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REDUCED DENSITY MATRIX VERSUS WAVE FUNCTION 67
where
is the 2-RDM written in first quantization language. The symbols denote
the Hamiltonians of two and three electrons respectively and is the two electron
repulsion operator.
Since this integro-differential equation depends not only on but also, through the
two integral terms, on and it is indeterminate [43].
An important property of the NCF equation is that in it the variational principle is
taken implicitly into account [42,44].
5.2. ORBITAL REPRESENTATION OF THE CONTRACTED SCHRÖDINGER
EQUATION (CSchE)
The matrix form in a spin-geminal representation (CSchE) of equation (34) was
obtained [18] in 1985 by applying the MCM.
The interest of contracting the matrix form of the Schrödinger equation by employing
the MCM, is that the resulting equation is easy to handle since only matrix opera-
tions are involved in it. Thus, when the MCM is employed up to the two electron
space, the geminal representation of the CSchE has the form [35]:
where the symbols have the same meaning as in the preceding sections. It must be
pointed out, that the contraction can also be carried out, up to the first order and
the result is:
5.3. ITERATIVE SOLUTION OF THE CSchE
It was suggested [35,45] that the indeterminacy of the CSchE could be removed
by replacing in it the 3- and the 4-RDM’s by their corresponding approximations
evaluated within the SRH formalism. After this replacement is performed, the matrix
equation can be solved with the help of relation (10) and
as auxiliary conditions.
Recently, a more powerful approach has been initiated. The different steps involved
in the procedure just proposed for solving the CSchE are:
