Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn–Sham potential

 

Egor Ospadov, Jianmin Tao, Viktor N. Staroverov, and John P. Perdew

1. ^aDepartment of Chemistry, The University of Western Ontario, London, ON N6A 5B7, Canada;
2. ^bDepartment of Physics, Temple University, Philadelphia, PA 19122;
3. ^cDepartment of Chemistry, Temple University, Philadelphia, PA 19122

 

 

Abstract

The Kohn–Sham potential veff(r) 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 ϵmax be the maximum occupied orbital energy of the noninteracting electrons. Then the equation veff(r)=ϵmax defines the surface at which classical electrons with energy ϵ≤ϵmax 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 Chem 62:47–53; Zhao DX, et al. (2018) Mol Phys 116:969–977] 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.

 

https://www.pnas.org/content/115/50/E11578