Systematic approach to Density Functional Theory

加州大学欧文分校的基隆·伯克获得了化学理论、模型和计算方法项目的一项奖励，以开发提高电子结构计算的准确性和可靠性的方法。现代化学和材料研究越来越依赖于电子结构计算，即求解电子的量子力学方程来预测或理解电子的物理化学性质。伯克的方法利用量子力学的非常基本的性质，以高度系统的方式推导出改进的近似。其智力价值在于比以前更深入地理解电子的量子本质，以一种显著减少错误的方式。影响可能是巨大的，因为它可以改进每年数千篇科学论文的电子结构计算，包括那些与药物发现、新催化剂和新物质相识别有关的论文。还有一个基础广泛的教育部分，因为研究生、本科生和高中生都参与了这项研究。伯克和他的研究小组结合了来自三个不同学科的理论方法。通过对决定量子效应强度的基本量普朗克常数的幂的渐近展开，使用了一种系统的非经验方法来进行密度泛函近似。对于模型系统，可以明确地找到近似，并且比以前的公式产生更准确的结果。对于现实的系统(分子和材料)，一般形式可以用来推导渐近精确的近似，这些近似大大改进了今天使用的那些，并约束了更复杂的方法。这些方法也被应用于无轨道电子结构计算问题，这有望使密度泛函理论(DFT)计算获得更大的距离和时间尺度。这项工作包括一种替代目前使用的DFT框架的策略，称为势函数理论。与热密度泛函的自然联系有可能在分子和热致密物质的含时密度泛函理论中得到有用的应用。

Kieron Burke of the University of California-Irvine is supported by an award from the Chemical Theory, Models and Computational Methods program to develop methods that improve the accuracy and reliability of electronic structure calculations. Modern chemical and materials research increasingly relies on electronic structure calculations, i.e., solving the equations of quantum mechanics for electrons to predict or understand physical and chemical properties. Burke's method uses very fundamental properties of quantum mechanics to derive improved approximations in a highly systematic fashion. The intellectual value is to understand the quantum nature of electrons more deeply than before, in a way that significantly reduces errors. The impact could be significant, as it could improve electronic structure calculations for thousands of scientific papers each year, including those related to drug discovery, and to the identification of new catalysts, and new phases of matter. There is also a broad-based educational component, as graduate, undergraduate, and high school students are involved in the research.Burke and his research group combine theoretical methods from three different disciplines. A systematic non-empirical approach to density functional approximation is used, via an asymptotic expansion in powers of Planck's constant, the fundamental quantity that determines the strength of quantum effects. For model systems, the approximations can be found explicitly, and yield far more accurate results than previous formulas. For realistic systems (molecules and materials), the general forms can be used to deduce asymptotically exact approximations that significantly improve on those in use today, and constrain more sophisticated approaches. The methods are also applied to the problem of orbital-free electronic structure calculations, which holds the promise of making much larger distance and time scales accessible to density functional theory (DFT) calculations. The work includes an alternative strategy to the DFT framework in use today, called potential functional theory. A natural connection with thermal DFT has the potential to lead to useful applications in the time-dependent density functional theory of molecules and of warm dense matter.