Density of States: IR Transitions in CO2 Molecule

In summary, the conversation discussed determining the density of states for a molecule like CO2 and its transitions at IR wavelengths. The molecule has 4 vibrational eigenmodes, 12 valence molecular orbitals, and transitions between electronic states in the UV-vis range. The rotational eigenmodes are in the microwave regime and can be calculated through normal mode analysis. Alternatively, one can use time correlation theory and normal mode analysis to calculate the IR spectra. There is no G(J) for vibrational modes, and the degeneracy is usually 1. There are public domain codes available for these calculations or one can implement their own.
  • #1
Steleo
13
0
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.
 
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  • #2
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.
 
  • #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.
 
  • #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?
Thanks
 
  • #5
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.
 

1. What is the density of states in the CO2 molecule?

The density of states in the CO2 molecule refers to the number of states or energy levels that are available to the molecule at a given temperature. In other words, it is a measure of the number of ways the molecule can store or distribute energy.

2. How is the density of states related to IR transitions in CO2?

The density of states is directly related to IR transitions in CO2 because it determines the likelihood of a molecule undergoing a transition from one energy state to another. A higher density of states means a higher probability of IR transitions occurring.

3. How does temperature affect the density of states in CO2?

Temperature has a direct impact on the density of states in CO2. As the temperature increases, the number of available energy states also increases, resulting in a higher density of states. This, in turn, leads to an increase in the number of IR transitions that can occur.

4. What factors determine the density of states in a molecule?

The density of states in a molecule is determined by various factors, including the molecular structure, energy levels of the constituent atoms, and temperature. Additionally, the type of molecule and its environment also play a role in determining the density of states.

5. How is the density of states calculated for a CO2 molecule?

The density of states for a CO2 molecule can be calculated using statistical mechanics, which takes into account the energy levels and temperature of the molecule. Alternatively, it can also be determined experimentally by measuring the number of IR transitions that occur at different temperatures.

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