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How is positive charge delocalized? I understand how negative charge can be delocalized. Electrons are mobile and they can move around. But what about positive charge? For example, consider this resonance structure and its composite:

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How exactly is that positive charge delocalized? Protons aren't mobile. I can't see any protons moving through the remaining pi-system.

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There are no protons moving - protons cannot move in resonance structures. In resonance structures all nuclei must remain fixed, only electrons can move. As you progress from the top-left resonance structure to the top-middle resonance structure you have taken the two pi electrons in what I'll call the 3-4 bond (position 1 being where the bromine is attached) and moved them between carbons 2 and 3, creating a pi bond between carbons 2 and 3 and simultaneously moving the electron vacancy (the positive charge, what a physicist would call a "hole") to carbon 4.

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I'm no expert but i think of it like this- there is a shortage of electrons, when the electrons try to satisfy two carbons in a double bond(in the empty p orbital), there is always a shortage somewhere else no matter what the electrons do, we can see this in the resonating structures, so finally they try to partially satisfy everyone with a partial double bond. Now think about it, isn't this easier to understand than delocalisation of a negative charge? Happy learning:)

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This is to supplement ron's answer. The positive charge is due to a deficit of electrons in that region, and that "electron hole" may be treated in many ways as if it is a particle (moving around due to certain rules, etc). Non-particle phenomena that functionally behave as particles are dubbed "quasiparticles", and there are a wide range of examples in physics (eg. phonons). In this and many other applications (such a semiconductor behavior), this positive charge caused by lower local electron density may be considered a quasiparticle.

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