Calculations on N2 and HF

For small basis sets and molecules, it is possible to calculate the full set of energies in the coupled-cluster hierarchy, from the Hartree-Fock to the full configuration-interaction (FCI) energy [18]. Although such 

In Table 1.2, we have listed the valence cc-pVDZ electronic energies and AEs of N2 and HF at different levels of coupled-cluster theory. The energies are given as deviations from the FCI values. Comparing the different levels of theory, we note that the error is reduced by one order of magnitude at each level. In particular, at the CCSDT level, there is a residual error of the order of a few kJ/mol in the calculated energies and AEs, suggesting that the CCSDTQ model is usually needed to reproduce experimental measurements to within the quoted errors bars (often less than 1 kJ/mol). 

Let us make two more observations about the convergence of the coupled-cluster hierarchy. First, it converges faster for HF than for N2, reflecting the more complicated electronic structure of the multiple bond in N2. Second, the cancellation of errors in the calculated AEs becomes less pronounced as we move up in the coupled-cluster hierarchy. The cancellation diminishes since the coupled-cluster expansions of the atoms 

Although the calculations reported here have been carried out in a small basis, there is no reason to believe that our conclusions regarding the convergence of the coupled-cluster hierarchy would be different had the calculations been carried out in larger basis. In particular, we conclude that the CCSDT model is incapable of predicting AEs to within 1 kJ/mol. 

---