CoupledClusterTechniken

Coupled cluster theory is a family of ab initio quantum chemical methods used to compute the electronic structure of molecules. It is based on an exponential ansatz for the electronic wavefunction, which provides a balanced description of dynamic correlation and yields size-extensive energies and good accuracy for a wide range of systems.

In the standard single-reference formulation, the wavefunction is written as Psi = exp(T) Phi0, where Phi0 is a single determinant reference (often Hartree–Fock). The cluster operator T is a sum of excitation operators T1 + T2 + T3 + …, corresponding to single, double, triple excitations relative to Phi0. The similarity-transformed Hamiltonian Hbar = e^{-T} H e^{T} is then used to derive nonlinear equations by projecting onto excited determinants, solving for the amplitudes t for the excitations. The quality of results is controlled by truncating T at some level, leading to methods such as CCSD (singles and doubles) and CCSD(T) (CCSD with a perturbative treatment of triples).

Extensions include CC with triples and quadruples: CCSDT, CCSDTQ; the equation-of-motion CC (EOM-CC) family for excited states, ionization potentials, and electron affinities; and local or spin-adapted variants that reduce cost. CC methods are known for high accuracy in single-reference regimes and for being size-extensive, i.e., energies scale properly with system size.

However, CC methods assume a predominantly single-reference character and can fail for systems with strong static correlation. They are computationally demanding: CCSD scales roughly as N^6 in the number of basis functions, and CCSD(T) scales about N^7, with memory and disk requirements growing steeply. Despite limitations, CC methods are widely used for benchmark-quality thermochemistry and reaction energies in chemistry.