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Density of States

  1. Aug 26, 2007 #1
    Hi All
    Im just wondering if there is an easy way to determine the density of states for a molecule such as CO2. I am interested in transitions at IR wavelengths so I'm wondering if there is an 'easy' way to get at the vibrational modes only to chuck into something like the Maxwell-Boltzmann distribution.
  2. jcsd
  3. Aug 26, 2007 #2


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    Density of states for an isolated molecule? I don't follow.

    The CO2 molecule has 4 vibrational eigenmodes - these are probably in the IR range. It has 12 valence molecular orbitals (from overlap of the one 2s and three 2p atomic orbitals of the 3 atoms). Transitions between the electronic states are in the UV-vis range. The rotational eigenmodes are in the microwave regime.
  4. Aug 26, 2007 #3
    the IR spectra of the gas phase molecule can be calculated through normal mode analysis.

    another way would be to calculate a set of states either by monte carlo or molecular dynamics, and then autocorrelate the dipole moment. formally this arises by being able to rewrite the fermi golden rule expression in terms of a TCF (interestly enough, a classical approach yields the same expression, see Frenkel or McQuarrie for details).

    look into time correlation theory and normal mode analysis. a suitable text such as herzberg will tell you all you'll want to know. there are public domain codes that will do these things or you can implement your own.
  5. Aug 26, 2007 #4
    Hi thanks for the replies,
    Sorry for being a bit unclear in the original question, basically I want to do something similar to http://webphysics.davidson.edu/alumni/jimn/Final/Pages/FinalMolecular.htm
    Where they plot the Maxwell-Boltzmann distribution for the rotational levels, however I want to do it for the vibrational modes. I'm really wondering whether G(J) is 4 for the vibrational modes of a molecule such as CO2?
  6. Aug 26, 2007 #5


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    1. Yes, you can do a similar thing with only the vibrational modes (but leaving out the fine structure from the rotational modes makes the system specific to ones where rotation is inhibited - this is rare, and in general, unphysical).

    2. There isn't a G(J) for the vibrational modes (there's no angular momentum involvement). The degeneracy of the vibration modes is 1 except in the rare case of commensurate eigenvalues.
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