Introduction

Coester and Kummel first developed the ideas that led to coupled-cluster theory in the late 1950s. The basic idea is that the correlated wave function of a many-body system $ \mid\Psi\rangle $ can be formulated as an exponential of correlation operators $ T $ acting on a reference state $ \mid\Phi\rangle $ $$ \mid\Psi\rangle = \exp\left(-\hat{T}\right)\mid\Phi\rangle\ . $$ We will discuss how to define the operators later in this work. This simple ansatz carries enormous power. It leads to a non-perturbative many-body theory that includes summation of ladder diagrams , ring diagrams, and an infinite-order generalization of many-body perturbation theory.