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WIREs Comput Mol Sci
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From configuration interaction to coupled cluster theory: The quadratic configuration interaction approach

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Abstract Configuration interaction (CI) theory has dominated the first 50 years of quantum chemistry before it was replaced by many‐body perturbation theory and coupled cluster theory. However, even today it plays an important role in the education of everybody who wants to enter the realm of quantum chemistry. Apart from this, full CI is the method of choice for getting exact energies for a given basis set. The development of CI theory from the early days of quantum chemistry up to our time is described with special emphasis on the size‐extensivity problem, which after its discovery has reduced the use of CI methods considerably. It led to the development of the quadratic CI (QCI) approach as a special form of size‐extensive CI. Intimately linked with QCI is the scientific dispute between QCI developers and their opponents, who argued that the QCI approach in its original form does not lead to a set of size‐extensive CI methods. This dispute was settled when it was shown that QCI in its original form can be converted into a generally defined series of size‐extensive methods, which however have to be viewed as a series of simplified coupled cluster methods rather than a series of size‐extensive CI methods. © 2013 John Wiley & Sons, Ltd. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Number of energy contributions E(n)(ABC ···) accounted for by QCI, CC, and MPn (n = 4, 5, 6, 7, 8, …) methods, where A, B, C, … denote S, D, T, Q, … contributions, respectively.

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Number of MPn (n = 6) energy contributions of the TTA, TAT, and TTT (A = S, D, Q, P) coupling type as accounted for by QCI and CC methods. The first entry (black) gives the total number, whereas the second entry (red) gives the number of terms only partly contained. Note that MP6 is the reference defining the total number of TT coupling contributions (11).

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Total number of MPn (n = 6) energy contributions E(n)(ABC) (Total: black) and number of MPn (n = 6) energy contributions E(n)(ABC) containing T effects (T: blue) as accounted for by QCI and CC methods. Some of these terms are only contained partly: (Total) in red; (T) in pink. In each case, the number of terms is given at the top of the bar (all terms) or the base of the bar (partly contained terms). Note that MP6 is the reference defining the total number of E(n)(ABC) contributions (36) as well as the total number of T contributions (25). Reproduced with permission from Ref. 118 (Copyright 1994, Springer) and Ref. 119 (Copyright 1997, Springer).

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