Revisiting the foundations of symmetry operation measures for electronic wavefunctions

An extension of the continuous symmetry measures for N-electron wavefunctions is proposed in order to solve some of the problems encountered with earlier definitions for this property that appear when dealing with molecules that present quasisymmetries close to a point group with degenerate irreducible representations. The mathematical origin of these problems is analyzed and it is shown, via some examples, how the newly defined symmetry operation measures are able to overcome them and give a correct answer for any type of symmetry operation.