Quantum electronic transport properties of 3d transition metal doped SnO monolayer for spin-thin film transistor

Electrochemical Behaviors and Doping Rules of NaRhO2 Cathode Materials for Sodium-Ion Batteries

“…As the GGA method was expected to underestimate the band gap of insulators, the Hubbard model was adopted to account for the Coulombic or repulsive interactions of the on-site d electrons. − DFT + U has been proposed to improve the description of systems with strongly correlated d electrons. However, due to the lack of a reasonable U value between calculations and experiments, the U parameter was determined through linear response approach for the Rh atom in NaRhO 2 . − Evaluation of the U parameter can be performed relying on the definition of U as the difference of the double derivatives of the total energy over the density of the interacting and noninteracting multielectron system, U = ∂ 2 E int ∂ q normalI 2 − ∂ 2 E non ∂ q normalI 2 where q I is the variation in electron density localized on atom I. Equivalently, U can be expressed as the difference in the second derivatives of the localized electron energies with respect to the density of the noninteracting and interacting systems U = ∂ 2 α normalI non ∂ q normalI 2 − ∂ 2 α normalI int ∂ q normalI 2 A linear response approach provides such an alternative route. , The U parameter can be evaluated as the difference in the diagonal elements of the inverse response functions for the noninteracting and interacting systems U = false( χ − 1 non − χ − 1 int false) II …”