Bandgaps, binding energies and charge transfer in density functional theory from a meta-generalized gradient approximation

密度泛函理论是许多粒子量子力学的一个特殊分支，其中基本量是粒子密度而不是波函数。借助密度泛函理论计算，人们可以预测原子、分子和固体的结构和性质。因此，该理论被用于化学、凝聚态物理和材料科学的许多领域，以便在计算机模拟中洞察材料的性质，这些模拟只基于量子力学的基本定律，即没有经验输入。例如，计算可以预测原子如何聚集形成分子和晶体，从而有助于发现和开发新材料。对于实际计算，我们需要描述交换和关联的量子力学多体效应的近似。交换关联泛函对密度泛函理论计算的精度和数值代价都起着决定性的作用。特别是对与能源相关的材料的重要性质的预测，例如太阳能电池材料的带隙或催化剂中的电荷转移现象，到目前为止需要使用计算昂贵的交换相关泛函。因此，模拟具有许多电子的大系统是困难的。这个项目的目的是开发一种新的交换和关联近似，它的计算成本适中，这样它就可以进行大型模拟，同时对带隙、结合能和电荷转移也是准确的。在一类特殊的交换相关近似中，将这些不同的性质结合在一起是可能的，这类近似被称为亚广义梯度近似。

Density functional theory is a special branch of many particle quantum mechanics in which the particle density and not the wavefunction is the fundamental quantity. With the help of density functional theory calculations one can predict the structure and the properties of atoms, molecules and solids. The theory therefore is used in many areas of chemistry, condensed matter physics and material science in order to gain insight into the properties of materials in computer simulations that are based only on the fundamental laws quantum mechanics, i.e., without empirical input. For example, calculations can predict how atoms assemble to form molecules and crystals, and can thus help to discover and develop new materials. For practical calculations one needs approximations that describe the quantum mechanical many-body effects of exchange and correlation. The exchange-correlation functional is decisive both for the accuracy and the numerical expense of density functional theory calculations. In particular the prediction of properties that are important in energy relevant materials, e.g., the band gaps of solar cell materials or charge-transfer phenomena in catalysts, so far requires the use of computationally expensive exchange-correlation functionals. Therefore, it is difficult to simulate large systems with many electrons. The aim of this project is to develop a new approximation for exchange and correlation that comes at moderate computational cost, so that it allows for large simulations, yet at the same time is accurate for band gaps, binding energies, and charge transfer. Bringing these different properties together is made possible within a special class of exchange-correlation approximations called meta-Generalized Gradient Approximations.