Ghent University, Center for Molecular Modeling, Technologiepark 903, B-9052 Zwijnaarde, Belgium.
J Chem Phys. 2012 Jan 7;136(1):014107. doi: 10.1063/1.3673321.
A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.
先前引入的分子单电子密度矩阵在原子和键上的分区[D. Vanfleteren 等人，J. Chem. Phys. 133, 231103 (2010)] 进行了详细研究。正交投影算子用于定义原子子空间，就像在自然布居分析中一样。正交投影算子使用递归方案构建。这些算子与化学有关，并且遵守从电子密度的 Hirshfeld-I 分区中熟悉的股东原则。该股东原则被扩展到密度矩阵中，其中正交投影被视为总和贡献的原子分数。所有计算都作为单电子 Hilbert 空间中的矩阵运算进行。本文提供了有关该递归方案的数学证明和数值证据。检查了使用这些股东投影算子的优点，包括共价键序、键极化和可转移性。
