Materials World Network: Solving Longstanding Problems of Density-Functional Theory with Quantum Monte Carlo

该材料世界网络（MWN）奖支持康奈尔大学和埃尔兰根-纽伦堡大学之间的联合研究项目，使用量子蒙特卡罗（QMC）方法来回答长期存在的问题，即半导体和绝缘体的Kohn-Sham带隙和真正的基本带隙的差异大小。这种差异就是所谓的导数不连续性--整数电子数下交换相关能的不连续性。 这是一个不仅在密度泛函理论（DFT）中具有重要基础意义，而且在材料带隙工程中具有重要实际意义的问题。 例如，准确预测无机半导体和廉价有机半导体的带隙对于设计光伏电池非常重要。这个建议的另一个目标是确定几乎精确的交换相关势的一些材料，将构成一个参考，在新的密度泛函的发展。该项目涉及培训美国和德国的研究生，学生和教师访问他们的伙伴机构，以及在国际会议上进行交流。美国和德国的研究生都将获得最先进的QMC和DFT方法的全面基础。 德国研究生将成为埃尔朗根-纽伦堡大学新成立的分子科学研究生院的成员，美国研究生将有机会参加那里提供的夏季和冬季学校。还将与巴黎大学的教师和研究生进行交流。计算出的近似精确的DFT量将通过网络广泛传播。

This Materials World Network (MWN) award supports a joint research project between Cornell University and Universitat Erlangen-Nurnberg to use quantum Monte Carlo (QMC) methods to answer the longstanding question of the size of the difference of the Kohn-Sham band gap and the true fundamental band gap of a semiconductors and insulators. This difference is the so called derivative discontinuity -- the discontinuity of the exchange-correlation energy at integer electron numbers. This is a question that is not only of great fundamental importance in density functional theory (DFT) but also of great practical significance for band-gap engineering of materials. For example, accurate predictions of the bandgaps of inorganic semiconductors and of inexpensive organic semiconductors is important for designing photovoltaic cells. Another goal of this proposal is to determine nearly exact exchange-correlation potentials for a number of materials that would constitute a reference in the development of new density functionals. Such a reference, so far, is missing for periodic systems.This project involves training US and the German graduate students and visits by the students and faculty to their partner institutions as well as exchanges at international conferences. Both the US and the German graduate students will receive a thorough grounding in state of the art QMC and DFT methods. The German graduate student will be a member of the newly founded Graduate School for Molecular Science at the University Erlangen-Nuremberg and the US graduate student will have the opportunity to attend summer and winter schools offered there. There will also be exchanges with faculty and graduate students at the University of Paris. The computed nearly exact DFT quantities will be dissminated widely via the web.