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A regional embedding method
Author(s) -
Zou P. F.
Publication year - 1992
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560440605
Subject(s) - embedding , matrix (chemical analysis) , inverse , second derivative , derivative (finance) , inversion (geology) , surface (topology) , energy (signal processing) , term (time) , basis (linear algebra) , mathematics , mathematical analysis , physics , chemistry , computer science , geometry , quantum mechanics , paleontology , chromatography , structural basin , artificial intelligence , financial economics , economics , biology
Abstract A new variational embedding method is derived. This method couples Nesbet's use of the R ‐matrix in the determination of the electronic structure of a crystal with the energy variational technique. The procedure is based on the observation that in many cases the properties for a spatial region of a system change by relatively small amounts when the region is transferred to another system. The transfer of the region from one system to another is accomplished by the embedding potential that is obtained by the inversion of the R ‐matrix and its energy derivative. It is shown that the interaction between two connected regions can be written as a surface term that is obtained by the continuity conditions on the wave function and its derivative on the surface. The existence of an identity resolution on the surface is demonstrated and this result is used to derive the R ‐matrix and its inverse. An application of this method to H 2 +is given, which shows that the method is accurate and reliable if one chooses the appropriate basis set to construct the R ‐matrix and to perform the variation. © 1992 John Wiley & Sons, Inc.