Double Harmonic Approximation IR intensties

In summary, the conversation discusses using the double harmonic approximation to determine IR spectral intensities. The equation used for this is I=(\frac{\delta \mu}{\delta Q})^{2}\frac{\pi N_{A}}{3c^{2}}, where I is the intensity, \mu is the dipole moment, Q is the normal mode coordinate, N_{A} is Avogadro's constant, and c is the speed of light. The standard units for dipole are debye, and for mass scaled coordinates they are unit-less, resulting in the final units of debye squared. To convert to the desired units of km/mol, you need to multiply the equation by 6.022x10^23
  • #1
DinosaurChemi
5
0
This feels silly asking but I have a question about units using the double harmonic approximation to determine IR spectral intensities. In the double harmonic approximation the intensity is given by
the square of the derivative of the dipole with respect to a normal mode coordinate times a scaling constant. Numerically this can be done by taking let say a 0.01 step along a mass scaled coordinates. The standard units of dipole are debye and mass scaled coordinates are unit-less so total units of debye squared. The scaling factor is Avagadro's constant divided by the speed of light squared. This gets me in units of times2 current2. Intensities are reported in km/mol. If anyone can give me a little help here I would appreciate it

Again the equation is:

[itex]I=(\frac{\delta \mu}{\delta Q})^{2}\frac{\pi N_{A}}{3c^{2}}[/itex]
 
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  • #2
Where I is the intensity, \mu is the dipole moment, Q is the normal mode coordinate, N_{A} is Avogadro's constant, and c is the speed of light. To convert from debye squared to km/mol, you need to multiply your expression by 6.022x10^23 (Avogadro's constant) and then divide by 3x10^10 (the speed of light squared). This will give you the intensity in km/mol.
 

1. What is the Double Harmonic Approximation method?

The Double Harmonic Approximation method is a theoretical approach used to calculate infrared (IR) intensities in molecules. It assumes that the molecule's potential energy surface can be approximated as a parabola and that the vibrational motion of the molecule follows a harmonic oscillator model.

2. How does the Double Harmonic Approximation method work?

The Double Harmonic Approximation method uses the equations of motion for a harmonic oscillator to calculate the vibrational frequencies and normal modes of a molecule. It then uses these values to calculate the IR intensities of the molecule's vibrational transitions.

3. What are the limitations of the Double Harmonic Approximation method?

The Double Harmonic Approximation method assumes that the molecule's potential energy surface is parabolic, which is not always the case. This can lead to inaccuracies in the calculated IR intensities. It also does not take into account anharmonicity, which is the deviation of the molecule's vibrations from the harmonic oscillator model.

4. How accurate is the Double Harmonic Approximation method?

The accuracy of the Double Harmonic Approximation method depends on the molecule and the level of theory used. In general, it provides good estimates for IR intensities in simple molecules but may not be as accurate for larger or more complex molecules.

5. What are the applications of the Double Harmonic Approximation method?

The Double Harmonic Approximation method is commonly used in computational chemistry to calculate IR spectra and aid in the interpretation of experimental IR spectra. It is also used in spectroscopic studies of molecules to determine their structures and properties.

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