Coupled-cluster theory energy

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). 

To improve on the CCSD description, we go to the next level of coupled-cluster theory, including corrections from triple excitations -see the third row of Table 1.4, where we have listed the triples corrections to the energies as obtained at the CCSD(T) level. The triples corrections to the molecular and atomic energies are almost two orders of magnitude smaller than the singles and doubles corrections. However, for the triples, there is less cancellation between the corrections to the molecule and its atoms than for the doubles. The total triples correction to the AE is therefore only one order of magnitude smaller than the singles and doubles corrections. 

Use of Equation (1) in numerical work requires a means of generating x(r, r i(o) as well as the average charge density. Direct variational methods are not applicable to the expression for E itself, due to use of the virial theorem. However, both pc(r) and x(r, r ico) (39-42, 109-112) are computable with density-functional methods, thus permitting individual computations of E from Eq. (1) and investigations of the effects of various approximations for x(r, r ico). Within coupled-cluster theory, x(r, r ico) can be generated directly (53) from the definition in Eq. (3) then Eq. (1) yields the coupled-cluster energy in a new form, as an expectation value. 

Finally, Levchenko and Krylov (2004) have defined spin-flip versions of coupled cluster theories along lines similar to those previously described for SF-CISD. Applications to date have primarily been concerned with the accurate computation of electronically excited states, but the models are equally applicable to computing correlation energies for ground states. 

Most of the models described above have also been implemented at correlated levels of tlieory, including perturbation theory. Cl, and coupled-cluster theory (of course, the DFT SCRF process is correlated by construction of the functional). Unsurprisingly, if a molecule is subject to large correlation effects, so too is the electrostatic component of its solvation free energy. 

The corrections in going from HF to MP2 are large (Table 7.3) and the computational effort increases dramatically for small improvements in energies and geometries. With a limited basis set such as DZP, it is clear that CCSD(T), which should be superior to MP4, cannot five up to its promise because the basis set is too small. A major conclusion is that there must be a good balance between attempted amount of electron correlation recovery and basis set size. It is advisable to use at least triple-f quality type basis sets for highly correlated methods such as coupled cluster theory. 

T. Korona, B. Jeziorski, One-electron properties and electrostatic interaction energies from the expectation value expression and wave function of singles and doubles coupled cluster theory. 

In two recent publications we have tried to characterize the excited state properties of 1 and 3 in order to facilitate their detection by LIF-spectroscopy. Our main tool in this effort has been equation of motion coupled cluster theory (EOM-CC). The EOM-CCSD method, which is equivalent to linear response CCSD, has been shown to provide an accurate description of both valence and excited states even in systems where electron correlation effects play an important role [39]. Computed transition energies for excitations that are of mainly single substitution character are generally accurate to within 0.1 eV. We have found the EOM-CCSD method to perform particularly well in combination with the doubly-augmented cc-pVDZ (d-aug-cc-pVDZ) basis set. This basis seems to provide equally balanced descriptions of ground and excited states,... 

Sekino H, Bartlett RJ (1984) A linear response, coupled-cluster theory for excitation energy. Int J Quantum Chem Symp 18 255—265. 

Christiansen O, Koch H, Halkier A, Jprgensen P, Helgaker T, Sanchez de Meras A (1996) Large-scale calculations of excitation energies in coupled-cluster theory The singlet excited states of benzene. J Chem Phys 105 6921-6939. 

Larsen H, Hald K, Olsen J, J0rgensen P (2001) Triplet excitation energies in full configuration interaction and coupled-cluster theory. J Chem Phys 115 3015-3020. 

Christiansen O, Koch H, Jprgensen P, Olsen J (1996) Excitation energies of H20, N2, and C2 in full configuration and coupled cluster theory. Chem Phys Lett 256 185-194. 

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