Stability analysis of a double similarity transformed coupled cluster theory

TL;DR

This paper analyzes the iterative dynamics of a double similarity transformed coupled cluster theory, revealing universal Feigenbaum behavior and proposing a reduced-dimension algorithm based on master-slave dynamics.

Contribution

It introduces a novel analysis of the iterative scheme's dynamics and suggests a new reduced-dimension coupled-cluster algorithm leveraging synergetics.

Findings

Iterative scheme exhibits universal Feigenbaum dynamics.

Cluster operators involving active orbitals dominate the dynamics.

Proposes a reduced-dimension algorithm based on master-slave dynamics.

Abstract

In this paper, we have analysed the time series associated with the iterative scheme of a double similarity transformed Coupled Cluster theory. The coupled iterative scheme to solve the ground state Schr{\"o}dinger equation is cast as a multivariate time-discrete map, the solutions show the universal Feigenbaum dynamics. Using recurrence analysis, it is shown that the dynamics of the iterative process is dictated by a small subgroup of cluster operators, mostly those involving chemically active orbitals, whereas all other cluster operators with smaller amplitudes are enslaved. Using Synergetics, we will indicate how the master-slave dynamics can suitably be exploited to develop a novel coupled-cluster algorithm in a much-reduced dimension.