Cluster methods

Kruger S and Rdsch N 1994 The moderately-large-embedded-cluster method for metal surfaces a density-functional study of atomic adsorption J. Phys. Condens Matters 8149... 

Brown R D and Y C Martin 1996. Use of Structure-Activity Data to Compare Structure-Base Clustering Methods and Descriptors for Use in Compound Selection. Journal of Chemia Information and Computer Science 36 572-583. 

There is a variation on the coupled cluster method known as the symmetry adapted cluster (SAC) method. This is also a size consistent method. For excited states, a Cl out of this space, called a SAC-CI, is done. This improves the accuracy of electronic excited-state energies. 

Figure 6 A schematic representation of two clustering methods, m which each point represents a single molecular conformation and the circles are the similarity cutoff distances used to define the clusters, (a) Three clusters are defined when overlapping clusters are grouped together, (h) Five clusters are defined when the overlaps are removed from one of the overlapping clusters.

Coupled Cluster methods, including doubles (energies and optimizations) or singles and doubles (energies only), and optional triples terms (CCD, CCSD, CCSD(T)). 

The structure of ozone is a well-known pathological case for electronic structure theory. Prior to the QCI and coupled cluster methods, it proved very difficult to model accurately. The following table summarized the results of geometry optimizations of ozone, performed at the MP2, QCISD and QCISD(T) levels using the 6-31G(d) basis set ... 

Since the singly excited determinants effectively relax the orbitals in a CCSD calculation, non-canonical HF orbitals can also be used in coupled cluster methods. This allows for example the use of open-shell singlet states (which require two Slater determinants) as reference for a coupled cluster calculation. 

Analogously to MP methods, coupled cluster theory may also be based on a UFIF reference wave function. The resulting UCC methods again suffer from spin contamination of the underlying UHF, but the infinite nature of coupled cluster methods is substantially better at reducing spin contamination relative to UMP. Projection methods analogous to those of the PUMP case have been considered but are not commonly used. ROHF based coupled cluster methods have also been proposed, but appear to give results very similar to UCC, especially at the CCSD(T) level. 

The use of Cl methods has been declining in recent years, to the profit of MP and especially CC methods. It is now recognized that size extensivity is important for obtaining accurate results. Excited states, however, are somewhat difficult to treat by perturbation or coupled cluster methods, and Cl or MCSCF based methods have been the prefen ed methods here. More recently propagator or equation of motion (Section 10.9) methods have been developed for coupled cluster wave functions, which allows calculation of exited state properties. 

Figures 11.9 and 11.10 compare the performance of the CCSD and CCSD(T) methods, based on either an RFIF or UHF reference wave function. Compared to the RMP plot (Figure 11.7), it is seen that the infinite nature of coupled cluster causes it to perform somewhat better as the reference wave function becomes increasingly poor. While the RMP4 energy curve follows the exact out to an elongation of 1.0A, the CCSD(T) has the same accuracy out to - 1.5 A. Eventually, however, the wrong dissociation limit of the RHF wave also makes the coupled cluster methods break down, and the energy starts to decrease.

The spin contamination makes the UCC energy curves somewhat too high in the intermediate region, but the infinite nature of coupled cluster methods makes them significantly better at removing unwanted spin states as compared to UMPu methods (Figure 11.8). 

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