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As a similar idea to the question A compound that absorbs all visible light, I am curious if there is a compound (or compounds) that absorb UV-A radiation (shown below)?
However, preferable the compound would have relatively good transmission in the UV-B and Visible wavelengths.
Yes, there are many such compounds. "The evolution of UVA protection" is a nice article detailing the progress on UVA blockers. I'm sure you're aware that sun care is a big business ($8.7 billion USD worldwide in 2013), so there is no shortage of chemists working in the area. In fact, there is enough (medical and clinical) focus that UVA (315-400 nm) has been subdivided into UVA1 (340-400 nm) and UVA2 (315-340 nm)
Here is a figure from the above link showing the UV spectra of some compounds. The top part shows UVA absorbers and the bottom half shows broad-spectrum UV absorbers.
and a table with the names of the compounds
BMBM was an early UVA absorber (solid blue line), but was photochemically unstable (dashed blue line), in other words, its blocking power deteriorated with UV exposure time. More recent UVA absorbers, like DHHB are photostable.
UVA absorbers belong to many different structural classes and contain many different types of functional groups. Here are few examples.
BMBM
DHHB
TDSA
