Integrals Lowdin transformation

The most important change in MSINDO with respect to SINDOl is a modification of the approximate Lowdin orthogonalization of the basis [253]. Only the first-order terms in overlap are retained in (6.38). In SINDOl the expansion was to second order. If only first-order terms are taken into account, no transformation of the two-electron integrals is necessary. The one-electron integrals are transformed... 

In the case of the two-electron integrals, this provides the traditional justification for the NDDO approximation [42] Numerical studies have shown that the three- and four-center as well as certain two-center two-electron integrals are indeed small in a Lowdin-orthogonalized basis and may therefore be neglected. For the remaining two-center two-electron NDDO integrals, the orthogonalization transformation leads to a moderate... 

The most important feature of the SINDOl method is that an orthogonalization transformation of the basis functions is taken into account exphcitly in solving the HF LCAO equations. The one-electron integral matrix H is transformed to Lowdin symmetrically orthogonahzed [225] AOs = S / x... 

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