Accurate Nonempirical Density-Functional Methods with Applications

量子化学是化学研究中一个高度专业化但又极其重要的分支。量子化学家工作的最显著成果是预测数学模型和计算机程序，它们被成千上万的工业界和学术界研究人员用作工具，用于解开化学过程的复杂性，预测物质在正常和极端条件下的物理性质，设计新材料，以及寻找具有目标药用特性的分子。我们的团队是开发此类工具的团队之一；我们专门研究一种叫做密度泛函理论（DFT）的量子力学技术。在之前的授权期内，我们提出了一种非常规的DFT方法，其中直接近似有效的单电子势而不是能量泛函。在接下来的五年中，我们将通过将基于势的DFT与非经验波函数方法相结合，将其准确性和实用性提升到一个新的水平。特别是，我们将(1)开发概念上的新方法来构建交换相关势，这将使研究人员能够设计出更好的密度泛函和多尺度方法，用于材料的计算机模拟；(2)利用我们的新工具——平均局部电子能量，更好地理解化学结构和性质之间的关系；(3)探索Schrödinger方程的特殊化简形式，揭示波函数方法与DFT之间的基本联系；(4)设计了一种新的密度泛函方法来研究时变多电子现象；(5)测试新的想法以克服现有近似函数的局限性；(6)根据模型电位构造精确的密度泛函。提议的研究成果将包括新的计算方法，用于研究反应机制，定量构效关系的分析，以及在材料科学，阿秒光谱学和其他领域的应用。在培养高素质人才方面，该研究将成为10篇研究生论文和5篇本科生论文的基础，并将为跨学科的合作贡献专业知识。

Quantum chemistry is a highly specialized yet critically important branch of chemical research. The most visible outcomes of the work of quantum chemists are predictive mathematical models and computer programs which are used as tools by thousands of researchers in industry and academia to unravel the intricacies of chemical processes, predict physical properties of matter under normal and extreme conditions, design new materials, and search for molecules with target medicinal properties. Our group is one of those that develop such tools; we specialize in a particular quantum-mechanical technique called density-functional theory (DFT). Over the previous granting period, we have advanced an unconventional approach to DFT in which one directly approximates effective one-electron potentials rather than energy functionals. In the next five years, we will take the potential-based DFT to a new level of accuracy and utility by bridging it with nonempirical wavefunction methods. In particular, we will (1) develop conceptually new methods for constructing exchange-correlation potentials which will enable researchers to devise better density-functional and multiscale methods for use in computer simulations of materials; (2) employ our new tool called the average local electron energy to obtain a better understanding of the relation between chemical structure and properties; (3) explore a special reduced form of the Schrödinger equation to uncover fundamental connections between wavefunction methods and DFT; (4) devise a new density-functional approach for studying time-dependent many-electron phenomena; (5) test new ideas to overcome limitations of existing approximate functionals; (6) construct accurate density functionals from model potentials. Tangible outcomes of the proposed research will include new computational methods for investigation of reaction mechanisms, analysis of quantitative structure-activity relationships, and for applications in materials science, attosecond spectroscopy, and other fields. In terms of highly qualified personnel training, the research will form the basis for 10 graduate and 5 undergraduate theses and will contribute expertise to collaborations across interdisciplinary boundaries.