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General orbital invariant MP2-F12 theory

机译：一般轨道不变式MP2-F12理论

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A general form of orbital invariant explicitly correlated second-order closed-shell Moller-Plesset perturbation theory (MP2-F12) is derived, and compact working equations are presented. Many-electron integrals are avoided by resolution of the identity (RI) approximations using the complementary auxiliary basis set approach. A hierarchy of well defined levels of approximation is introduced, differing from the exact theory by the neglect of terms involving matrix elements over the Fock operator. The most accurate method is denoted as MP2-F12/3B. This assumes only that Fock matrix elements between occupied orbitals and orbitals outside the auxiliary basis set are negligible. For the chosen ansatz for the first-order wave function this is exact if the auxiliary basis is complete. In the next lower approximation it is assumed that the occupied orbital space is closed under action of the Fock operator [generalized Brillouin condition (GBC)]; this is equivalent to approximation 2B of Klopper and Samson [J. Chem. Phys. 116, 6397 (2002)]. Further approximations can be introduced by assuming the extended Brillouin condition (EBC) or by neglecting certain terms involving the exchange operator. A new approximation MP2-F12/3C, which is closely related to the MP2-R12/C method recently proposed by Kedzuch [Int. J. Quantum Chem. 105, 929 (2005)] is described. In the limit of a complete RI basis this method is equivalent to MP2-F12/3B. The effect of the various approximations (GBC, EBC, and exchange) is tested by studying the convergence of the correlation energies with respect to the atomic orbital and auxiliary basis sets for 21 molecules. The accuracy of relative energies is demonstrated for 16 chemical reactions. Approximation 3C is found to perform equally well as the computationally more demanding approximation 3B. The reaction energies obtained with smaller basis sets are found to be most accurate if the orbital-variant diagonal Ansatz combined with localized orbitals is used for the first-order wave function. This unexpected result is attributed to geminal basis set superposition errors present in the formally more rigorous orbital invariant methods. (c) 2007 American Institute of Physics.
机译：推导了一般形式的轨道不变显式相关的二阶闭壳Moller-Plesset微扰理论（MP2-F12），并给出了紧致的工作方程。通过使用互补辅助基集方法解决恒等式（RI）近似，可以避免多电子积分。引入了定义良好的近似等级的层次结构，该层次不同于精确的理论，因为它忽略了Fock算子上涉及矩阵元素的项。最准确的方法表示为MP2-F12 / 3B。这仅假设被占用的轨道与辅助基础集外部的轨道之间的福克矩阵元素可以忽略。对于为一阶波动函数选择的ansatz，如果辅助基础完整，则这是精确的。在下一个较低的近似值中，假设在Fock算子的作用下，所占据的轨道空间是封闭的[广义布里渊条件（GBC）];这相当于Klopper和Samson的近似值2B [J．化学物理116，6397（2002）]。可以通过假设扩展的布里渊条件（EBC）或忽略某些涉及交换算子的术语来引入其他近似值。一种新的近似MP2-F12 / 3C，与Kedzuch最近提出的MP2-R12 / C方法密切相关。 J.量子化学。 [第105卷，929（2005）]中描述。在完整的RI基础上，此方法等效于MP2-F12 / 3B。通过研究21个分子相对于原子轨道和辅助基集的相关能的收敛，来测试各种近似（GBC，EBC和交换）的影响。相对能量的准确性已针对16个化学反应进行了证明。发现近似值3C与计算上更苛刻的近似值3B表现相同。如果将轨道变量对角线Ansatz与局域轨道结合起来用于一阶波函数，则发现使用较小基集获得的反应能量是最准确的。这种出乎意料的结果归因于形式上更严格的轨道不变方法中存在的双子基集叠加误差。 （c）2007年美国物理研究所。

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