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I am teaching my self the basics of chemistry and I have done lewis dot structure before. Right now I am going into carbon chemistry which often use structure formulas to represent compounds. There is this formula called the expanded structure, and from what I can see, the expanded formula is just the same as the Lewis except we use the lines to represent bonds etc?

So my main question is whats the difference between them and do we have to assign the formal charges in the expanded structure formula? Also, do we show the dots (valence electrons) in the expanded formula? Thank you.

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Yes. Extended molecular structures replace dots with line emphasising electron pairs that are shared between two atoms. In other words each line does represent a bond. Most often the EMS omit electrons that are not directly involved in bonds. As such the depiction of electrons between C and O in, e.g., a carbonyl group is simply sketched as C=O. However, whenever the presence of lone pairs is relevant to the discussion, those are explicitly shown.

In case in which the structure does not correspond to a single Lewis structure, the most important one is depicted and the situation is considered to be known to the reader. An archetype example is benzene. It can be sketched as having three double bonds but their delocalization is assumed. Those six delocalized electrons can be depicted as an inner ring, an expedient which is more evocative but must be abandoned when fine details are to be discussed (mechanisms of reaction or mesomeric effects). Moreover a circle in aromatic rings doesn't always represent six electrons.

Finally you can find depiction of delocalized electrons as variously dotted lines enveloping the group of atoms over which they do delocalize, for instance a kind of "cloud" around the two oxigens of a carboxylate anion. Their meaning is usually clear.

To the second question: on the light of the above yes, formal charge are to be assigned. They are usually important while discussing the relative stability of limiting forms which enter the description of the actual hybrid of resonance.

https://en.m.wikipedia.org/wiki/Lewis_structure. Particularly the subsections Resonance and Usage and limitations.

Edit: For sake of clarity I must add that unpaired electrons are always depicted. Indeed they are always of chemical relevance!

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