Analysis of the Extended Coupled-Cluster Method in Quantum Chemistry

Understand

The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schr\"odinger equation is here developed.

• We prove an existence and uniqueness result, both in the full infinite-dimensional amplitude space as well as for discretized versions of it.
• The extended coupled-cluster method is formulated as a critical point of an energy function using a generalization of the Rayleigh-Ritz principle: the bivariational principle.
• This gives a quadratic bound for the energy error in the discretized case.