Coupled cluster expansion

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... 

With the triples correction added, the error relative to experiment is still as large as 15 kJ/mol. More importantly, we are now above experiment and it is reasonable to assume that the inclusion of higher-order excitations (in particular quadruples) would increase this discrepancy even further, perhaps by a few kJ/mol (judging from the differences between the doubles and triples corrections). Extending the coupled-cluster expansion to infinite order, we would eventually reach the exact solution to the nonrelativistic clamped-nuclei electronic Schrodinger equation, with an error of a little more than 15 kJ/mol. Clearly, for agreement with experiment, we must also take into account the effects of nuclear motion and relativity. 

T. V. Voorhis and M. Head-Gordon, Two-body coupled cluster expansions. J. Chem. Phys. 115, 5033 (2001). 

As to the content of Volume 20, the Editors would like to thank the authors for their contributions, which give an interesting picture of part of the current state of art of the quantum theory of matter from computational methods of optimizing the electronic energy and molecular conformations, over coupled-cluster expansion methods for the study of the open-shell correlation problem and the calculation of lifetimes of metastable states by means of the method of complex scaling, to a survey of the current state of surface structural chemistry. 

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

The purpose of introducing the coupled-cluster expansion (Eq. (45)) is that it provides us with a convenient way of approximating the FCI coefficients, at least when the Hartree-Fock model is a good one. For example, we may base our approx-... 

CCSD(T) Coupled cluster expansion with single and double excitations,... 

Restricting the coupled-cluster expansion to single and double (CCSD) excitations, i.e.. 

Let us remark that estimates of 3R can be obtained fi om other approaches to the correlation problem in atoms and molecules, such as, for example, limited configuration interaction or coupled cluster expansions. ... 

In section 6.1 we briefly describe the single reference Brillouin-Wigner coupled cluster expansions. The multireference case is considered in more detail in section 6.2. 

SINGLE REFERENCE BRILLOUIN-WIGNER COUPLED CLUSTER EXPANSIONS... 

Like CC, BWCC is fully extensive. Furthermore, the truncated forms of the Brillouin-Wigner coupled cluster expansion involving single and double substitutions usually designated BWCCD corresponding to the approximation (67) and BWCCSD corresponding to the approximation... 

Single state coupled cluster expansions and multireference coupled cluster expansions based on the generalized Brillouin-Wigner pertm bation theory have been described elsewhere [19]. The generalized Brillouin-Wigner perturbation theory can also be applied to the configuration interaction problem. 

MULTIREFERENCE BRILLOUIN-WICNER COUPLED CLUSTER EXPANSION... 

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