I know this is complicated, but I'll ask. How do you calculate the color of a compound with pen and paper? Everyone knows that iron(II) sulfate is yellowish. How do I know without looking at it?
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1$\begingroup$ This is an awesome question, I wish I knew how to answer this well but I can only point you in the right direction. It comes down to looking at the orbitals and seeing which transitions an electron can make, since this is exactly what corresponds to the frequency of light as you may be aware of $E=h \nu$. Transition metals tend to get their colors from the d-orbitals and organic compounds get their colors from conjugated $\pi$-systems in general. I wish I could discuss and explore this more with you but the site doesn't allow this kind of thing apparently. $\endgroup$– user19026Commented Sep 20, 2015 at 14:00
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Since this is quite a broad question, I will also only be able to provide an answer in very broad terms.
The short answer is: You cannot. At least not with (a real) pen and (real) paper.
The slightly longer answer is: With a simple pen and paper approach this is virtually impossible. Even the use of more elaborate methods like MO theory can lead you to completely wrong results. Electronic transitions involve excited states, which can be incredibly hard to calculate. In most cases you can get an approximate spectrum by using time-dependent density functional theory. This can be right for the wrong reasons - it is still somewhat a crude theory. The best results you will get with multi-reference methods or big automated computations, which may take a long time on a supercomputer.
In other words: There is not easy, general, rigorous way to determine the colour of a compound.
answered Sep 20, 2015 at 14:29