A new approach for the two-electron cumulant in natural orbital functional theory
A new approach for the two-electron cumulant in natural orbital functional theory
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自然轨道泛函理论中双电子累积量的一种新方法
DOI：
10.1002/qua.20858
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发表时间：
2006
影响因子：
2.2
通讯作者：
M. Piris
中科院分区：
文献类型：
--
作者：
M. Piris
累积量展开产生了二矩阵D的有用分解，其中成对相关矩阵（累积量）与一矩阵Γ的反对称乘积断开。提出了一种新的显式反对称方法，该方法以两个对称矩阵Δ和Λ作为占据数的泛函，计算封闭壳层系统单重基态的两粒子累积量矩阵.它产生一个自然的轨道功能，减少到两个电子系统的总能量的精确表达式。矩阵Λ的函数形式很容易推广到任何具有偶数个电子的系统。Δ的对角元素等于占用数的平方，双矩阵的N-可表示性正的必要条件对矩阵Δ的非对角元素施加了几个限制。著名的中值定理和部分和规则获得的非对角元素的Δ提供了一个处方，推导出一个实用的功能。特别地，当给定轨道i的库仑相互作用{Jij}的平均值{J}占据所有轨道j ∈ i时，假定其等于{Kii/2}，得到了接近于自相互作用校正的GU泛函，但两矩阵费米子反对称成立。在HF占据轨道之间的Λ矩阵元中增加一项，以保证正确描述最低占据能级的占据数。在57个分子的全变分有限基组计算的功能进行了测试。它给出了合理的分子能量在平衡几何形状。偶极矩的计算值与实验数据符合得很好。© 2005 Wiley Periodicals，Inc.国际量子化学杂志，2006年
The cumulant expansion gives rise to a useful decomposition of the two-matrix D in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one-matrix Γ. A new explicit antisymmetric approach for the two-particle cumulant matrix in terms of two symmetric matrices, Δ and Λ, as functionals of the occupation numbers is proposed for singlet ground states of closed-shell systems. It produces a natural orbital functional that reduces to the exact expression for the total energy in two-electron systems. The functional form of matrix Λ is readily generalized to any system with an even number of electrons. The diagonal elements of Δ equal the square of the occupation numbers, and the N-representability positivity necessary conditions of the two-matrix impose several bounds on the off-diagonal elements of matrix Δ. The well-known mean value theorem and the partial sum rule obtained for the off-diagonal elements of Δ provide a prescription for deriving a practical functional. In particular, when the mean values {J} of the Coulomb interactions {Jij} for a given orbital i taking over all orbitals j ≠ i are assumed to be equal {Kii/2}, a functional close to self-interaction-corrected GU functional is obtained, but the two-matrix fermionic antisymmetric holds. An additional term for the matrix elements of Λ between HF occupied orbitals is proposed to ensure a correct description of the occupation numbers for the lowest occupied levels. The functional is tested in fully variational finite basis set calculations of 57 molecules. It gives reasonable molecular energies at the equilibrium geometries. The calculated values of dipole moments are in good agreement with the available experimental data. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006