visible light - Why isn't the color of a molecule a combination of the colors of its component atoms?

I was watching a documentary on youtube regarding Quantum Physics when it introduced the wavelengths of light emitted. Did a bit more research over the internet and I believe I understand the gist of why each atom gives off different colors. Here's a brief summary of what I've read:

An atom of a particular element has several shells of electrons, and each shell is a different energy. When the atoms are heated up, some of the electrons can jump up to shells with higher energy, but they don't stay there very long. When the electrons fall down again to a lower energy shell, they give off that energy as a photon (a "particle" of light). The amount of energy of the photon given off is the difference in energy between the two shells, and determines the wavelength of the light.

With all that taken into consideration, why is it that a molecule isn't a combination of its component atoms? More precisely, how is the color of a molecule determined?

Answer

I'll do that teacher thing and turn your question around back at you. Why isn't the spectrum of the lithium atom just the spectrum of the hydrogen atom plus the spectrum of the helium atom? And, for that matter, why is the helium spectrum not simply two copies, somehow, of the hydrogen spectrum? Why do atoms have unique spectra in the first place?

The answer to my question is that an atom with proton number $Z$ can have a fundamentally different excitation spectrum (and chemistry) from some other atom with proton number $Z+1$ because that extra electron interacts with all the other electrons that were in the atom already.

That's also the answer to your question. In the same way, when you combine two hydrogen atoms and an oxygen atom to make water, there isn't a "hydrogen electron" in the same way as in a bare hydrogen atom, or even a hydrogen molecule. A "hydrogen electron" in a water molecule is interacting with both hydrogen nuclei, and the oxygen nucleus, and the other nine electrons in the system, which makes its excitation spectrum fundamentally different from the spectrum of an electron interacting with a free proton.