Self-consistent electron pair method

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. 

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. 

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

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. ... 

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. 

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]. 

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. ... 

Introductory descriptions of Hartree-Fock calculations [often using Rootaan s self-consistent field (SCF) method] focus on singlet systems for which all electron spins are paired. By assuming that the calculation is restricted to two electrons per occupied orbital, the computation can be done more efficiently. This is often referred to as a spin-restricted Hartree-Fock calculation or RHF. 

Another strategy to separate the QM part from the MM one is to freeze the pair of electrons in the broken bond (assumed to be a single bond). This has been suggested first by Warshel and Levitt [22] and the method has been developed recently at the semiempirical [23,241 and ab initio levels [26-281 as the local self-consistent field (LSCF) method. 

In an interdisciplinary volume such as the present, it does not seem appropriate to give any sort of detailed coverage to the theoretical methods currently in use (, 7 ). It must be noted, however, that the Hartree-Fock or Self-Consistent-Field (SCF) method remains at the core of electronic structure theory. Although SCF theory is sometimes adequate in describing potential energy surfaces, this has turned out more often not to be the case. That is, electron correlation, which incorporates the instantaneous repulsions of pairs of electrons, can have a qualitative effect on the topology of fluorine hydrogen potential surfaces. 

Recently, the effects of static and dynamic structural fluctuations on the electron hole mobility in DNA were studied using a time-dependent self-consistent field method [33]. The motion of holes was coupled to fluctuations of two step parameters of a duplex, rise and twist (Fig. 1), namely the distances and the dihedral angles between base pairs, respectively. The hole mobility in an ideally ordered poly(G)-poly(C) duplex was found to be decreased by two orders of magnitude due to twisting of base pairs and static energy disorder. A hole mobility of 0.1 cm V s was predicted for a homogeneous system the mobility of natural duplexes is expected to be much lower [33]. In this context, one can mention several theoretical studies, based on band structure approaches, to estimate the electrical conductivity of DNA [85-87]. 

In the last configuration a particle-hole pair is considered in the system promoting an electron from the valence band (i = h) to a conduction band (i = e). For this reason the method is also called constrained DFT. The excitation energy of the many-electron system is the difference in total energy between two self-consistent calculations with the occupations described above, i.e. ... 

---