相对论Cholesky分解密度矩阵MP2
Relativistic Cholesky-decomposed density matrix MP2
摘要：
本文介绍了相对论Cholesky分解密度（CDD）矩阵的二阶Møller-Plesset微扰理论（MP2）能量。的工作方程制定在通常的中间体MP2时，采用分辨率的身份近似（RI）的两个电子积分。这些中间体是通过将我们先前提出的基于双组分原子轨道的MP2（J. Chem. Phys. 145，014107（2016））的占据和虚拟四元数伪密度矩阵替换为相应的枢轴四元数Cholesky因子而获得的。虽然工作在Kramers限制的形式主义，我们得到一个正式的自旋轨道开销为16和28的库仑和交换贡献的2C MP2相关能量，分别相比，非相对论（NR）自旋自由CDD-MP2的实现。这种紧凑的四元数公式也可以很容易地在任何其他算法中探索，以计算2C MP2能量。四元数的Cholesky因素变得稀疏的大分子，并与一个块式筛选，块稀疏矩阵乘法算法，我们观察到一个有效的二次缩放的总壁时间的重元素含有线性分子的系统大小的增加。1C和2C计算的总运行时间由交换能的收缩决定。我们还研究了一个庞大的含碲超分子配合物。对于这样庞大的三维延伸的分子，本筛选方案具有大得多的前因子，并且不太有效。
英文摘要：
In the present article, we introduce the relativistic Cholesky-decomposed density (CDD) matrix second-order Møller-Plesset perturbation theory (MP2) energies. The working equations are formulated in terms of the usual intermediates of MP2 when employing the resolution-of-the-identity approximation (RI) for two-electron integrals. Those intermediates are obtained by substituting the occupied and virtual quaternion pseudo-density matrices of our previously proposed two-component atomic orbital-based MP2 (J. Chem. Phys. 145, 014107 (2016)) by the corresponding pivoted quaternion Cholesky factors. While working within the Kramers-restricted formalism, we obtain a formal spin-orbit overhead of 16 and 28 for the Coulomb and exchange contribution to the 2C MP2 correlation energy, respectively, compared to a non-relativistic (NR) spin-free CDD-MP2 implementation. This compact quaternion formulation could also be easily explored in any other algorithm to compute the 2C MP2 energy. The quaternion Cholesky factors become sparse for large molecules and, with a block-wise screening, block sparse-matrix multiplication algorithm, we observed an effective quadratic scaling of the total wall time for heavy-element containing linear molecules with increasing system size. The total run time for both 1C and 2C calculations was dominated by the contraction to the exchange energy. We have also investigated a bulky Te-containing supramolecular complex. For such bulky, three-dimensionally extended molecules the present screening scheme has a much larger prefactor and is less effective.
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