标题： 量子化学中Hartree-Fock自洽场方法的数学与计算综述 显示英文标题

标题： A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

摘要： 我们在这里回顾量子化学中哈特里-福克理论的基本主题。从分子哈密顿量出发，利用并讨论玻恩-奥本海默近似，我们得到了哈特里和哈特里-福克方程用于电子问题。重点放在最终方程理论推导中最相关的数学方面，以及关于其解的存在性和唯一性的结果上。所有具有不同自旋限制的哈特里-福克版本都从一般情况系统地提取出来，从而提供了一个统一的框架。然后，回顾了一电子轨道空间的离散化，并介绍了鲁坦-霍尔形式主义。这导致了与高斯基组的构建和选择相关的基础概念的阐述，重点关注算法效率问题。最后，我们以一个部分结束这篇综述，该部分评论并联系了现代发展的最相关方面（特别是与线性标度方法设计相关的内容）。整个工作是有意作为入门性的并且相当自成体系的，以便对非专家有用，他们希望在跨学科应用中使用量子化学方法。此外，这里汇集了许多分散在文献中的材料，以方便理解并作为实用的参考。 显示英文摘要

摘要： We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.