Development and Application of Nonempirical Density-Functional Methods

Staroverov教授的小组发展了电子结构理论--量子科学的一个分支，用于理解化学键合和预测化学反应的结果。他专门研究密度泛函理论（DFT）的方法，并在Kohn-Sham有效势（DFT的基本成分）的探索方面拥有全球公认的领导地位。DFT的力量还没有完全实现，因为这种方法必须依赖于未知的交换相关泛函的不完美近似。这项建议的首要目标是通过探索计算精确Kohn-Sham势和近似交换相关泛函的高度原创的新方法来提高DFT的能力。短期目标属于三个相互关联的主题。计算方法。所有实际的DFT计算都使用基组，但是Kohn-Sham有效势是通过推导出的公式计算的，就好像基组从来不存在一样，这导致了令人困惑的不一致。为了解决这个问题，我们将开发一种前所未有的方法来构建在所有情况下都能正常工作的交换相关势。我们还将设计一个数值上的上级程序计算交换相关势从有限基组密度，这将成为密度嵌入计划的一部分，用于计算材料的研究。最后，我们将探索一个新的想法，使密度泛函近似正确地工作与拉伸键的分子，这将大大扩大现有的密度泛函在计算催化的权力。理论框架。我们将开始一个系统的探索一种新的方法来计算有效的潜力，在有限的基础上，以消除现有的方法用于这一目的的歧义。我们还将通过推导数学测试来推进有效势理论，这将使DFT研究人员能够判断他们的模型在有限基组中计算分子性质是否具有物理意义。化学应用。我们将解决功能材料化学中的两个难题：硼-甲偶氮染料的基态和电子激发态之间的本质区别是什么，可以解释这些分子的不寻常的光学性质？为什么传统的密度泛函不能描述晶体硼的结构？这些问题的答案将指导实验化学家制造高效的能量转换材料，并将开辟改进DFT的新途径。这项研究的成果将对成千上万的科学家很重要，他们以软件包的形式使用DFT来解决理论，有机，无机和材料化学中的问题。Staroverov教授的学员将获得一套特殊的技术和专业技能，以及为他们在科学和技术领域具有高度影响力的职业生涯做好准备的形成性经验。

Prof. Staroverov's group develops electronic structure theory-a branch of quantum science used to understand chemical bonding and predict outcomes of chemical reactions. He specializes in the approach called density-functional theory (DFT) and holds a globally recognized leadership position in the exploration of Kohn-Sham effective potentials, the fundamental ingredients of DFT. The power of DFT is not yet fully realized because this method has to rely on imperfect approximations to the unknown exchange-correlation functional. The overriding goal of this proposal is to advance the capabilities of DFT by exploring highly original new ways of computing exact Kohn-Sham potentials and approximating the exchange-correlation functional. The short-term objectives fall within three interrelated themes. Computational methods. All practical DFT calculations use basis sets, but Kohn-Sham effective potentials are computed by formulas derived as if basis sets never existed, which leads to confusing inconsistencies. To address this issue, we will develop an unprecedented method for constructing exchange-correlation potentials that works properly in all situations. We will also devise a numerically superior procedure for computing exchange-correlation potentials from finite-basis-set densities, which will become part of density-embedding schemes used in computational materials research. Finally, we will explore a novel idea to make density-functional approximations work correctly for molecules with stretched bonds, which will drastically expand the power of existing density functionals in computational catalysis. Theoretical framework. We will initiate a systematic exploration of a new way to compute effective potentials in finite basis sets in order to eliminate the ambiguities of existing methods used for that purpose. We will also advance the theory of effective potentials by deriving mathematical tests which will enable DFT researchers to tell whether their models are physically sensible for calculating molecular properties in finite basis sets. Chemical applications. We will tackle two puzzles in the chemistry of functional materials: What are the essential differences between the ground and electronically excited states of boron-formazanate dyes that can explain the unusual optical properties of these molecules? Why do conventional density functionals fail for describing crystalline boron hydrides? Answers to these questions will guide experimental chemists making efficient energy conversion materials and will open up new ways of improving DFT. The outcomes of this research will be important to thousands of scientists who use DFT in the form of software packages to solve problems in theoretical, organic, inorganic, and materials chemistry. Prof. Staroverov's trainees will gain an exceptional set of technical and professional skills, and a formative experience preparing them for highly impactful careers in science and technology.