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The Mn-O bonds of Mn2O7 have more covalent character than those of MnO2. This makes sense when imagining Mn2O7 to consist of Mn7+ ions and O2- ions; the high charge of the cations give them a high polarizing power, leading to the Mn-O bonds having high covalent character.

However, in nature, bonds are not "ionic with covalent character" or "covalent with ionic character," they are simply bonds. Therefore, I am curious if it is possible to explain the difference in the covalent character of Mn2O7 and MnO2 when viewing the bonds as covalent to start. In this case, is the explanation for the covalent bonds that the Mn atoms gain a high positive charge due to the highly electronegative oxygens, allowing the Mn to pull electrons back in? In other words, the oxygens inductively pull on each other's electrons by making the manganese more positively charged, leading to all of the electrons being more evenly shared between the manganese and oxygens?

The inductive effect and polarizing power explanations both seem to be describing the same phenomenon: the manganese atoms in Mn2O7 have a high positive charge (when viewing Mn2O7 as ionic, that charge is the +7 oxidation state; when viewing Mn2O7 as covalent, that charge is the partial positive charge due to the oxygens), causing them to pull electrons better, leading to highly covalent bonds with the oxygens. In general, can we say that highly positively charged atoms in a molecule pull electrons better (and therefore have a higher electronegativity), whether we are measuring that charge by the atom's oxidation state or by looking at the charge due to polar covalent bonds? It would make sense if this were true, because oxidation states represent the charges if all bonds are ionic, which is the extreme of polar bonds. Even if an atom's charge isn't as high as its oxidation state, I imagine that a higher oxidation state still corresponds to a higher actual charge.

On a side note, why do we only talk about polarizing power in the context of ionic bonding (or at least why have I only seen it used in the context of ionic bonding, such as in Fajan's Rules)? Can we talk about polarizing power of partial charges created due to electronegativity differences? For example, in the ketone RCOR', could we say that the carbonyl carbon has some polarizing power due to its partial positive charge, causing it to withdraw electrons from the R and R' groups? I think this is simply a way of describing the inductive effect. Maybe the reason we never talk about polarizing power in this kind of context because it is simpler to sum up the effect as "the carbonyl oxygen withdraws electrons from nearby atoms through the inductive effect?"

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Your understanding of the inductive effect and polarising power/polarisability is a bit inaccurate in some places.

The inductive effect is a result of the polarisation of sigma bonds (often as a result of differences in electronegativity.) This is first and foremost a covalent effect. For example, acyl chlorides are more reactive than aldehydes because the electronegative chlorine atoms pull electron density from the electrophilic carbonyl carbon, resulting in a stronger electrophile. The implicit fact that is not stated here is that this electron-withdrawing effect is through a sigma bond.

On the other hand, Fajan's Rule is a result of a cation with sufficiently high polarising power (high charge density) meeting an anion with sufficiently high polarisability (huge polarisable electron cloud often expressed as an anion of low charge density). Notice instead of dealing with the donation of electron density through a sigma bond where usually the discussion of electronegativity comes into play, Fajan's rule has little or no relation to electronegativity but rather the actual charge of the various species.

So, coming back to the question of Manganese (VII) Oxide and Manganese (IV) Oxide. From the view of inductive effects, the strength of the "covalent" bonds in these two species should inherently be the same due to the same difference in electronegativity. However, by applying Fajan's rule, it is obvious that because of the significantly higher polarising power of the Manganese (VII) species, Manganese (VII) Oxide has more covalent character.

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