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Some compounds are more fluorescent than others, and some of those are Rhodamine, Phenolphtalin, naphthalene, anthracene etc. I want to know why these exact molecules undergo such phenomena, what is the effect of conjugation in excitation and emission ?

(please be specific about this question)

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Absorption and emission in the UV/vis range is usually the result of electrons being excited to and deexcited from molecular orbitals that are unoccupied in the ground state. The energy involved in these processes is largely dependent on the energy gaps of the MOs involved (especially the HOMO-LUMO gap).

Many of the molecular orbitals in conjugated molecules form large $\pi$-systems (that's basically the definition of conjugated molecules). Due to the smaller overlap, the energy splitting between $\pi$ and $\pi^*$ orbitals is smaller than in $\sigma$, $\sigma^*$ pairs. This effect is more pronounced in larger $\pi$-systems. One often finds that the frontier orbitals (i.e. HOMO, LUMO and often HOMO-1, LUMO+1 etc.) are dominated by $\pi$-systems, if they are present in the molecule. Due to the relatively smaller energy gap in conjugated molecules, one finds absorption in lower energy ranges and often with higher probabilities.

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I do assume that the basic principles and rules of fluorescence are known to the reader. These are provided at a basic but sufficient level by, e.g., the enter "Fluorescence" at Wikipedia.

Being clear that fluorescence efficiency is the output of the fluorescence radiative and several non-radiative de-excitation channels , the question can be put as Can we quantify the weight of the latter? To my knowledge the answer is not. Except calculations are made for each specific molecule in the specific environment, there are not real easy rules at hand. Designing new fluorescent molecules substantially requires experience and feeling, not to say try and "errors". For instance, If a fragment is known to be luminescent , we can expect some luminescence from a molecule containing it. But it is not given, at least not in the sense that luminescence efficiency can be predicted within a few percents.

The same is true for several characteristics in material synthesis . There are designing rules but nothing similar to an analytical function. The same is true if you limit the question on how effectively extended the conjugated system you are going to attain is.

I keep this answer qualitative exactly because I am not aware of something not empirical . A physics robust answer will "reduce" to the listing of the various process involved or must be a short treatise on molecular physics and the fate of excited states. Or case by case computations.

A few working rules can be nevertheless given. For example, more rigid is the molecule higher the luminescence yeld , or lower the gap lower is the yeld, etc. This is particularly true if the system is supposed isolated. It is clear that often a substituent can have no effect in the isolated molecule scenario but even invert the situation in , for example , solution (via interaction with the solvent molecules).

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