Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster,Journal of Chemical Theory and Computation

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Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2021-10-13 , DOI: 10.1021/acs.jctc.1c00730
Ádám Margócsy ₁ , Ágnes Szabados ₂

Affiliation

A new scheme is introduced in Multi-Reference (MR) Coupled Cluster (CC) based on the MR Generalized Normal Ordering (MRGNO) and the corresponding MR Generalized Wick Theorem (MRGWT) of Kutzelnigg and Mukherjee. The key element is the identification of a structure in MRGWT generated terms, facilitated by Goldstone diagram techniques. This allows for bundling the many terms of the MRGWT expansion and introduces a hierarchy in the equations that can be harnessed in devising approximations. One- and two-particle interaction vertices are found to be uniformly substituted for their counterpart dressed by density cumulants. This allows for a straightforward rewriting of the ordinary energy expression of CC with interaction dressed (id) one- and two-particle terms and reveals the presence of three- and higher-rank dressed interaction vertices too. Cumulants appearing out of dressed interaction vertices contribute to the amplitude equations and can be interpreted to have an amplitude dressing role. Dressing of one- and two-particle interaction vertices is the most straightforward to implement and does not hinder computational feasibility, provided that the reference function involves strictly limited active space sizes. The Generalized Valence Bond wave function, underlying pilot numerical tests, fulfills this criterion. Results on multiple bond breaking scenarios point to the need of stepping beyond one- and two-particle id. An extremely simple version of incorporating amplitude dressing in addition to one- and two-particle id is seen to cure the potential energy curves remarkably, stimulating further investigations along this line.

中文翻译：

多参考耦合簇中累积量的顶点修整

基于 MR 广义正态排序 (MRGNO) 和 Kutzelnigg 和 Mukherjee 的相应 MR 广义 Wick 定理 (MRGWT)，在多参考 (MR) 耦合簇 (CC) 中引入了一种新方案。关键要素是通过戈德斯通图技术在 MRGWT 生成的术语中识别结构。这允许捆绑 MRGWT 扩展的许多项，并在方程中引入层次结构，可用于设计近似值。发现一粒子和二粒子相互作用顶点被密度累积量修饰的对应顶点统一替换。这允许使用交互修饰 (id) 一粒子和二粒子项直接重写 CC 的普通能量表达式，并揭示三阶和更高阶修饰交互顶点的存在。出现在修饰交互顶点之外的累积量对振幅方程有贡献，并且可以解释为具有振幅修饰作用。一粒子和二粒子相互作用顶点的修整是最容易实现的，并且不妨碍计算可行性，前提是参考函数涉及严格限制的活动空间大小。作为试点数值测试基础的广义价键波函数满足这一标准。多个键断裂场景的结果表明需要超越一粒子和二粒子 id。除了一个和两个粒子 id 外，还可以看到一个极其简单的结合振幅修整的版本，显着地治愈了势能曲线，刺激了沿着这条线的进一步研究。

更新日期：2021-11-09

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