Above are some spectral emission lines for hydrogen, helium and neon.
Using the Schroedinger equation, it's possible to derive the colours that hydrogen will emit when light is fired at it. A little more complicated (although beyond my rudimentary knowledge of quantum mechanics), the same can be done for helium, and so on.
Of course as we progress to molecules, even the relatively small $C_5H_{11}Br$, it's (I'm told) very hard to predict the colours emitted from first principles, and even then incorrect assumptions must be made (like the Born-Oppenheimer approximation), so upon progressing to larger molecules, we find that these simplifications diverge from experiment.
My question is this: with the advent of computers, are we able to (in practice, not theoretically in a few decades) accurately compute the colours given off by a molecule by numerically solving the laws of quantum mechanics for complicated systems? Much like nonlinear differential equations can now be 'solved' with computers without any simplifying assumptions (like $\sin(x) \approx x$), is it in humanity's capacity today to approximate colours from first principles, so that computing time is the only restraint? Note the difference between an incorrect model of reality (Born-Oppenheimer), and one that converges to the correct one (even if slowly).