Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory.
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory.
复制标题
张量超收缩密度拟合。四次标度二阶和三阶 Møller-Plesset 微扰理论。
DOI：
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发表时间：
2012
影响因子：
4.4
通讯作者：
T. Martínez
中科院分区：
文献类型：
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作者：
E. Hohenstein;R. Parrish;T. Martínez
已经开发了许多近似来帮助处理电子排斥积分（ERI）张量的O（N(4)）增长，其中N是用于表示电子波函数的单电子基函数的数量。其中，密度拟合（DF）近似是目前最广泛使用的，尽管它通常无法改变相对于分子大小的计算工作的潜在比例。我们提出了一种利用三中心重叠积分的稀疏性的方法，通过张量分解来获得密度拟合的低秩近似（张量超收缩密度拟合或THC-DF）。这种新的近似将四阶ERI张量减少到五个矩阵的乘积，同时减少了存储需求，并增加了重新组合项和减少缩放行为的灵活性。作为一个例子，我们证明了二阶和三阶摄动理论（MP2和MP3）的尺度缩减，表明两者都可以在O（N(4)）次操作中完成。这应该与MP2和MP3的通常缩放行为O（N(5)）和O（N(6)）进行比较。THC-DF技术也可以应用于电子结构理论中的其他方法，如耦合簇和组态相互作用，有望在计算效率和存储减少方面取得显着进步。
Many approximations have been developed to help deal with the O(N(4)) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be carried out in O(N(4)) operations. This should be compared to the usual scaling behavior of O(N(5)) and O(N(6)) for MP2 and MP3, respectively. The THC-DF technique can also be applied to other methods in electronic structure theory, such as coupled-cluster and configuration interaction, promising significant gains in computational efficiency and storage reduction.