论文标题
基于Arponen的扩展理论的一类耦合群集方法的保证收敛
Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory
论文作者
论文摘要
基于Arponen的扩展耦合群集理论，引入了广泛的耦合群集方法。这类方法是根据群集运算符的坐标转换来制定的。提出了基于Arponen的双向原理的耦合群集方法的误差分析的数学框架，其中，能量的翻转梯度的局部强单调性的概念是中心的。提出了一般的数学结果，描述了足够的坐标转换条件，以保留局部强的单调性。结果应用于提出的方法类别，其中包括标准和二次耦合群集方法，以及Arponen的扩展耦合群集理论的规范版本。提出了一些数值实验，并讨论了规范坐标的使用。
A wide class of coupled-cluster methods is introduced, based on Arponen's extended coupled-cluster theory. This class of methods is formulated in terms of a coordinate transformation of the cluster operators. The mathematical framework for the error analysis of coupled-cluster methods based on Arponen's bivariational principle is presented, in which the concept of local strong monotonicity of the flipped gradient of the energy is central. A general mathematical result is presented, describing sufficient conditions for coordinate transformations to preserve the local strong monotonicity. The result is applied to the presented class of methods, which include the standard and quadratic coupled-cluster methods, and also Arponen's canonical version of extended coupled-cluster theory. Some numerical experiments are presented, and the use of canonical coordinates for diagnostics is discussed.
