Coupled-cluster correlation energies

The coupled cluster correlation energy is therefore determined completely by the singles and doubles amplitudes and the two-electron MO integrals. 

Tew, D.P., Klopper, W., Neiss, C., Hattig, C. Quintuple- quality coupled-cluster correlation energies with triple- basis sets. Phys. Chem. Chem. Phys. 2007, 9, 1921-30. 

Evaluated with the aug-cc-pVTZ basis set. Coupled-cluster methods estimated via an addition of the difference between MP2 and coupled-cluster correlation energies with the aug-cc-pVDZ basis set to the MP2/aug-cc-pVTZ energies. 

IVible 8 Coupled-cluster Correlation Energies (in m h) for Be, LiH, and Ne from Pair Function Expansions in a Two-particle Basis Set of Gaussian Geminals... 

Keywords Block correlated coupled cluster method energy surface Size-extensivity error... 

Comparing the last two entries in Figure 4.7, the all-electron Douglas-Kroll coupled cluster result for A te is in perfect agreement with the RPPA [156, 157]. Figure 4.8 shows the relativistic effects in dissociation energies. Here, relativistic effects are very sensitive to the level of electron correlation and basis sets used. RPPA... 

For all intents and purposes then, we are concerned here with the CCSD (coupled cluster with all single and double substitutions [30]) correlation energy. Its convergence is excruciatingly slow Schwartz [31] showed as early as 1963 that the increments of successive angular momenta l to the second-order correlation energy of helium-like atoms converge as... 

Another approach of this kind uses the approximate Brueckner orbitals from a so-called Brueckner doubles, coupled-cluster calculation [39, 40]. Methods of this kind are distinguished by their versatility and have been applied to valence ionization energies of closed-shell molecules, electron detachment energies of highly correlated anions, core ionization... 

The CCS, CC2, CCSD, CC3 hierarchy has been designed specially for the calculation of frequency-dependent properties. In this hierarchy, a systematic improvement in the description of the dynamic electron correlation is obtained at each level. For example, comparing CCS, CC2, CCSD, CC3 with FCI singlet and triplet excitation energies showed that the errors decreased by about a factor 3 at each level in the coupled cluster hierarchy [18]. The CC3 error was as small as 0.016 eV and the accuracy of the CC3 excitation energies was comparable to the one of the CCSDT model [18]. 

The electron correlation problem remains a central research area for quantum chemists, as its solution would provide the exact energies for arbitrary systems. Today there exist many procedures for calculating the electron correlation energy (/), none of which, unfortunately, is both robust and computationally inexpensive. Configuration interaction (Cl) methods provide a conceptually simple route to correlation energies and a full Cl calculation will provide exact energies but only at prohibitive computational cost as it scales factorially with the number of basis functions, N. Truncated Cl methods such as CISD (A cost) are more computationally feasible but can still only be used for small systems and are neither size consistent nor size extensive. Coupled cluster... 

---