Commonly used semilocal density functional approximations for the exchange-correlation energy fail badly when the true two dimensional limit is approached. We show, using a quasi-two-dimensional uniform electron gas in the infinite barrier model, that the semilocal level can correctly recover the exchange-correlation energy of the two-dimensional uniform electron gas. We derive new exact constraints at the semilocal level for the dimensional crossover of the exchange-correlation energy and we propose a method to incorporate them in any exchange-correlation density functional approximation.
@article{arxiv.0906.5037,
title = {Dimensional crossover of the exchange-correlation energy at the semilocal level},
author = {Lucian A. Constantin},
journal= {arXiv preprint arXiv:0906.5037},
year = {2015}
}