Find Reduced Mass for Polyatomic Molecules

In summary: It's a quirk of the 1/r potential which is not present for the harmonic oscillator potential. In summary, when trying to find the reduced mass for a polyatomic molecule, it is not as straightforward as it is for diatomic molecules. The concept of reduced mass is most useful for two constituent molecules, and does not have a simple formula for molecules with more than two constituents. This is because the reduced Hamiltonian depends on the way relative coordinates are chosen, and in general there will not be a single answer for the reduced mass. This is due to the different vibration modes of the molecule, which can vary depending on the number and arrangement of the atoms.
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Iceking20
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How could we find the reduced mass for polyatomic molecule ?
Summary: How could we find the reduced mass for polyatomic molecule ?

I have problem with reduced mass of poly atomic moleculs because for diatomic molecules you can easily find out the reduced mass by M¹M²/M¹+M²,but I don't think with this way we can find reduces mass for example for fe²o³?
 
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That will depend on the vibration mode and in general there won't be a single answer, you can't use the effective mass for everything.

I moved this thread to the quantum mechanics forum.
 
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mfb said:
That will depend on the vibration mode and in general there won't be a single answer, you can't use the effective mass for everything.

I moved this thread to the quantum mechanics forum.
Can you give an example for one of the modes because I want to have perspective about it
 
  • #4
Iceking20 said:
Summary: How could we find the reduced mass for polyatomic molecule ?

Summary: How could we find the reduced mass for polyatomic molecule ?

I have problem with reduced mass of poly atomic moleculs because for diatomic molecules you can easily find out the reduced mass by M¹M²/M¹+M²,but I don't think with this way we can find reduces mass for example for fe²o³?
In general, the inverse reduced mass is the sum of the inverse masses of the constituents. For 2 constituents one gets your formula.

However, the concept of a reduced mass is indeed most useful for the case of 2 constituents only, where the center of mass frame leaves a 1-particle problem with the reduced mass.

For more than 2 constituents, no such simple recipe works, and the reduced Hamiltonian depends on the way relative coordinates are chosen.
 
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Iceking20 said:
Can you give an example for one of the modes because I want to have perspective about it
Everything. Even if we take a molecule with three atoms in a straight, symmetric line it will have vibrations along that line (contraction/extension) and vibrations orthogonal to it (making it slightly "L"-shaped). In the first case only the outer atoms move, in the second case all atoms move.
 

FAQ: Find Reduced Mass for Polyatomic Molecules

1. What is the definition of reduced mass for polyatomic molecules?

The reduced mass for polyatomic molecules is a measure of the effective mass of the molecule, taking into account the masses of all the atoms and their relative positions in the molecule.

2. How is the reduced mass calculated for polyatomic molecules?

The reduced mass is calculated by taking the reciprocal of the sum of the reciprocals of the individual masses of the atoms in the molecule, weighted by their distances from the center of mass.

3. What is the significance of the reduced mass in polyatomic molecules?

The reduced mass is important in understanding the vibrational and rotational motion of polyatomic molecules. It affects the energy levels and frequencies of these motions, and can also be used to calculate other properties such as bond lengths and force constants.

4. How does the reduced mass change with different atomic masses in a polyatomic molecule?

The reduced mass decreases as the mass of the atoms in the molecule increases. This is because the heavier atoms contribute less to the overall mass, and their distances from the center of mass are typically larger.

5. Can the reduced mass be negative for polyatomic molecules?

No, the reduced mass cannot be negative for polyatomic molecules. It is a positive value that represents the effective mass of the molecule in its vibrational and rotational motions.

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