The Coupled Cluster (CC) method is a widely used and highly successful high precision
method for the solution of the stationary electronic Schrödinger
equation, with its practical convergence properties being similar to that of a
corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been
analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in
[Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous
space, giving a root equation for an infinite dimensional, nonlinear Coupled Cluster
operator that is equivalent the full electronic Schrödinger equation [Rohwedder, 2011]. In
this paper, we combine both approaches to prove existence and uniqueness results,
quasi-optimality estimates and energy estimates for the CC method with respect to the
solution of the full, original Schrödinger equation. The main property used is a local
strong monotonicity result for the Coupled Cluster function, and we give two
characterizations for situations in which this property holds.