Single, double, triple, and quadruple excitations

The convergence behaviour of the MP expansion is obviously crucial to the success of the method, and numerous investigations have been carried out [9, 10]. Neither MP2 nor MP3 are entirely satisfactory. These implicitly require the first-order wave function, which involves only double excitations. MP4, if carried out completely, involves single, double, triple and quadruple excitations. It is more expensive than CISD, say, but often produces better results. MP5 and higher orders are likely to be impractically expensive. 

Coupled-cluster with single, double, triple, and quadruple excitation cluster operators... 

Kucharski SA, Bartlett RJ (1991) Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations. Theor Chim Acta 80 387 105. 

T2 contains a nonzero first-order component contributions to Tj, T3, and T4 first appear in second order because the corresponding second-order wavefunc-tion contains single, double, triple, and quadruple excitations. 

S. A. Kucharski and R.. Bartlett, /. Chem. Phys., 97, 4282 (1992). The Coupled-Cluster Single, Double, Triple, and Quadruple Excitation Method. 

It allows single, double, triple and quadruple excitations for. / > so that the second order correction to the free energy of interaction is... 

Fig. 5. Electron configuration diagrams showing the configurations correspronding to the HF wave function, and the various possible excited configurations. For this 4-electron system, the combination of single, double, triple, and quadruple excitations constitutes full CL However, with an infinite basis set, there would be an infinite number of unoccupied orbitals (instead of the two shown here) to promote the electrons into, and thus an infinite number of determinants would be required to obtain the exact solution to the Schrodinger equation.

Early comparisons of this sort were based on work by Handy and coworkers [37], who developed an efficient direct FCI approach in terms of determinants. Using a double-zeta (DZ) basis set, they considered stretching the 0-H bond lengths in the H2O molecule to 1.5 and 2.0 times their equilibrium values. The FCI results showed that even the restricted Hartree-Fock (RHF) based fourth-order many-body perturbation theory (MBPT) approach [38], which includes the effect of single, double, triple and quadruple excitations, did not accurately describe the stretching of the bond the error increased from 0.6 kcal/mole at to 10.3 kcal/mole... 

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