Approximating constant potential DFT with canonical DFT and electrostatic corrections.

The complexity of electrochemical interfaces has led to the development of several approximate density functional theory (DFT)-based schemes to study reaction thermodynamics and kinetics as a function of electrode potential. While fixed electrode potential conditions can be simulated with grand canonical ensemble DFT (GCE-DFT), various electrostatic corrections on canonical, constant charge DFT are often applied instead. In this work, we present a systematic derivation and analysis of the different electrostatic corrections on canonical DFT to understand their physical validity, implicit assumptions, and scope of applicability. Our work highlights the need to carefully address the suitability of a given model for the problem under study, especially if physical or chemical insight in addition to reaction energetics is sought. In particular, we analytically show that the different corrections cannot differentiate between electrostatic interactions and covalent or charge-transfer interactions. By numerically testing different models for CO2 adsorption on a single-atom catalyst as a function of the electrode potential, we further show that computed capacitances, dipole moments, and the obtained physical insight depend sensitively on the chosen approximation. These features limit the scope, generality, and physical insight of these corrective schemes despite their proven practicality for specific systems and energetics. Finally, we suggest guidelines for choosing different electrostatic corrections and propose the use of conceptual DFT to develop more general approximations for electrochemical interfaces and reactions using canonical DFT.

Interactions of ions across carbon nanotubes.

The interactions between a pair of Li+ ions across a semiconducting (8,0)CNT and a conducting (5,5)CNT has been investigated by density functional theory. The direct Coulomb interaction between the ions is almost completely screened. The band structure of the CNTs is not affected by the Li+ ions, but the Fermi level is raised to accommodate the extra electrons. Because of the unique band structure of CNTs this results in an effective attraction between the ions, which is greater for the (8,0)CNT. In contrast, a Cl- ion inside a CNT forms a chemical bond which modifies the band structure. Again, the electrostatic field of the ion is almost completely screened outside of the tube. Nevertheless, the adsorption of a Li+ ion outside is favored by a Cl- ion inside. This apparent attraction is mainly caused by a lowering of the work function of the CNT by the presence of the Cl-.