I'm going through some papers about HSQ (hydrogen silsesquioxane) and keep seeing this fractional notation being used: HSiO

_{3/2} , SiO

_{4/2} , H

_{2}SiO

_{2/2} , H

_{3}SiO

_{1/2}.

Example paper:

https://www.physik.hu-berlin.de/de/x-ray/publications/pdf/caster_kowarik_jramanspectroscopy_2009_hsq_cars.pdfI understand that the proper formula for HSQ is [HSiO

_{3/2}]2n. Because we can't have fractional atoms, it's always multiplied by an even number and as such the fraction is never a consideration. But then why are the fractions maintained in the other compounds, and not reduced to SiO

_{2} and H

_{2}SiO ?

Does keeping the fraction confer some structural information ? I've tried to find out what this notation means, but could not find a proper explanation.

I guess what I'm trying to find out is, what do the numerator and denominators mean, formally, in those formulas ? If it's that the oxigen atoms share outside bonds, why not write the compound as SiO

_{4}^{−4} ? If the numerator is the number of atoms, what does the denominator represent ? And is it always /2 ? Can we have /x , where x is a different integer ? I've never seen this type of notation before. Does the denominator mean that the valence electrons are halved ? If you look at the linked paper's figure 1 where they draw out the cage, there's only one SiO

_{4} entity. The oxigen atoms are not shared with another SiO

_{4} entity, they connect to a H

_{3}SiO

_{1/2}, or a HSiO

_{3/2}. I am really confused by this notation because I've not seen it in any textbook, and it's not formally defined.

Would it be correct then to say that silicon dioxide SiO

_{2} is made up of SiO

_{4/2} entities in which all oxygen atoms are shared with others ? Where 4 stands for four oxygens, and 2 means that each oxygen is shared between two SiO

_{4} entities ?

I've also asked this question on chemistry stackexchange but haven't gotten very far with my search for an answer.

https://chemistry.stackexchange.com/questions/151392/what-does-fractional-notation-represent-in-molecular-formulas-such-as-sio4-2-or