Coupled-cluster methods, development

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. 

Recent developments in computational chemistry have established the exact structure of carbocations by combining computational and experimental results.78,79 Furthermore, accurate 1H and 13C NMR chemical shifts of carbocations and other organic molecules can be calculated with the application of recent coupled cluster methods, such as GIAO-CCSD(T).80... 

The Soviet Union s military invasion of Czechoslovakia in August 1968 had a significant impact on the development of computational and theoretical chemistry in Canada. The troubles in Czechoslovakia led to Jiri Cizek and Joe Paldus accepting appointments at the University of Waterloo in 1968. Their many achievements include the first ab initio study of the coupled cluster method.104... 

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. 

Two ongoing developments support the tenability of the coupled-cluster method, an inherently complicated procedure. The first is the increas-... 

Full-scale treatments of correlation effects, found to be necessary to repair some of the known deficiencies of the HF model wavefunction, generally are done by Configuration Interaction theory [l),(5j. With highly developed computer codes it has been found possible to include more than 10s — 10 determinants, either explicitly or implicitly in the wavefunction expansion. Unfortunately, procedures for selecting the most important terms in the Cl expansion have proved to be a source of difficulty, despite successes of Coupled Cluster methods and related schemes (6],[7]. 

Multireference coupled cluster methods, which started development more recently, are generally divided into two types. Hilbert space CC methods use multiple reference functions to obtain a description of a few states, including the reference state (for a review see (4)). Fock space methods (for a review see (5)), on the other hand, provide direct state-to-state energy differences, relative to some common reference state. The Fock space approach is particularly well-suited to the calculation of ionization potentials (IPs), electron affinities (EAs), and excitation energies (EEs). For principal IPs and EAs, FSCC is equivalent (6, 7) to the EOM-IP and EOM-EA CC methods (1, 2, 7, 8). In this paper, we will focus primarily on the IP problem. 

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