Outline of Elongation Method

As shown in Fig. 6.2 (stepl), the density matrix in the orthogonal atomic orbital (OAO) basis is transferred from AO basis by X, where the following idempotence relation of the density matrix in an OAO basis 

A regional orbital (RO) space is constructed by separately diagonalizing the 

1) 0AO belonging to A and B regions, respectively. These eigenvectors span the RO space. The transformation from OAOs to ROs is given by the direct sum of and T, where and are the eigenvectors of 

Except for orthogonalization tails the ROs given above are completely local- 

Finally, the unitary transformation from CMO to RLMO is given in the Fig. 6.2 (step 5). After transferring TC back to the AO basis by using X, we can get the RLMO coefficients in the AO basis as shown in the right hand side of the Fig. 6.2 (step 5). 

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