The effect of the Hund's J terms in the DFT+U+J family of corrective functionals for (semi)local spin-density functional theory is assessed for a series of four octahedrally coordinated Fe(II) spin-crossover molecules spanning the covalent end of the ligand field spectrum. We report values and analyze trends for the Hubbard U and Hund's J parameters determined via minimum-tracking linear response for all valence atomic subspaces and relevant spin states. These parameters are then systematically applied by using simplified rotationally invariant Hubbard functionals to identify the simplest technique capable of yielding reliable adiabatic energy differences with respect to CASPT2/CC benchmarks. Consistent with previous findings, DFT+U improves the underlying DFT electronic density toward the CASPT2 reference, whereas the inclusion of an unlike-spin Hund's J energy term exerts only a marginal additional effect. Notably, the inclusion of this canonical, positively signed Hund's J term fails to remedy, and in fact, exacerbates the deficiencies of DFT+U in describing adiabatic energy differences in strongly covalent molecular systems. It further reveals intrinsic limitations of the contemporary DFT+U+J framework in simultaneously reproducing the charge distribution and energetics of these systems and hints at directions for its improvement.

The effect of the Hund's J terms in various DFT+U+J corrections to semi-local spin-density functional theory is assessed for a series of four octahedrally coordinated Fe(II) spin-crossover molecules spanning the covalent end of the ligand field spectrum. We report values and analyze trends for the Hubbard U and Hund's J parameters determined via minimum-tracking linear response for all valence atomic subspaces and relevant spin states in these molecules. We then methodically apply them via simplified rotationally-invariant Hubbard functionals in search of the simplest combination to yield reliable adiabatic energy differences with respect to those obtained using CASPT2/CC. The observed failure of canonical, positively-signed Hund's J terms in furthering the already robust capacity of DFT+U to obtain accurate energetics prompts an evaluation of their limitations when seeking to account for the static correlation phenomena in such strongly covalent systems and suggests directions for their improvement.

Abinit is a widely used scientific software package implementing density functional theory and many related functionalities for excited states and response properties. This paper presents the novel features and capabilities, both technical and scientific, which have been implemented over the past 5 years. This evolution occurred in the context of evolving hardware platforms, high-throughput calculation campaigns, and the growing use of machine learning to predict properties based on databases of first-principle results. We present new methodologies for ground states with constrained charge, spin, or temperature; for density functional perturbation theory extensions to flexoelectricity and polarons; and for excited states in many-body frameworks including GW, dynamical mean field theory, and coupled cluster. Technical advances have extended Abinit high-performance execution to graphical processing units and intensive parallelism. Second-principles methods build effective models on top of first-principle results to scale up in length and time scales. Finally, workflows have been developed in different community frameworks to automate Abinit calculations and enable users to simulate hundreds or thousands of materials in controlled and reproducible conditions.

Members of the DFT+U family of functionals are increasingly prevalent methods of addressing errors intrinsic to (semi-) local exchange-correlation functionals at minimum computational cost, but require their parameters U and J to be calculated in situ for a given system of interest, simulation scheme, and runtime parameters. The SCF linear response approach offers ab initio acquisition of the U and has recently been extended to compute the J analogously, which measures localized errors related to exchange-like effects. We introduce a renovated post-processor, the lrUJ utility, together with this detailed best-practices guide, to enable users of the popular, open-source Abinit first-principles simulation suite to engage easily with in situ Hubbard parameters and streamline their incorporation into material simulations of interest. Features of this utility, which may also interest users and developers of other DFT codes, include $n$-degree polynomial regression, error analysis, Python plotting facilities, didactic documentation, and avenues for further developments. In this technical introduction and guide, we place particular emphasis on the intricacies and potential pitfalls introduced by the projector augmented wave (PAW) method, SCF mixing schemes, and non-linear response, several of which are translatable to DFT+U(+J) implementations in other packages.

High-performance batteries, heterogeneous catalysts, and next-generation photovoltaics often centrally involve transition metal oxides (TMOs) that undergo charge or spin-state changes. Demand for accurate DFT modeling of TMOs has increased in recent years, driving improved quantification and correction schemes for approximate DFT's characteristic errors, notably those pertaining to self-interaction and static correlation. Of considerable interest, meanwhile, is the use of DFT-accessible quantities to compute parameters of coarsegrained models such as for magnetism. To understand the interference of error corrections and model mappings, we probe the prototypical Mott-Hubbard insulator NiO, calculating its electronic structure in its antiferromagnetic I/II and ferromagnetic states. We examine the pronounced sensitivity of the first-principles calculated Hubbard parameters U and J to choices concerning projector augmented wave (PAW) based population analysis, we reevaluate spin quantification conventions for the Heisenberg model, and we seek to develop best practices for calculating Hubbard parameters specific to energetically metastable magnetic orderings of TMOs. Within this framework, we assess several corrective functionals using in situ calculated U and J parameters, e.g., DFT+U and DFT+U+J. We find that while using a straightforward workflow with minimal empiricism, the NiO Heisenberg parameter RMS error with respect to experiment was reduced to 13%, an advance upon the state-of-the-art. Methodologically, we used a linear-response implementation for calculating the Hubbard U available in the open-source plane-wave DFT code ABINIT. We have extended its utility to calculate the intra-atomic exchange coupling J; however, our findings are anticipated to be applicable to any DFT+U implementation.

In density functional theory calculations of materials and molecules, it is conventional to neglect the relativistic magnetostatic contribution of unpaired electron spins to the total energy and potential. For small systems, the magnetostatic contribution to the total energy is negligible, yet it is not obvious that it remains negligible in extended systems with high spin magnetic moment. We make use of a mathematical shortcut, using a fictitious magnetic charge density, to calculate the magnetic field and to determine the degree to which this relativistic effect can be ignored in electronic structure calculations. Using this, we compare the strength of the magnetostatic energy to the electrostatic energy. This ratio is consistently on the order of 10−5, which is on the order of 1/c2 in atomic units, as is expected from its formula.