Cluster expansion methods size-extensivity

The CASSCF method itself is not very useful for anything else than systems with few electrons unless an effective method to treat dynamical correlation effects could be developed. The Multi-Reference Cl (MRCI) method was available but was limited due to the steep increase of the size of the Cl expansion as a function of the number of correlated electrons, the basis set, and the number of active orbitals in the reference function. The direct MRCI formulation by P. Siegbahn helped but the limits still prevented applications to larger systems with many valence electrons [20], The method is still used with some success due to recent technological developments [21], Another drawback with the MRCI approach is the lack of size-extensivity, even if methods are available that can approximately correct the energies. Multi-reference coupled-cluster methods are studied but have not yet reached a state where real applications are possible. 

The 1inked-cluster theorem for energy, from the above analysis, is a consequence of the connectivity of T, and the exponential structure for ft. Size-extensivity is thus seen as a consequence of cluster expansion of the wave function. Specfic realizations of the situation are provided by the Bruckner—Goldstone MBPT/25,26/, as indicated by Hubbard/27/, or in the non-perturbative CC theory as indicated by Coester/30,31/, Kummel/317, Cizek/32/, Paldus/33/, Bartlett/21(a)/ and others/30-38/. There are also the earlier approximate many-electron theories like CEPA/47/, Sinanoglu s Many Electron Theory/28/ or the Cl methods with cluster correction /467. 

Cluster expansion representation of a wave-function built from a single determinant reference function [1] has been eminently successful in treating electron correlation effects with high accuracy for closed shell atoms and molecules. The cluster expansion approach provides size-extensive energies and is thus the method of choice for large systems. The two principal modes of cluster expansion developments in Quantum Chemistry have been the use of single reference many-body perturbation theory (SR-MBPT) [2] and the non-perturbative single reference Coupled Cluster (SRCC) theory [3,4]. While the former is computationally economical for the first few orders of the perturbation expansion... 

Although gas phase clusters can be generated by a number of techniques, adiabatic expansions are the most widely utilized method for the generation of vdW clusters. A wealth of information regarding the energetics, dynamics, and structures of clusters has been recently obtained due to the availability of many new and improved experimental techniques. Although a number of spectroscopic techniques have been utilized in investigating vdW clusters, mass spectrometry (MS) is extensively employed for the study of clusters, as it enables size selective... 

The problem in these experiments is to get cluster specific information. The cluster beam is usually generated as a distribution of different cluster sizes and a liquid-He-cooled bolometer is not able to discriminate between the different masses. But even a mass spectrometer is only of limiting help because of the extensive fragmentation which occurs when these weakly bound clusters are ionized. A way out of this problem is either to use very dilute mixtures in the expansion and to take the high resolution spectrum itself for identification which works mainly for dimers and a few trimers or to carry out the experiments with size selected clusters. We have recently developed a method which selects smaller clusters by a scattering process with a He beam. This technique has been successfully applied to infrared photodissodation experiments. After the first experimental results on C2H4 dimers... 

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