Random phase approximation with second-order screened exchange for current-carrying atomic states

Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals

The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.

Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings

A method for computing NMR shieldings with the direct random phase approximation (RPA) and the closely related σ-functionals [Trushin, E.; Thierbach, A.; Görling, A. Toward chemical accuracy at low computational cost: density functional theory with σ-functionals for the correlation energy. J. Chem. Phys. 2021, 154, 014104] is presented, which is based on a finite-difference approach. The accuracy is evaluated in benchmark calculations using high-quality coupled cluster values as a reference. Our results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional. NMR shieldings computed with direct RPA using a Hartree-Fock reference are significantly more accurate than MP2 shieldings and comparable to CCSD shieldings. Also, the basis set convergence is analyzed and it is shown that at least triple-zeta basis sets are required for reliable results.

Stretched or noded orbital densities and self-interaction correction in density functional theory

Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC.

Magnetic-Field Density-Functional Theory (BDFT): Lessons from the Adiabatic Connection

We study the effects of magnetic fields in the context of magnetic field density-functional theory (BDFT), where the energy is a functional of the electron density ρ and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may provide a viable route to the study of many magnetic phenomena using density-functional theory (DFT). The relationship between BDFT and CDFT is developed and clarified within the framework of the four-way correspondence of saddle functions and their convex and concave parents in convex analysis. By decomposing the energy into its Kohn-Sham components, we demonstrate that the magnetizability is mainly determined by those energy components that are related to the density. For existing density functional approximations, this implies that, for the magnetizability, improvements of the density will be more beneficial than introducing a magnetic-field dependence in the correlation functional. However, once a good charge density is achieved, we show that high accuracy is likely only obtainable by including magnetic-field dependence. We demonstrate that adiabatic-connection (AC) curves at different field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength. In contrast, if all AC curves are calculated at the equilibrium geometry of the field-free system, then the curves change strongly with increasing field strength due to the increasing importance of static correlation. This holds also for density functional approximations, for which we demonstrate that the main error encountered in the presence of a field is already present at zero field strength, indicating that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation.