3
$\begingroup$

Can one relate the frequencies of vibrational modes within a molecule to the molecule's HOMO/LUMO energies?

$\endgroup$
2
  • 3
    $\begingroup$ No researched question is dumb. $\endgroup$ – M.A.R. Jul 6 '15 at 20:21
  • $\begingroup$ There are 3N-5(6) vibrational modes of a molecule and a single HOMO-LUMO gap. What kind of relations are you looking for? $\endgroup$ – Greg Jul 7 '15 at 12:56
7
$\begingroup$

No, I could not think of any relation between them. Orbital energies are solutions of the electronic Schrödinger equation, and as such, they describe the electronic state of a molecular system. Vibrational frequencies are solutions of the nuclear Schrödinger equation, and as such, they describe the nuclear state of a molecular system. The quantities that describe the electronic state are not related to the quantities that describe the nuclear one simply because they describe two different subsystems: the electronic and the nuclear one.

Note that usually we treat these two subsystems as being independent of each other (the Born-Oppenheimer approximation), but even if you go beyond that, what you'll see is that changes in the nuclear subsystem (say, changes in geometry during vibrations) might affect the electronic state. Consequently, molecular vibrations in principle can alter HOMO/LUMO (as well as any other orbital) energies, but I doubt this interdependence of electronic and nuclear states is the relation you're looking for.

$\endgroup$
2
  • $\begingroup$ Right. Slight changes in orbital shapes and energies during vibrations is not what I am looking for. I was hoping that since HOMO-LUMO transitions within a molecule correspond to new localizations in a molecule that you could get a numerical value for delataE based on differences in two vibrational modes. But your answer is thorough and makes sense. Thank you. $\endgroup$ – Musicpulpite Jul 6 '15 at 20:47
  • 3
    $\begingroup$ @Musicpulpite, so, if I understand you correctly, you would like to somehow estimate the excitation energy from the knowledge of vibrational frequencies for the molecule in its ground as well as in an excited state. If so, then, as I said, I don't think there is a relation between two. And besides, the "HOMO-LUMO gap" (the energy difference between HOMO & LUMO) should not be used to estimate the excitation energy anyway. $\endgroup$ – Wildcat Jul 6 '15 at 21:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.