多电子量子力学库仑问题到O（N^（2/3）存储的实用和严格的简化
Practical and Rigorous reduction of the Many-Electron Quantum-Mechanical Coulomb Problem to O(N^(2/3) Storage
摘要：
人们默认，对于由N个函数组成的实际基组，解决量子力学中的双电子库仑问题需要在小N极限下存储O（N^4）个积分。对于局部化函数，在大N极限下，或者对于平面波，由于闭包，存储可以减少到O（N^2）积分。这里，它表明，存储可以进一步减少到O（N^{2/3}）的可分离基函数。一个实用的算法，使用标准的一维高斯正交和，证明。由此产生的算法允许同时存储，或快速重建，任何两个电子库仑积分所需的多电子计算，在每一个处理器的大规模并行计算机，即使这样的处理器有非常有限的内存和磁盘空间。例如，对于涉及9171个平面波的基础的计算，有效地存储所有库仑积分所需的存储器从2.8Gbytes减少到小于2.4Mbytes。
英文摘要：
It is tacitly accepted that, for practical basis sets consisting of N functions, solution of the two-electron Coulomb problem in quantum mechanics requires storage of O(N^4) integrals in the small N limit. For localized functions, in the large N limit, or for planewaves, due to closure, the storage can be reduced to O(N^2) integrals. Here, it is shown that the storage can be further reduced to O(N^{2/3}) for separable basis functions. A practical algorithm, that uses standard one-dimensional Gaussian-quadrature sums, is demonstrated. The resulting algorithm allows for the simultaneous storage, or fast reconstruction, of any two-electron coulomb integral required for a many-electron calculation, on each and every processor of massively parallel computers even if such processors have very limited memory and disk space. For example, for calculations involving a basis of 9171 planewaves, the memory required to effectively store all coulomb integrals decreases from 2.8Gbytes to less than 2.4 Mbytes.
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