Coupled-cluster theory large-scale calculations

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. 

O. Christiansen, H. Koch, A. Halkier, P. Jorgensen, T. Helgaker, and A. S. De Meras,/. Chem. Phys., 105, 6921 (1996). Large-Scale Calculations of Excitation Energies in Coupled-Cluster Theory The Singlet Excited States of Benzene. 

In order to use wave-function-based methods to converge to the true solution of the Schrodinger equation, it is necessary to simultaneously use a high level of theory and a large basis set. Unfortunately, this approach is only feasible for calculations involving relatively small numbers of atoms because the computational expense associated with these calculations increases rapidly with the level of theory and the number of basis functions. For a basis set with N functions, for example, the computational expense of a conventional HF calculation typically requires N4 operations, while a conventional coupled-cluster calculation requires N7 operations. Advances have been made that improve the scaling of both FIF and post-HF calculations. Even with these improvements, however you can appreciate the problem with... 

Density-functional theory (DFT) is one of the most widely used quantum mechanical approaches for calculating the structure and properties of matter on an atomic scale. It is nowadays routinely applied for calculating physical and chemical properties of molecules that are too large to be treatable by wave-function-based methods. The problem of determining the many-body wave function of a real system rapidly becomes prohibitively complex. Methods such as configuration interaction (Cl) expansions, coupled cluster (CC) techniques or Moller Plesset (MP) perturbation theory thus become harder and harder to apply. Computational complexity here is related to questions such as how many atoms there are in the molecule, how many electrons each atom contributes, how many basis functions are... 

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