Find Reduced Mass for Polyatomic Molecules

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    Molecular Vibration
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Discussion Overview

The discussion focuses on finding the reduced mass for polyatomic molecules, particularly addressing the complexities that arise compared to diatomic molecules. Participants explore the implications of molecular structure and vibration modes on the concept of reduced mass.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how to find the reduced mass for polyatomic molecules, noting that the standard formula for diatomic molecules may not apply.
  • Another participant suggests that the reduced mass depends on the vibration mode of the molecule and indicates that there may not be a single answer applicable to all cases.
  • A later reply emphasizes that for more than two constituents, the concept of reduced mass becomes more complex, as it relies on the choice of relative coordinates and does not have a straightforward formula.
  • Participants discuss that even in simple configurations, such as three atoms in a straight line, different vibration modes can affect how the atoms move, complicating the determination of reduced mass.

Areas of Agreement / Disagreement

Participants generally agree that the determination of reduced mass for polyatomic molecules is more complex than for diatomic ones, with multiple competing views on how to approach the problem remaining unresolved.

Contextual Notes

The discussion highlights limitations in applying the reduced mass concept to polyatomic molecules, particularly regarding the dependence on vibration modes and the choice of coordinates, which are not fully resolved.

Iceking20
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TL;DR
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
 
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.
 

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