Bridging the gap between accurate ab initio many-body theory and simple density-functionals

密度泛函理论是当今量子力学方法的最前沿，用于描述分子和材料，这些分子和材料是各种技术的基石。该方法的预测能力和准确性的关键是处理电子的量子力学交换和相关相互作用。目前这些贡献的近似值仅限于一个狭窄的舒适区的适用性-本提案中的工作将开发新的近似值，以显着扩大可行的应用范围。描述能量的交换和相关贡献的方法通常是基于电子密度分布及其梯度的相对简单的模型。采用基于多电子波函数的第一性原理方法可以获得更高的精度。在这项工作中，我们构建了一个共同的框架，这些昂贵的高精度的方法与简单的密度泛函近似的比较。该框架为新的简单模型的发展提供了新的见解-特别是密度的高阶导数被强调为描述电子相关性的关键变量。基于这个量的泛函将在这项工作中开发，开辟了更准确和更强大的相关性处理的道路-消除困扰当今近似的错误取消。

Density-functional theory is at the forefront of today's quantum mechanical approaches for the description of the molecules and materials that are the building blocks for a diverse range of technologies. The key to the predictive power and accuracy of the approach is the treatment of the quantum mechanical exchange and correlation interactions of the electrons. Present-day approximations for these contributions are limited to a narrow comfort zone of applicability - the work in this proposal will develop new approximations to significantly expand the range of viable applications. Methods to describe the exchange and correlation contributions to the energy are often relatively simple models based on the electronic density distribution and its gradient. Higher accuracy can be obtained using first-principles techniques based on the many-electron wave function. In this work we construct a common framework for the comparison of these expensive high accuracy approaches with simple density-functional approximations. This framework gives new insight into the development of new simple models - in particular the higher derivatives of the density are highlighted as a key variables for the description of electronic correlation. Functionals based on this quantity will be developed in this work, opening the way to more accurate and robust correlation treatments - removing error cancellations that plague present-day approximations.