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In general, organic molecules with no conjugated double bonds will tend to be "white" because they do not absorb photons with wavelengths in the visible range, they just scatter them. The color depends between the difference in energy between the highest occupied molecular orbital ("HOMO") and the lowest unoccupied molecular orbital ("LUMO"). The HOMO-LUMO gap for the average non-conjugated organic molecule tends to found in the UV range, which is invisible to most of us. In general, as you add more PI bonds into a conjugated system, the energy required for an electron to jump from the bonding HOMO to the antibonding LUMO is reduced. Hence, adding more conjugated PI bonds to system will "red-shift" the compound. Other substituents will affect the electronics and hence the color, as well as the surrounding environment around the chromophore (for example, in fluorescent proteins with the same chromophore but different amino acids surrounding it, and all three human opsins absorb different wavelengths using the same retinal molecule).

 

For a good treatment on MO's I recommend you Ian Flemming's Molecular Orbitals and Organic Chemical Reactions. The first chapter talks a lot about conjugation.

 

This applies to organic molecules without metals.

Metals have different electronics and often times the color of their complexes depend on the reduction state of the metal, that is, the number of electrons present in their d-orbitals.

 

There are more complications when it comes to color, such as "why is solid elemental sulfur yellow?" or how to explain the color of some solid metals and minerals, while many of these can be explained purely with electronics of the molecular orbitals, sometimes other optical phenomenon need to be invoked (especially with more complicated materials).

 

There's a video on it here:

https://www.youtube.com/watch?v=rt3aR87SFQI

 

Also, here's a list with the color of elements:

http://www.periodictable.com/Properties/A/Color.html

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