I am trying to find the color of an organic molecule, crystal violet, theoretically. Crystal violet

I suspect that the color is due to the large conjugated system. My question is, how would I go about finding the energy levels of such a system? I know how to solve the Schrodinger equation for a particle in a ring or a box (i.e. benzene, or a poly-diene) to solve for energy levels and find the lowest-wavelength transition. But how would I do it for this sort of molecule?

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    $\begingroup$ You need something more sophisticated than particle in a box, probably (at least) Huckel theory. $\endgroup$ – orthocresol Feb 17 '19 at 17:44
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    $\begingroup$ Using some decent software. $\endgroup$ – Mithoron Feb 17 '19 at 17:54
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    $\begingroup$ You would have to make ridiculous simplifications. For starters, this molecule is not perfectly planar. $\endgroup$ – Karl Feb 17 '19 at 21:46
  • $\begingroup$ The photophysics of this and similar molecules is very interesting. The excited state decays non-exponentially and strongly depends on solvent viscosity and both effects are due to twisting of phenyl groups, so the excited state is definitely not planar. $\endgroup$ – porphyrin Feb 18 '19 at 9:16
  • $\begingroup$ @Oscar Lanzi. It is of course planar around the center. The fact that conjugation will depend or will force planarity is right one should determine as per the question. The comment you refer to is unnecessary, it can be made for every polyene, even. $\endgroup$ – Alchimista Feb 18 '19 at 10:31

For a reliable and experimentally comparable answer, you really need to use a numerical method rather than a pencil and paper estimation. For an organic system this size you'll probably be safe using time-dependent density functional theory (TDDFT). Most computational chemistry packages have this built in. Off the top of my head, I know that Gaussian (commercial–standard for organic molecules like this), and GAMESS (free) both have TDDFT built in.

If you're intent on using a toy method you could use Hückel theory as orthocresol suggested. You could in principle tune the parameters of such a model until the excitation energy matches the experimental result, but I don't see what additional physical insight this would give you.

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