Cluster expansion methods linked clusters

The cluster expansions of the correlation functions and potentials of mean force can be found by studying the semi-invariant expansion of logg( n ) and by the use of the linked cluster theorem. The method is a straightforward extension of those given in the preceding section and details can be found in the paper by Allnatt and Cohen.3 The linked cluster method is simpler and... 

T introduces true n-particle correlation, and products like T T etc., arising out of the expansion eq.(3.2 ), generate simultaneous presence of k-particle amd m-particle correlations in a (k+m)-fold excited determinants etc. The truncation of T == T then corresponds to the pair—correlation model of Sinanoglu, while incorporating higher excited states with several disjoint pair excitations induced through the powers T - The amplitudes for T may be called linked or connected clusters for n electrons. The difficulty of a linear variation method such as Cl lies in its inability to realize the cluster expansion structure eq.(3.2),in a simple and practicable manner. 

The exponential cluster expansion has a long history in statistical physics, where it is known as the Ursell and Mayer linked-cluster expansion for the partition function [68]. A very general argument for the exponential form of the exact wave function can be found in a paper on the origins of the CC method by Kiimmel [69]. Nonetheless,... 

Multireference many-body methods. Perspective on Linked-cluster expansions for the nuclear many-body problem ... 

Many-body methods, based on the linked-cluster expansion (LCE), were first developed by Brueckner [1] and Goldstone [2] in the 1950s for nuclear physics problems. Perturbation-theory applications to atomic and molecular systems (in a numerical, one-center frame) were pioneered by Kelly [3] in the early 1960s. Basis sets were later introduced, first in second-order [4] and then in third-order [5]. The 1970s saw a proliferation of molecular applications with basis sets, under the names of many-body perturbation theory (MBPT) [6] or the Moller-Plesset method [7]. Nowadays, many-body methods offer some of the most powerful tools in the quantum chemistry arsenal, in particular the coupled-cluster (CC) method, and are available in many widely used quantum chemistry program packages. 

T/ie Goldstone expansion is rederived by elementary time-independent methods, starting from Brillouin-Wigner (BW) perturbation theory. Interaction energy terms AE are expanded out of the BW energy denominators, and the series is then rearranged to obtained the linked-cluster result. ... 

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