Cumulant reconstruction of the three-electron reduced density matrix in the anti-Hermitian contracted Schrödinger equation.
Cumulant reconstruction of the three-electron reduced density matrix in the anti-Hermitian contracted Schrödinger equation.
复制标题
反厄米收缩薛定谔方程中三电子约化密度矩阵的累积重构。
DOI：
--
复制
发表时间：
2007
影响因子：
4.4
通讯作者：
D. Mazziotti
中科院分区：
文献类型：
--
作者：
A. DePrince;D. Mazziotti
文献中对非最小基组中三电子约化密度矩阵（3-RDM）重建的准确性存在不同的观点。本文论证了Valdemoro（V）[F. Colmenero等人，A 47，971（1993）]、Nakatsuji和Yasuda（NY）[Phys.Rev.Lett.1994]。76，1039（1996）]，Mazziotti（M）[Phys.Rev.A60，3618（1999）]，和Valdemoro-Tel-Perez-Romero（VTP）[Many-electron Densities and Density Matrices，由J. Cioslowski编辑（Kluwer，Boston，2000）]。在计算上，我们扩展了以前的研究，以研究各种分子，包括LiH，HF，NH（3），H（2）O和N（2），Slater型，双zeta和极化双zeta基组在平衡和非平衡几何。与全组态相互作用的3-RDM相比，重构的3-RDM在非最小基组中不仅体现了一阶展开（V）的精确性，而且体现了二阶修正（NY、M和VTP）的重要作用.在非平衡几何下的计算进一步表明，累积泛函可以从多参考2-RDM重构3-RDM，具有合理的精度，这与最近的反厄米收缩薛定谔方程（ACSE）和正则对角化的多参考公式有关。从理论上讲，我们对M泛函进行了详细的微扰分析，以识别其二阶分量。有了这些二阶分量，我们连接的M，NY，和VTP重建的第一次，从M功能派生的NY和VTP泛函。最后，这些3-RDM重建在ACSE中使用[D. Mazziotti，Phys. Rev. Lett. 97，143002（2006）]来计算基态能量，并与收缩薛定谔方程和几种波函数方法的能量进行比较。
Differing perspectives on the accuracy of three-electron reduced-density-matrix (3-RDM) reconstruction in nonminimal basis sets exist in the literature. This paper demonstrates the accuracy of cumulant-based reconstructions, developed by Valdemoro (V) [F. Colmenero et al., Phys. Rev. A 47, 971 (1993)], Nakatsuji and Yasuda (NY) [Phys. Rev. Lett. 76, 1039 (1996)], Mazziotti (M) [Phys. Rev. A 60, 3618 (1999)], and Valdemoro-Tel-Perez-Romero (VTP) [Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000)]. Computationally, we extend previous investigations to study a variety of molecules, including LiH, HF, NH(3), H(2)O, and N(2), in Slater-type, double-zeta, and polarized double-zeta basis sets at both equilibrium and nonequilibrium geometries. The reconstructed 3-RDMs, compared with 3-RDMs from full configuration interaction, demonstrate in nonminimal basis sets the accuracy of the first-order expansion (V) as well as the important role of the second-order corrections (NY, M, and VTP). Calculations at nonequilibrium geometries further show that cumulant functionals can reconstruct the 3-RDM from a multireferenced 2-RDM with reasonable accuracy, which is relevant to recent multireferenced formulations of the anti-Hermitian contracted Schrodinger equation (ACSE) and canonical diagonalization. Theoretically, we perform a detailed perturbative analysis of the M functional to identify its second-order components. With these second-order components we connect the M, NY, and VTP reconstructions for the first time by deriving both the NY and VTP functionals from the M functional. Finally, these 3-RDM reconstructions are employed within the ACSE [D. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)] to compute ground-state energies which are compared with the energies from the contracted Schrodinger equation and several wave function methods.