标题： 量子化学中哈特里-福克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： 我们在这里回顾了量子化学中Hartree-Fock理论的基本主题。 从分子哈密顿量出发，通过使用和讨论Born-Oppenheimer近似，得出电子问题的Hartree和Hartree-Fock方程。 特别强调了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。 所有具有不同自旋限制的Hartree-Fock版本都从一般情况中系统地提取出来，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，并引入了Roothaan-Hall形式。 这导致了与构建和选择高斯基组相关的基本概念的阐述，重点在于算法效率问题。 最后，我们以一个部分结束综述，其中评论并联系了最相关的现代发展（特别是与线性尺度方法设计相关的部分）到之前讨论的问题。 整个工作是故意作为入门材料并且相对自包含，以便为希望在跨学科应用中使用量子化学方法的非专家提供帮助。 此外，许多在文献中分散的内容已被汇集在此，以促进理解并作为便捷的参考。 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.