DFT) approach to model pancake bonds. Our generalized self-interaction correction extends DFT's reference system of noninteracting electrons, by introducing electron-electron interactions within an active space. We show that a small variation on our previous derivation recovers a DFT-corrected complete active space method proposed by Pijeau and Hohenstein. Comparison of the two approaches shows that the latter provides reasonable dissociation curves for single bonds and pancake bonds, including excited states inaccessible to conventional linear response time-dependent DFT. The results motivate broader adoption of wavefunction-in-DFT approaches for modeling pancake bonds.

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

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.

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

Unification of Perdew-Zunger self-interaction correction, DFT+U, and Rung 3.5 density functionals

This Communication presents a unified derivation of three different approximations used in density functional theory (DFT): the Perdew-Zunger self-interaction correction (PZSIC), the Hubbard correction DFT+U, and the Rung 3.5 density functionals. All three approximations can be derived by introducing electron self-interaction into the Kohn-Sham (KS) reference system of noninteracting electrons. The derivation uses the Adiabatic Projection formalism: one projects the electron-electron interaction operator onto certain states, introduces the projected operator into the reference system, and defines a density functional for the remainder. Projecting onto individual localized KS orbitals recovers our previous derivation of the PZSIC [B. G. Janesko, J. Phys. Chem. Lett. 13, 5698-5702 (2022)]. Projecting onto localized atom-centered orbitals recovers a variant of DFT+U. Projecting onto localized states at each point in space recovers Rung 3.5 approaches. New results include an "atomic state PZSIC" that does not require localizing the KS orbitals, a demonstration that typical Hubbard U parameters reproduce a scaled-down PZSIC, and a Rung 3.5 variant of DFT+U that does not require choosing atom-dependent states.