A new mathematical technique to simplify group functions
Résumé
We know that HF or more generally CASSCF wave functions are invariant under a
unitary transformation of the occupied orbitals. This can be taken advantage of
to obtain a "localized" version of a "delocalized" wave function.
More generally, the question of determining the set of transformations preserving the structure of a
wavefunction of a certain form, for example, Valence Bond (VB), or Antisymmetrized Geminal Product (AGP)
or Antisymmetrized Group Function (AGF), while leaving it unchanged can be raised.
(I mean for instance T(AGP)=AGP'=AGP the transformed AGP is the same AGP but expressed with different geminals).
I propose to introduce a general (and state-of-the-art) mathematical method that addresses this problem
and partially solve it.
The knowledge of these transformations can be useful to a number of applications.
How to find the complete set of transformations is still an open problem.
To our knowledge the method we will introduce is the best one available but only retrieve
a certain class of solutions.