Nonlocal exchange and correlation energy functionals using the Yukawa potential as ingredient: Application to the linear response of the uniform electron gas

Abstract

We show that the reduced, dimensionless Yukawa potential ${y}_{\ensuremath{\alpha}}$ can be employed as an important ingredient in the construction of the exchange and correlation energy functionals. A functional based on ${y}_{\ensuremath{\alpha}}$ provides a better description of the exchange and correlation linear response functions of the homogeneous electron gas, not only at small wave vectors, where gradient expansions are correct, but also at large wave vectors, where semilocal exchange and correlation functionals fail badly. Moreover, the ${y}_{\ensuremath{\alpha}}$ ingredient gives a realistic description of the exchange energy and potential at the nuclear cusp and the inner atomic core, where the semilocal ingredients (i.e., the reduced gradient and Laplacian of the density) are not suitable, causing divergence of the potential. Thus, the ${y}_{\ensuremath{\alpha}}$ ingredient can be attractive for the development of various exchange-correlation functionals.