Larger molecules have smaller HOMO-LUMO Gaps?

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Larger molecules generally exhibit smaller HOMO-LUMO gaps, particularly in the context of conjugated systems, where the gap decreases as the size of the molecule increases. In contrast, for saturated molecules, the HOMO-LUMO gap remains largely independent of the molecule's size. It's important to note that if this trend held universally, there would be no insulators, highlighting the complexity of chemical behavior. Additionally, in larger conjugated molecules, phenomena such as Peierls instability can lead to the emergence of new energy gaps, complicating the relationship between molecular size and electronic properties.
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Is it true that in general, larger molecules will have smaller HOMO-LUMO gaps?

In this case consider that we are comparing long vs short saturated molecules,
and long vs. short conjugated molecules.
 
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If it were true in general, there wouldn't be any insulators.
 
When it comes to chemistry, in general there are no reliable generalities.
 
In saturated molecules, the gap will hardly depend on system size while in conjugated systems, it will decrease with system size. However, in larger conjugated molecules, new gaps may open due to the Peierls instability.
 
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