Benchmarking DFT approximations for studying apatites.

Despite the growing interest in apatites, available experimental studies on their properties are limited in scope. Researchers, therefore, are increasingly resorting to predictions using density functional theory (DFT). However, large deviations can be seen between DFT-based estimates and experimental results, presumably due to approximations made in DFT models.

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [Kanungo, B. 2024, 15, 323-328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is rSCAN 50, a 50% global hybrid of exact exchange with rSCAN, which may be less correct than rSCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters.

Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights.

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, which has been known for ∼30 years. The conventional explanation is that the Hartree-Fock theory yields the more accurate density.

Exact and Model Exchange-Correlation Potentials for Open-Shell Systems.

The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities.

Exchange correlation potentials from full configuration interaction in a Slater orbital basis.

Ryabinkin-Kohut-Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, full configuration interaction computations in the Slater orbital basis are employed to give quality input to RKS, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction.

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis.

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis.

A Comparison of Exact and Model Exchange-Correlation Potentials for Molecules.

Accurate exchange-correlation (XC) potentials for three-dimensional systems─via solution of the density functional theory (DFT) problem─are now available to test the quality of DFT approximations. Herein, the XC potential for seven molecules─dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne─are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals.

Exact exchange-correlation potentials from ground-state electron densities.

The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity-the electron density-without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore.