Using the semiclassical neutral atom theory, we extend to fourth order the modified gradient expansion of the exchange energy of density functional theory. This expansion can be applied both to large atoms and solid-state problems. Moreover, we show that it can be employed to construct a simple and non-empirical generalized gradient approximation (GGA) exchange-correlation functional competitive with state-of-the-art GGAs for solids, but also reasonably accurate for large atoms and ordinary chemistry.

翻译：使用半古典中性原子理论,我们将密度功能理论交换能量的经修改梯度膨胀扩大到第四顺序。这种膨胀可以适用于大型原子和固态问题。此外,我们证明,它可以用来构建一个简单和非经验性通用梯度近似(GGA)的交换-关系功能竞争力,与最先进的GGGAs的固态相竞争,但对于大型原子和普通化学而言,也相当准确。