Page 87 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

72 C. VALDEMORO
auxiliary conditions, very good approximations have recently been obtained by using
this method.
In order to see an example of how these suplementary conditions are imposed let us
consider the approximation of a 3-RDM in terms of the 2-RDM. Since an RDM
cannot have any negative diagonal element when such an element occurs it is put equal
to zero. Until now the negative diagonal elements found were of the type
where M represents the approximated 3-RDM. By comparing the approximated
matrix with the exact one it was apparent that the deffect in was compensated
very closely by an excess in the element therefore this element was corrected
in accordance. After this correction was performed the new elements (M´) had the
value:

It has been shown [48] that the related off-diagonal elements obey
definite symmetry relations which must be maintained after the corrections indicated
above have been applied.