Coupled-cluster method truncated at quadruples

Abstract

The coupled-cluster (CC) equations including single, double, triple, and quadruple excitation amplitudes (CCSDTQ) are derived diagramatically, and the complete set of CCSDTQ equations are presented. These equations have been programmed and an iterative reduced linear equation method is used to solve these equations. The potential curves for the dissociation of a model system with a single bond (Li2 and LiH) is calculated using CC doubles (CCD), singles and doubles (CCSD), singles, doubles, and triples (CCSDT), and CCSDTQ. These calculations demonstrate the magnitude of the CC contributions arising from single, double, triple, and quadruple excitation amplitudes to the stretching of a chemical bond.

Ab initiopair potential energy curve for the argon atom pair and thermophysical properties of the dilute argon gas. I. Argon–argon interatomic potential and rovibrational spectra

“…Because of numerical inaccuracies for some larger values of the results for distances between = 0.54 nm and = 0.70 nm had to be smoothed with a polynomial fitted to the ratio of Δ (Q) and daV6dZ CCSD(T) corr . For = 0.38 nm we were also able to test the error in using the perturbational instead of the full iterative treatment of the quadruple excitations (CCSDTQ [28]) in analogy to Δ T−(T) . This difference was, at least with an aVDZ+(3321) basis set, only 0.10 K. Taking into consideration the enormous computational effort for the CCSDTQ method this effect was neglected.…”

Communication: The performance of non-iterative coupled cluster quadruples models

“…In these cases, including the effect of connected quadruple excitations proves necessary. Alas, the full iterative CC singles, doubles, triples, and quadruples (CCSDTQ) model 24 exhibits a staggering asymptotic O(N 10 ) scaling, which is bound to prevent it from routine applications in anything but the niche of atoms and modestsized molecules. For this reason, CC quadruples models have been devised that scale non-iteratively as anything from O(N 7 ) to O(N 10 ).…”

Inspector-Executor Load Balancing Algorithms for Block-Sparse Tensor Contractions

“…The addition of quadruples provides chemical accuracy, albeit at great computational cost. CCSDTQ [26], [27], [33] requires O(N 10 ) computation and O(N 8 ) storage, while the perturbative approximation to quadruples, CCSDT(Q) [25], [28], [8], [22], reduces the computation to O(N 9 ) and the storage to O(N 6 ). Such methods have recently been called the "platinum standard" because of their unique role as a benchmarking method that is significantly more accurate than CCSD(T) [40].…”