,

where is the wave function is the reference function (e.g. Hartree-Fock function), and is the cluster operator:

,

where in the formalism of second quantization:

In the above formulae and denote the creation and anihilation operators and *i,j* stand for occupied and *a,b* for unoccupied orbitals.

In the simplest version one considers only operator (double excitations). This method is called coupled cluster with doubles (CCD in short).

The coupled cluster equations are usually derived using diagrammatic technique and result in nonlinear equations which can be solved in an iterative way.