CoupledClusterTheorie

Coupled Cluster Theory (German: Coupled-Cluster-Theorie) is a post-Hartree–Fock approach in quantum chemistry used to describe electron correlation in many-electron systems. The central idea is to represent the correlated wavefunction as an exponential ansatz acting on a single-determinant reference, typically the Hartree–Fock determinant: |Ψ⟩ = e^T |Φ0⟩. The cluster operator T comprises excitation operators: T = T1 + T2 + T3 + ..., corresponding to singles, doubles, triples, and higher excitations relative to |Φ0⟩.

Common truncations include CCSD (singles and doubles) and CCSD(T) (CCSD with a perturbative triples correction). The energy is computed as E_CC = ⟨Φ0| e^{-T} H e^{T} |Φ0⟩, while the amplitudes Tμ are determined by solving the projected equations ⟨Φμ| e^{-T} H e^{T} |Φ0⟩ = 0 for all excited determinants μ. This yields a set of nonlinear equations solved iteratively.

A key feature of CC methods is that they are size-extensive and typically size-consistent, in contrast to truncated configuration interaction methods. They often provide high accuracy for ground-state energies of closed-shell systems and can be extended to excited states through approaches such as equation-of-motion CC (EOM-CC) and various response theories.

Computational cost increases rapidly with system size: CCSD scales roughly as N^6 and CCSD(T) as about N^7, where N measures system size. Limitations include the reliance on a single reference determinant; near-degeneracies or bond-breaking regions may require multi-reference techniques. Historically, CC theory was introduced by Coester and Kümmel in 1958 and developed by Čížek in 1960, and it remains widely implemented across quantum chemistry software for accurate energies and properties.