Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis.
Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis.
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DOI：
10.1063/1.4984591
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发表时间：
2017-03
期刊：
影响因子：
--
通讯作者：
Benjamin Helmich-Paris;S. Knecht
中科院分区：
文献类型：
--
作者：
Benjamin Helmich-Paris;S. Knecht
在这篇文章中，我们展示了如何用轨道能量分母(OEDs)的拉普拉斯变换来表述原子和活性分子轨道基中的部分收缩n电子价二阶微扰理论(NEVPT2)能量。由于原子轨道基函数本质上是局域性的，而且活跃轨道的数目相对较少，所以我们的公式特别适合于线性尺度NEVPT2的实现。在我们的公式中，有两种NEVPT2能量贡献，这两种贡献在所涉及的两电子积分中的活跃轨道数不同。那些涉及不含或只有一个活性轨道的积分的积分可以完全在AO基下表示为单参考二阶M&Plesset微扰理论，并受益于稀疏的活性伪密度矩阵--特别是当活性分子轨道只局限在分子的一部分时。相反，涉及两个或三个活动轨道的积分的能量贡献可以从推广到活动轨道对的库仑矩阵和交换矩阵中获得。此外，我们还证明了拉普拉斯变换的部分压缩的NEVPT2与含时的NEVPT2[A.Y.Sokolov和G.K.-L.Chan，J.Chem]是一样的。太棒了。144,064102(2016年)]当用内收缩近似计算全活性中间体。此外，我们还指出，对于多参考微扰理论，寻找最优的数值拉普拉斯变换参数是特别具有挑战性的，因为8个不同的OEDs之间的拟合范围可能会变化许多个数量级。根据基于精度的标准分别为每个OED选择求交点的数量，使我们能够可靠地控制NEVPT2能量中的误差。
In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis functions are inherently localized and the number of active orbitals is comparatively small, our formulation is particularly suited for a linearly scaling NEVPT2 implementation. In our formulation, there are two kinds of NEVPT2 energy contributions, which differ in the number of active orbitals in the two-electron integrals involved. Those involving integrals with either no or a single active orbital can be formulated completely in the AO basis as single-reference second-order Møller-Plesset perturbation theory and benefit from sparse active pseudo-density matrices-particularly if the active molecular orbitals are localized only in parts of a molecule. Conversely, energy contributions involving integrals with either two or three active orbitals can be obtained from Coulomb and exchange matrices generalized for pairs of active orbitals. Moreover, we demonstrate that Laplace-transformed partially contracted NEVPT2 is nothing less than time-dependent NEVPT2 [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)] iff the all-active intermediates are computed with the internal-contraction approximation. Furthermore, we show that for multi-reference perturbation theories it is particularly challenging to find optimal parameters of the numerical Laplace transformation as the fit range may vary among the 8 different OEDs by many orders of magnitude. Selecting the number of quadrature points for each OED separately according to an accuracy-based criterion allows us to control the errors in the NEVPT2 energies reliably.