Local space approximation

An interesting approach to the problem of calculating the local wave function of a fragment in interaction with its surrounding has been proposed by Kirtman and de Melo [88]. Their approach is based on the density matrix formulation of the HF problem. The zeroth order approximation to the density matrix of the total system is a simple direct sum of the density matrices of the fragments, provided that the AO basis is orthogonal by construction or it is properly orthogonalized. 

The first-order corrections due to the interaction are calculated so that the idempotency of the density matrix be preserved. According to McWeeny [94] the most general form of this first-order correction to Rq is 

Using the variation condition one can derive a linear equation for Xq which, in turn, can be used to evaluate the first-order correction to the density matrix. This leads to an iterative scheme involving matrix manipulations in the local space. It is important to note that Kirtman s treatment describes not only inductive but delocalization effects, as well. A practical limitation is that one should work with orthogonal AO basis sets therefore the calculations have been done with semiempirical ZDO model Hamiltonians [91], or with explicitly Lowdin-orthogonalized basis sets in ab initio calculations. 

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Kirtman B (1999) Local Space Approximation Methods for Correlated Electronic Structure Calculations in Large Delocalized Systems that are Locally Perturbed. 203 147-166 Kita Y, see Tohma H (2003) 224 209-248 KleiJ AW, see Kreiter R (2001) 217 163-199 Klein Gebbink RJM, see Kreiter R (2001) 217 163-199... 

Kirtman B (1999) Local Space Approximation Methods for Correlated Electronic Structure Calculations in Large Delocalized Systems that are Locally Perturbed. 203 147 -166 Klopper W, Kutzelnigg W, Muller H, Noga J, Vogtner S (1999) Extremal Electron Pairs - Application to Electron Correlation, Especially the R12 Method. 203 21 -42 Knochel P,see Betzemeier B (1999) 206 61-78 Kozhushkov SI, see de Meijere A (1999) 201 1-42 Kozhushkov SI, see de Meijere A (2000) 207 89-147 Kozhushkov SI, see de Meijere A (2000) 207 149-227 Kutzelnigg W, see Klopper W (1999) 203 21 - 42... 

Kirtman formulated a density matrix treatment using a separated pair an-satz [86], He derived variational equations in the local space approximation to determine fragment wave functions and discussed the role of strong orthogonality in the localization of the wave function. 

Local Space Approximation Methods for Correlated Electronic Structure Calculations... 

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