The one-electron picture in the Piris natural orbital functional 5 (PNOF5)
The one-electron picture in the Piris natural orbital functional 5 (PNOF5)
复制标题
Piris 自然轨道泛函 5 (PNOF5) 中的单电子图
DOI：
--
复制
发表时间：
2013
影响因子：
1.7
通讯作者：
J. Ugalde
中科院分区：
文献类型：
--
作者：
M. Piris;J. M. Matxain;X. López;J. Ugalde
自然轨道泛函理论提供了分子中单电子图像的两种互补表示，即自然轨道(NO)表示和正则轨道(CO)表示。前者直接源于求解相应的欧拉方程的优化过程，而后者是通过对NO表示中得到的拉格朗日乘子矩阵的对角化而得到的。一般情况下，除了特殊的Hartree-Fock情形外，单粒子约化密度矩阵(1-RDM)和拉格朗日不能同时化为对角形式。1-RDM在NO表示中是对角线的，但拉格朗日不是对角线的，它只是一个厄米矩阵。相反，在CO表示中，拉格朗日是对角线的，但不是1-RDM。把这两个表象结合起来，我们就有了关于占位数和轨道能量的全貌。Piris自然轨道泛函5一般导致分子轨道在NO表象中的局域化。相应地，它提供了一幅与经验价壳层电子对排斥理论和Bent规则以及理论价键方法相一致的轨道图。另一方面，等效的CO表示可以提供与分子对称性相适应的离域分子轨道。借助于扩展的库普曼定理，我们证明了当1-RDM保持接近对角线形式时，与CoS有关的单粒子能量可以产生合理的主电离势。通过几个例子说明了NOS和CoS之间的关系，表明这两种轨道表示是相辅相成的。
The natural orbital functional theory provides two complementary representations of the one-electron picture in molecules, namely, the natural orbital (NO) representation and the canonical orbital (CO) representation. The former arises directly from the optimization process solving the corresponding Euler equations, whereas the latter is attained from the diagonalization of the matrix of Lagrange multipliers obtained in the NO representation. In general, the one-particle reduced-density matrix (1-RDM) and the Lagrangian cannot be simultaneously brought to the diagonal form, except for the special Hartree-Fock case. The 1-RDM is diagonal in the NO representation, but not the Lagrangian, which is only a Hermitian matrix. Conversely, in the CO representation, the Lagrangian is diagonal, but not the 1-RDM. Combining both representations we have the whole picture concerning the occupation numbers and the orbital energies. The Piris natural orbital functional 5 leads generally to the localization of the molecular orbitals in the NO representation. Accordingly, it provides an orbital picture that agrees closely with the empirical valence shell electron pair repulsion theory and the Bent’s rule, along with the theoretical valence bond method. On the other hand, the equivalent CO representation can afford delocalized molecular orbitals adapted to the symmetry of the molecule. We show by means of the extended Koopmans’ theorem that the one-particle energies associated with the COs can yield reasonable principal ionization potentials when the 1-RDM remains close to the diagonal form. The relationship between NOs and COs is illustrated by several examples, showing that both orbital representations complement each other.