A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems.

The method of constructing semilocal density functional for exchange in two dimensions using one of the premier approaches, i.e., density matrix expansion, is revisited, and an accurate functional is constructed. The form of the functional is quite simple and includes no adjustable semiempirical parameters. In it, the kinetic energy dependent momentum is used to compensate nonlocal effects of the system. The functional is then examined by considering the very well-known semiconductor quantum dot systems. And despite its very simple form, the results obtained for quantum dots containing a higher number of electrons agrees pretty well with that of the standard exact exchange theory. Some of the desired properties relevant for the two-dimensional exchange functional and the lower bound associated with it are also discussed. It is observed that the above parameter-free semilocal exchange functional satisfies most of the discussed conditions.