Here are a few generic examples of what works best.
I suspect the symmetry may be indicative?
"I only wanted Uncle Vern standing by his new car (a Hudson) on a clear day. I got him and the car. I also got a bit of Aunt Mary's laundry, and Beau Jack, the dog, peeing on a fence, and a row of potted tuberous begonias on the porch and 78 trees and a million pebbles in the driveway and more. It's a generous medium, photography." -- Lee Friedlander
Centrosymmetric molecular structures are commonly seen in dyes and other colorants as they tend to have relatively narrow bulk EM resonances (lightwave resonance) The elongated, high length to diameter ratio, which is effectively doubled in the centrosymmetric structure, is responsible for what we term "antenna effect" today. The antenna (dye molecule) can be touching or attached to something else (like SiO2, or silver salt, or other metallic oxide) and the charge selectively transferred. Organic dyes used to be the only way to get these long-ish chains (100-500nm or more) but now there are other ways being developed and a ton left to explore.
Many "good" dyes absorb, fluoresce and reradiate at the same time, and there is a lot of what is referred to as excitonic activity. Lightwaves provide the energy and excitons, phonons, electrons all get into the act.
No, AFAIK, they do not. Of course, that would put them into the UV region and we do not routinely measure there. My tests and ours at work normally ran from 400 - 700 nm. However, IR dyes that sensitize AgX at 800 - 900 nm do not show secondary peaks at 400 or so, and I am basing my assumption on these longer chain examples as well as the more common dyes.
Symmetry is not needed as much as conjugation, that is the double bonds shown. Symmetry is often there because a given molecule is easy to make.