Coupled Cluster - Wavefunction Ansatz

Wavefunction Ansatz

Coupled-cluster theory provides the exact solution to the time-independent Schrödinger equation

where is the Hamiltonian of the system. The wavefunction and the energy of the lowest-energy state are denoted by and E, respectively. Other variants of the coupled-cluster theory, such as equation-of-motion coupled cluster and multi-reference coupled cluster may also produce approximate solutions for the excited states (and sometimes ground states) of the system.

The wavefunction of the coupled-cluster theory is written as an exponential ansatz:

,

where is a Slater determinant usually constructed from Hartree–Fock molecular orbitals. is an excitation operator which, when acting on, produces a linear combination of excited Slater determinants (see section below for greater detail).

The choice of the exponential ansatz is opportune because (unlike other ansätze, for example, configuration interaction) it guarantees the size extensivity of the solution. Size consistency in CC theory, however, depends on the size consistency of the reference wave function. A drawback of the method is that it is not variational.