Cioslowski Jerzy, Strasburger Krzysztof
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
J Phys Chem Lett. 2025 Jan 23;16(3):710-716. doi: 10.1021/acs.jpclett.4c03166. Epub 2025 Jan 10.
The concept of natural densitals (NDs) and their amplitudes is introduced. These quantities provide the spectral decomposition of the cumulant of the two-electron density that, by definition, quantifies the extent of electron correlation. Consequently, they are ideally suited for a rigorous description of electron correlation effects in Coulombic systems. Spin-summed and spin-resolved versions of the NDs and their amplitudes are defined, and their properties are discussed in detail. Unlike the nonnegative-valued occupation numbers of the natural orbitals (NOs), these amplitudes exhibit diverse sign patterns that emerge within different regimes of electron correlation. The descriptive power of this property is vividly illustrated with the ground state of the H molecule, in which the subtle interplay of various types of electron correlation is captured in detail by a straightforward examination of the amplitudes of the NDs alone. Offering the most compact bilinear representations of (a property analogous to that of the NOs with respect to the 1-matrix), the NDs open up entirely new vistas in the analysis of electronic structures of atoms and molecules.
引入了自然密度函数（NDs）及其振幅的概念。这些量提供了双电子密度累积量的谱分解，根据定义，该累积量量化了电子关联的程度。因此，它们非常适合用于严格描述库仑系统中的电子关联效应。定义了NDs及其振幅的自旋求和和自旋分辨版本，并详细讨论了它们的性质。与自然轨道（NOs）的非负占据数不同，这些振幅表现出在不同电子关联区域内出现的多种符号模式。通过对H分子基态的研究，生动地说明了这一性质的描述能力，在该研究中，仅通过直接检查NDs的振幅就能详细捕捉到各种类型电子关联的微妙相互作用。由于NDs提供了（类似于NOs相对于1-矩阵的性质）最紧凑的双线性表示，它们为原子和分子的电子结构分析开辟了全新的视野。
