Find Reduced Mass for Polyatomic Molecules

[Iceking20]

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?

 

[mfb]

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.

 

[Iceking20]

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

 

[A. Neumaier]

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.

 

[mfb]

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.