We present a parameter-free method for an accurate determination of long-range van der Waals interactions from mean-field electronic structure calculations. Our method relies on the summation of interatomic C6 coefficients, derived from the electron density of a molecule or solid and accurate reference data for the free atoms. The mean absolute error in the C6 coefficients is 5.5% when compared to accurate experimental values for 1225 intermolecular pairs, irrespective of the employed exchange-correlation functional. We show that the effective atomic C6 coefficients depend strongly on the bonding environment of an atom in a molecule. Finally, we analyze the van der Waals radii and the damping function in the C6R(-6) correction method for density-functional theory calculations.

First-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation for the exchange-correlation functional is crucial, as it strongly affects the accuracy of DFT calculations. This study compares the performance capabilities of three approximations on the energetics, mechanical and electronic properties, and crystal structure of NaAlP₂O₇, which is an insulator with a wide band gap that suppresses its electronic conductivity. Two of these approximations are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) and the other on the strongly constrained and appropriately normed (SCAN) meta-GGA. We explore these materials as a contribution to the development of new solid electrolytes (SEs) for sodium-ion batteries (NIBs), which have the potential to mitigate challenges related to lifecycle, safety, and low ionic conductivity. The performance of these batteries largely emanates from the extraordinary demand for high-performing energy storage technologies. This study revealed that PBEsol accurately predicted lattice parameters that closely aligned with experimental values. However, r2SCAN provided the most reliable predictions of the structural and electronic properties of the NaAlP₂O₇ solid electrolyte compared to PBE and PBEsol. Findings demonstrated that the material is structurally, mechanically, electronically, and thermodynamically stable, but exhibits vibrational instability, which may scatter ions and reduce ionic conductivity due to the presence of imaginary frequencies. Our results highlight the importance of selecting appropriate functionals for solid electrolyte DFT computations. The r2SCAN functional appears to be a promising choice for calculating NaAlP₂O₇ properties.

simplest approximations is the local-density approximation (LDA), where the functional depends only on the density at the coordinate where the functional is Density functional theory (DFT) is a computational quantum mechanical modeling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using fun Density functional theory (DFT) is a computational quantum mechanical modeling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals – that is, functions that accept a function as input and output a single real number. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered sufficiently accurate for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. Computational costs are relatively low when compared to traditional methods, such as exchange only Hartree–Fock theory and its descendants that include electron correlation. Since, DFT has become an important tool for methods of nuclear spectroscopy such as Mössbauer spectroscopy or perturbed angular correlation, in order to understand the origin of specific electric field gradients in crystals. DFT sometimes does not properly describe: intermolecular interactions (of critical importance to understanding chemical reactions), especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces, dopant interactions and some strongly correlated systems; and in calculations of the band gap and ferromagnetism in semiconductors. The incomplete treatment of dispersion can adversely affect the accuracy of DFT (at least when used alone and uncorrected) in the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects (e.g. in biomolecules). New DFT methods have been designed to overcome this problem,…

Understanding molecular adsorption on surfaces underpins many problems in chemistry and materials science. Accurately and efficiently describing the adsorption has been a challenging task for first-principles methods as the process can involve both short-range chemical bond formations and long-range physical interactions, e.g., van der Waals (vdW) interaction. Density functional theory presents an appealing choice for modeling adsorption reactions, although calculations with many exchange-correlation density functional approximations struggle to accurately describe both chemical and physical molecular adsorptions. Here, we propose an efficient density functional approximation that is accurate for both chemical and physical adsorption by concurrently optimizing its semilocal component and the long-range vdW correction against the prototypical adsorption CO/Pt(111) and Ar₂ binding energy curve. The resulting function opens the door to accurate and efficient modeling of general molecular adsorption.