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The Kohn–Sham potential$v_{\text{eff}}\left(\mathbf{r}\right)$is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn–Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let${ϵ}_{\text{max}}$be the maximum occupied orbital energy of the noninteracting electrons. Then the equation$v_{\text{eff}}\left(\mathbf{r}\right)={ϵ}_{\text{max}}$defines the surface at which classical electrons with energy$ϵ\le {ϵ}_{\text{max}}$would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997)Int J Quantum Chem62:47–53; Zhao DX, et al. (2018)Mol Phys116:969–977] by our consideration of the Kohn–Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.

 

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.