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When we do the reduction of the reducible representation generated from the total wavefunction expressed as product of MOs of appropriate symmetry, we can find the direct sum of more than one irreducible representation.

How to distinguish them? Can we find the way to espress functions of the basis set which generate irreducible representations from the original product of MOs?

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  • $\begingroup$ Projection operators can be used to extract irreducible representations. $\endgroup$
    – Hans Wurst
    Commented Aug 31, 2023 at 21:00
  • $\begingroup$ @HansWurst so if a have, for example, a Slater determinant of spin-MOs have I only to apply the projection operator? But how to apply it to a product of functions? $\endgroup$
    – Chemistry.
    Commented Sep 1, 2023 at 6:02
  • $\begingroup$ Operators acting on this product are obtained forming the tensor product of the single particle operators. $\endgroup$
    – Hans Wurst
    Commented Sep 1, 2023 at 7:12
  • $\begingroup$ @HansWurst and the use of these operators has some practical applications? Maybe to decrease the computational cost of some computation? $\endgroup$
    – Chemistry.
    Commented Sep 1, 2023 at 13:02
  • $\begingroup$ @HansWurst last curiosity: with this projection operator can I, for example, combine Salter determinant which describe atomic terms to find correct function for the specific crystal field? And from a correlation diagram between the limits of infinity crystal field and infinity repulsion can I obtain informations on which of these determinants will be combined? $\endgroup$
    – Chemistry.
    Commented Sep 1, 2023 at 14:20

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