Fundamental Studies of Electron Correlation with Applications to DFT

应用量子力学(QM)可以理解原子、分子及其反应。为了在化学体系(称为量子化学)中准确地使用量子力学，我们需要了解电子如何与分子中的原子核相互作用，以及如何相互作用。问题是，对于含有多个电子的系统，QM方程不能精确求解，因此主流计算量子化学建立在近似的单电子模型上，该模型以平均方式处理电子-电子相互作用。然而，电子是瞬间相互作用的，因此它们的运动是相互关联的。这两种方法的不同之处被称为“电子关联”。我们不能忽视电子关联，因为关联能在大小上类似于形成或断裂化学键的能量。我们应用量子化学的每个系统都需要更便宜、更准确的方法来计算这种关键的相互作用。这项建议的第一部分涉及通过优雅的级数求解方法精确计算两电子和一个核的基本模型系统的电子关联。这种方法增加了几个优点，因为它在计算上非常高效和准确。我们将计算高精度的电子关联数据，以全面了解电子如何相互作用，即使在很长的范围内也是如此。本提案的第二部分涉及使用这种新的、高精度的关联数据来开发化学科学中使用最广泛的技术之一，密度泛函理论(DFT)。DFT目前被用来提供新的知识，并支持从纳米材料和矿物学到生物分子和药物发现等领域的实验研究。它的成功源于其计算速度和可靠性的独特平衡，但随着DFT扩展到更复杂和更奇异的化学区域，关键潜在近似的缺陷开始显现。这限制了当前DFT可寻址的系统的复杂性。在这项工作中，我们将设计和开发两个用于DFT的新的相关函数，通过将创新的新形式与新的高精度数据相匹配。第一种形式将基于一种形式，该形式准确地模拟从弱电子关联极限到强电子关联极限的所有点的电子关联。第二种涉及一种全新的功能形式。这些新泛函旨在带来的优势是提高精确度，不仅适用于标准应用，也适用于更复杂和/或奇异的化学体系，以及具有显著远程、低密度行为的系统，例如石墨烯或二维量子点。成功的泛函将在Molpro计算化学程序包中实现，以便世界各地的计算科学家能够获得高精度的方法，用于他们自己的尖端研究，加强新知识的发现，以便在现实世界中直接应用。这项建议的最后部分涉及编写新的代码来模拟三体系统的激发态。它将直接包括电子-电子距离，以准确地模拟电子的关联运动和原子核的运动。这将使我们能够探测激发态的电子动力学，并计算包括核运动在内的光谱性质。光谱是许多科学领域的重要技术：包括大气化学、天体化学和天体物理观测，因此可以帮助我们理解例如温室效应和宇宙的结构。特别强调里德堡原子(大轨道原子)，因为它们在量子计算中是非常热门的。

Atoms, molecules and their reactions can be understood by applying quantum mechanics (QM). In order to use QM accurately in a chemical system (known as quantum chemistry), we need to understand how the electrons interact with the nuclei of the atoms in a molecule, and with each other. The problem is that the equations of QM cannot be solved exactly for systems with more than one electron, and so mainstream computational quantum chemistry is built on approximate one-electron models that treat the electron-electron interactions in an average way. However, electrons interact instantaneously and so their motion is correlated. The difference between these two approaches is known as 'electron correlation'. We cannot ignore electron correlation because the correlation energy is similar in size to the energy of making or breaking chemical bonds. Every system to which we apply quantum chemistry needs cheaper, accurate, methods for calculating this critical interaction. The first part of this proposal involves accurately calculating the electron correlation of the basic model system of two electrons and a nucleus, via an elegant series solution method. This method adds several advantages in that it is extremely computationally efficient and accurate. We will calculate highly accurate electron correlation data to develop a full understanding of how electrons interact, even at long range.The second part of this proposal involves using this new, highly accurate, correlation data to develop one of the most widely used techniques in the chemical sciences, density functional theory (DFT). DFT is currently used to provide new knowledge, and to support experimental studies, in areas ranging from nanomaterials and mineralogy to biomolecules and drug discovery. Its success derives from its unique balance of computational speed and reliability, but as DFT is stretched to more complex and exotic chemical regimes, the flaws of key underlying approximations begin to show. This puts a limit on the complexity of systems addressable by current DFT. In this work, we will design and develop two new correlation functionals for use in DFT, by fitting innovative new forms to the new highly accurate data. The first will be based on a form that accurately models electron correlation at all points from the weak to the strong electron correlation limit. The second involves an entirely new functional form. The advantage these new functionals aim to bring is increased accuracy, not only for standard applications, but also for more complex and/or exotic chemical regimes, and for systems where long-range, low-density behavior is prominent, e.g. graphene or 2-D quantum dots. Successful functionals will be implemented in the Molpro computational chemistry package so that computational scientists worldwide can gain access to high accuracy methods for use in their own cutting-edge research, enhancing the discovery of new knowledge for direct applications in the real world.The final part of this proposal involves writing new code to model excited states of three-body systems. It will include directly the electron-electron distance to model accurately the correlated motion of the electrons, and the motion of the nucleus. This will enable us to probe the electron dynamics in excited states and to calculate spectroscopic properties with nuclear motion included. Spectroscopy is an important technique in many areas of science: including atmospheric chemistry, astrochemistry, and astrophysical observations and thus can help us understand e.g. the greenhouse effect and structure of the universe. A particular emphasis will be on Rydberg atoms (large orbit atoms), as these are extremely topical in quantum computing.