Compressing the Four-Index Two-Electron Repulsion Integral Matrix using the Resolution-of-the-Identity Approximation Combined with the Rank Factorization Approximation,Journal of Chemical Theory and Computation

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Compressing the Four-Index Two-Electron Repulsion Integral Matrix using the Resolution-of-the-Identity Approximation Combined with the Rank Factorization Approximation
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2019-02-27 00:00:00 , DOI: 10.1021/acs.jctc.8b01256
Buu Q. Pham ₁ , Mark S. Gordon ₁

Affiliation

The four-index two-electron repulsion integral (4–2ERI) matrix is compressed using the resolution-of-the-identity (RI) approximation combined with the rank factorization approximation (RFA). The 4–2ERI is first approximated by the RI product. Then, the singular value decomposition (SVD) approximation is used to eliminate low-weighted singular vectors. The SVD RI approximation maintains the canonical form of the RI approximation and introduces a tunable compression factor. The characteristics of the SVD RI approximation along with the stochastic RI and natural auxiliary function approximation were numerically examined by applying these methods to the closed-shell second-order Møller–Plesset perturbation theory (MP2). The results show that, while the SVD RI approximation yields large errors for absolute properties (e.g., the correlation energy), it provides accurate relative properties (potential energy surface, binding energy) of the applied ab initio method (e.g., RHF, MP2).

中文翻译：

压缩使用分辨率的最认同逼近结合的四个指数的双电子排斥积分矩阵秩分解逼近

使用标识分辨率（RI）近似与秩分解近似（RFA）组合，对四指数两电子排斥积分（4-2ERI）矩阵进行压缩。首先通过RI乘积来近似4–2ERI。然后，使用奇异值分解（SVD）逼近消除低加权奇异矢量。SVD RI近似值保持RI近似值的规范形式，并引入了可调的压缩因子。通过将这些方法应用于闭壳二阶Møller-Plesset微扰理论（MP2），对SVD RI逼近，随机RI和自然辅助函数逼近的特征进行了数值检验。结果表明，尽管SVD RI逼近会带来绝对属性（例如，相关能量）的较大误差，

更新日期：2019-02-27

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