Might molecular symmetry operations exist “partially”?

A new paradigm about molecular symmetry is proposed. We advance the idea that, beside the symmetry operations possessed "in full" by a molecule and canonically characterizing its point group, other symmetry operations could exist "in part". As a matter of fact, the schematic representation of the molecule as built by the "Dreiding molecular modeling kit" is, obviously, too crude. In a more realistic description, the atoms should not be considered as point masses (since they take up up a certain volume) and their positions in the molecular structure should considered to be affected by a certain statistical uncertainty. Following this approach, here we suggest to construct suitable matrices to describe the "overlap" between the "virtual" images of the molecule before and after the "hypothetical" symmetry operations; then, by evaluating a properly defined parameter (function of the determinant of the overlap matrix), it will be possible to quantify how much a residual "symmetry operation" is present in the molecule, in a range from 0 to 100%, due to the less idealized description of the "object molecule". Demonstrative examples of this approach are extensively described in the present work, for cases where "traces" of residual symmetry operations are significant, amounting to values from about 20% to about 35%. In my opinion, the present work should be included in the general efforts to overcome and broaden the current canonical concepts and approaches to determine what are the symmetry operations the molecules are endowed with, so allowing for the possibility of exploring symmetry "grey scales" useful, for example, to possibly explain surprising experimental results (as, for example, the detection of unexpected signals, from some kind of spectroscopy, unexplainable otherwise).