(Polar molecules, Non-polar molecules, etc.)
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No they do not; they are treated as single electron density therefore can repulse only as much. Angles change from the influence of lone pairs which has a larger repulsion since they take up more space than bonded atoms. Knowing that atoms are bonded with either double or triple bonds only help formulate the VSEPR model to determine if there are any lone pairs that influence its structure.
Lavelle discussed in lecture that the number of bonds should not affect the regions of electron density. Thus, with the information we have now, it is best to assume that double and triple bonds do not affect shape. However, of course there may be nuances to this, but I think that we can stick to this assumption based off what we learned so far.
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