Edmiston-Ruedenberg localization procedure

The Edmiston-Ruedenberg localization procedure /58/ consists of an intrashell transformation of selfrepulsion energy until the sum... 

Given these encouraging preliminary results, further investigation of the effect of SIC on reaction barriers is warranted. For more complicated reactions, it is likely that the initial scheme used here will need to be elaborated, either by going to better localization methods (e.g. Edmiston-Ruedenberg localization [79]), or by incorporating the SIC term in the self-consistent procedure, which is more expensive. 

Although the localization by energy criteria (Edmiston-Ruedenberg) may be considered more fundamental than one based on distance (Boys) or atomic charge (Pipek-Mezey), the difference in computational effort means that the Boys or Pipek-Mezey procedures are often used in practice, especially since there is normally little difference in the shape of the final LMOs. 

As to the localization of occupied orbitals the conventional procedures (Edmiston-Ruedenberg (Edmiston etal., 1963), Boys (Boys, 1966) might not be the most suitable because they do not restrict the magnitude of the off-diagonal Fock matrix elements. Regarding the localization of virtual orbitals, they cannot be localized uniquely into... 

A localization procedure similar to that of Edmiston and Ruedenberg has been proposed by Suthers and Linnett" for FSGO wave functions. The two electron... 

A recently often used practical method is that of proposed by Pipek and Mezey [26], Their intrinsic localization is based on a special mathematical measure of localization. It uses no external criteria to. define a priori orbitals. The method is similar to the Edmiston-Ruedenberg s localization method in the a-n separation of the orbitals while it works as economically as the Boys procedure. For the application of their localization algorithm, the knowledge of atomic overlap integrals is sufficient. This feature allows the adoption of their algorithm for both ab initio and semiempirical methods. The implementation of die procedure in existing program systems is easy, and this property makes the Pipek-Mezey s method very attractive for practical use. 

The NBO procedure is not the only localization technique for transforming delocalized MOs into the intuitive Lewis structure description. Foster and Boys, Edmiston and Ruedenberg," and Pipek and Mezey reported alternative localization procedures that provide additional bridges between MO and VB theories. From the organic chemist s point of view, these approaches are conceptually similar to NBO and, for the sake of brevity, will not be discussed here. 

In CH4, the equivalent C—H orbitals are determined by symmetry. In other molecules with less symmetry, e.g. HjO, CjHg, etc., t may be determined so as to minimize the magnitude of the exchange terms - in Eq. (144), or by a similar criterion. Localized orbitals have been studied extensively by Pople, Linnett and Hall >. Very recently, Ruedenberg and Edmiston have developed a procedure for calculating them based on the "minimum exchange criterion. ... 

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