Cumulants, Partitioning, and Projections
Cumulants, Partitioning, and Projections
复制标题
累积量、划分和投影
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
P. Fulde
中科院分区：
文献类型：
--
作者：
P. Fulde
在第一章中。4.讨论了常用于描述分子中电子关联的构型相互作用和微扰方法，并指出了“尺寸一致性问题”。能量是一个广泛的量，即，当系统的大小加倍时，它的值也会加倍。在确定能量时，任何近似都应保留这一特征。当像（4.1.1）式那样的构型-相互作用展开式在固定数量的电子-空穴激发后终止时，情况就不是这样了：只有当所有占据轨道的激发都被包括在内时，CI尺寸才是一致的。正如Chap中所指出的那样。4.瑞利-薛定谔微扰理论不存在布里渊-维格纳微扰理论存在的尺寸一致性问题。即使在瑞利-薛定谔微扰理论，我们得到不同的贡献的能量，这是不成比例的情况下，大系统的体积。然而，我们已经看到，它们相互抵消，例如，在（4.2.14）中，具有尺寸扩展的最终结果。这种抵消在场论方法中常见的基态能量的图解方法[5.1]中变得特别明显。图以图形的方式表示微扰展开的不同项。不连通图产生的贡献与体积不成比例;通过仅使用链接或连接图，可以确保所有近似值保持大小一致性。
In Chap. 4 we discussed configuration-interaction and perturbational methods often used to describe electron correlations in molecules drawing attention to the “size-consistency problem”. The energy is an extensive quantity, i.e., it doubles its value when the size of the system doubles. This feature should be preserved by any approximation when determining the energy. This is not the case when a configuration-interaction expansion like (4.1.1) is terminated after a fixed number of electron-hole excitations: only when excitations out of all occupied orbitals are included is a CI ansatz size consistent. As pointed out in Chap. 4, the Rayleigh-Schrodinger perturbation theory does not suffer from the size-consistency problem while the Brillouin-Wigner one does. Even within the Rayleigh-Schrodinger perturbation theory we obtain different contributions to the energy, which are not proportional to the volume in case of large systems. However, we have seen that they mutually cancel as evidenced, for example, in (4.2.14) with a size extensive final result. This cancellation becomes particularly apparent in diagrammatic approaches to the ground-state energy common in field-theoretical methods [5.1]. Diagrams represent different terms of a perturbation expansion in a pictorial way. The disconnected diagrams yield contributions not proportional to the volume; by working with linked or connected diagrams only, one ensures that all approximations preserve size consistency.