Self-consistent electron pairs

Dykstra, C. E., R. A. Chiles, and M. D. Garrett. 1981. Recent Computational Developments with the Self-Consistent Electron Pairs Method and Application to the Stability of Glycine Conformers. J. Comput. Chem. 2, 266-272. 

Wemer, H.-J. 2000. Perspective on Theory of Self-consistent Electron Pairs. An Iterative Method... 

Even though computers were an essential tool in quantum chemical calculations, the main challenge was the further development of methods and concepts to describe even more facets of chemistry and with higher accuracy. Methods that account for electron correlation were extended to be able to describe energy surfaces more reliably. Several variants of the CEPA Ansatz (CEPA-1, CEPA-2) were developed as well as the method of self-consistent electron pairs (SCEP). Formulations using canonical or localized orbitals (e.g., pair natural orbitals, PNO, as a kind of optimized virtual orbitals) were put forth. These methods were extensively used for two decades, primarily in Germany, until coupled cluster formulations became more popular. ... 

W. Meyer, /. Chem. Phys., 64, 2901 (1976). Theory of Self-Consistent Electron Pairs. An... 

Self-Consistent-Electron- Pair Theory which is due to an efficient operator formalism for obtaining the necessary matrix elements. The procedures noted in this paragraphs were developed only recently, so that one may expect that their further development will bring yet more computational gain. 

SCEP Self-Consistent Electron Pair. A correlation technique that considers electrons two at a time. 

There is no room here to collect together all important achievements in quantum chemistry which are strongly or loosely connected to geminals or at least, their development was perhaps motivated by the successes or failures of geminal theories (cf. e.g. the self-consistent electron pair method by Meyer and its reformulations [69,70,71], or the connections to valence bond theory [72]). We have to mention an important book by Hurley [73] in which significant attention was paid to geminals and their localization. 

The general approach used in LSA methods to introduce electron correlation is based on Meyer s [22] self-consistent electron pair (SCEP) theory, later extended by Ahlrichs [23] and Dykstra et al. [24-27]. Additional important improvements in SCEP theory were made by Saebo and Pulay [28-36] leading ultimately to their very successful local correlation treatment. We have adopted many of the specific features devised by Saebo and Pulay. Indeed, at first glance, the similarity between their treatment and ours might be more evident than the differences. However, the LSA deals particularly with the situation where a calculation of the entire system is impractical at any level. Thus, in contrast with Saebo and Pulay s procedure, our method applies even for the HF model. Moreover, because we start with isolated fragments the LSA method can be utilized to treat fully delocalized problems like chemisorption on a metal surface which are not amenable to a local correlation treatment. 

Dykstra, C.E. Schaefer, H.F. The vinylidene-acetylene rearrangement A self-consistent electron pairs study of a model unimolecular reaction. J. Am. Chem. Soc. 1978, 100, 1378-1382. 

III. THE INTERNALLY CONTRACTED MULTICONFIGURATION REFERENCE SELF-CONSISTENT ELECTRON-PAIR METHOD... 

An alternative method, named internally contracted Cl, was suggested by Meyer and was applied by Werner and Reinsch in the MCSCF self-consistent electron-pair (SCEP) approach. Here only one reference state is used, the entire MCSCF wavefunction. The Cl expansion is then in principle independent of the number of configurations used to build the MCSCF wavefunction. In practice, however, the complexity of the calculation also strongly depends on the size of the MCSCF expansion. A general configuration-interaction scheme which uses, for example, a CASSCF reference state, therefore still awaits development. Such a Cl wavefunction could preferably be used on the first-order interacting space, which for a CASSCF wavefunction can be obtained from single and double substitutions of the form ... 

R. Ahhichs and E. Driessler, Determination of pair natural orbitals. A new method to solve the multiconfiguration Hartree-Eock problem for two-electron wave functions, Theor. Chim. Acta, 36 (1975) 275. W. Meyer, Theory of self-consistent electron pairs. An iterative method for correlated many-electron... 

Closely related to CEPA are the method of self-consistency electron pairs (SCEP) [138] and also the coupled-pair functional approach (CPF) [139]. 

Perspective on Theory of self-consistent electron pairs. 

Key words Electron correlation - Configuration interaction - Direct configuration interaction - Self-consistent electron pair theories - Local correlation... 

The possibility of a very efficient Cl treatment of two-electron wavefunc-tions was realized first by Ahlrichs and Driessler. Meyer then showed with the development of the self-consistent electron-pair (SCEP) method that the great structural simplicity, e.g. of Eq. (33), can basically be carried over to the treatment of n-electron systems, e.g. within the framework of a single-reference CI(D) treatment. Since then, various improvements and extensions have been proposed, of which we mention especially the generalization to the MR-CI(SD) case. ... 

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