Mayer I
Chemical Research Center, Hungarian Academy of Sciences, P.O. Box 17, H-1525, Budapest, Hungary.
Phys Chem Chem Phys. 2006 Oct 28;8(40):4630-46. doi: 10.1039/b608822h. Epub 2006 Aug 29.
The paper gives an overview, generalization and systematization of the different energy decomposition schemes we have devised in the last few years by using both the 3-D analysis (the atoms are represented by different parts of the physical space) and the Hilbert space analysis in terms of the basis orbitals assigned to the individual atoms. The so called "atomic decomposition of identity" provides us the most general formalism for analyzing different physical quantities in terms of individual atoms or pairs of atoms. (The "atomic decomposition of identity" means that we present the identity operator as a sum of operators assigned to the individual atoms.) By proper definitions of the atomic operators, both Hilbert-space and the different 3-D decomposition schemes can be treated on an equal footing. Several different but closely related energy decomposition schemes have been proposed for the Hilbert space analysis. They differ by exact or approximate treatment of the three- and four-center integrals and by considering the kinetic energy as a part of the atomic Hamiltonian or as having genuine two-center components, too. (Also, some finite basis correction terms may be treated in different manners.) The exact schemes are obtained by using the "atomic decomposition of identity". In the approximate schemes a projective integral approximation is also introduced, thus the energy components contain only one- and two-center integrals. The diatomic energy contributions have also been decomposed into terms of different physical nature (electrostatic, exchange etc.) The 3-D analysis may be performed either in terms of disjunct atomic domains, as in the case of the AIM formalism, or by using the so called "fuzzy atoms" which do not have sharp boundaries but exhibit a continuous transition from one to another. The different schemes give different numbers, but each is capable of reflecting the most important intramolecular interactions as well as the secondary ones--e.g. intramolecular interactions of type C-H[...]O.
本文对我们在过去几年中设计的不同能量分解方案进行了概述、归纳和系统化，这些方案同时运用了三维分析（原子由物理空间的不同部分表示）以及基于分配给各个原子的基轨道的希尔伯特空间分析。所谓的“单位分解的原子化”为我们提供了最通用的形式体系，用于根据单个原子或原子对来分析不同的物理量。（“单位分解的原子化”意味着我们将单位算子表示为分配给各个原子的算子之和。）通过对原子算子的恰当定义，希尔伯特空间和不同的三维分解方案能够在同等基础上进行处理。针对希尔伯特空间分析，已经提出了几种不同但密切相关的能量分解方案。它们的区别在于对三中心和四中心积分的精确或近似处理方式，以及将动能视为原子哈密顿量的一部分还是也具有真正的双中心分量。（此外，一些有限基校正项可能会以不同方式处理。）精确方案是通过使用“单位分解的原子化”得到的。在近似方案中，还引入了投影积分近似，因此能量分量仅包含单中心和双中心积分。双原子能量贡献也已被分解为具有不同物理性质的项（静电、交换等）。三维分析既可以按照AIM形式体系那样根据不相交的原子域进行，也可以使用所谓的“模糊原子”，这些原子没有清晰的边界，而是呈现出从一个到另一个的连续过渡。不同的方案给出不同的数值，但每种方案都能够反映最重要的分子内相互作用以及次要相互作用——例如C-H[…]O类型的分子内相互作用。
