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

密度泛函理论是多粒子量子力学的一个特殊的分支，其中粒子密度而不是波函数是基本量。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深入了解材料的性质，这些计算机模拟仅基于量子力学的基本定律，即，没有经验的输入。例如，计算可以预测原子如何组装形成分子和晶体，从而有助于发现和开发新材料。在实际计算中，我们需要描述交换和关联的量子力学多体效应的近似值。交换相关泛函对于密度泛函理论计算的精确度和数值开销都是决定性的。特别是预测在能源相关材料中重要的性质，例如，太阳能电池材料的带隙或催化剂中的电荷转移现象迄今为止需要使用计算上昂贵的交换相关泛函。因此，很难模拟具有许多电子的大型系统。该项目的目的是开发一种新的近似交换和相关性，其计算成本适中，因此它允许进行大型模拟，但同时对于带隙，结合能和电荷转移是准确的。把这些不同的属性放在一起是可能的一类特殊的交换相关近似称为元广义梯度近似。

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.