CCSDTQ

CCSDTQ stands for coupled-cluster singles, doubles, triples, and quadruples. It is an electronic structure method within the family of coupled-cluster theories, designed to include all connected excitations up to quadruples in the cluster operator. In CC theory, the correlated wavefunction is expressed as |Ψ> = e^T |Φ0>, where T = T1 + T2 + T3 + T4, with Tn representing n-fold excitations relative to a reference Hartree-Fock determinant |Φ0>. By including T4, CCSDTQ provides a highly accurate description of electron correlation, improving on CCSDT and CCSDT(Q) for small to medium-sized systems.

CCSDTQ is often used for high-accuracy benchmark calculations, thermochemistry, and reaction energetics where precise energies are essential. It tends to yield energies closer to full configuration interaction than lower-order coupled-cluster methods, particularly for systems where quadruple excitations contribute noticeably. However, the method is extremely computationally demanding, with memory and CPU requirements that scale steeply with system size (typically on the order of N^10 in conventional implementations, where N relates to the basis set size or system size). This limits practical applications to relatively small molecules or to benchmark studies.

In practice, CCSDTQ is employed when accuracy justifies the cost, often to calibrate more affordable approaches or to serve as a reference for testing new methods. It is part of the hierarchy of coupled-cluster methods, situated above CCSD, CCSDT, and perturbative quadruples corrections, and below full configuration interaction in terms of exactness.