# For diatomic molecule, why are there two vibrational degree of freedoms at high temperture?

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## Main Question or Discussion Point

For diatomic molecule, why is the vibrational degree of freedom equal to two at high temperature?
Why not just one?
Thank you very much.

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ehild
Homework Helper
The energy of the vibration is the sum of the potential energy and the kinetic energy. The first is determined by the change of the distance between the atoms, the other is determined by their speeds. Speed and distance are the two degrees of freedom.

ehild

For diatomic molecule, why is the vibrational degree of freedom equal to two at high temperature?
You are mistaken. Diatomic molecules have exactly one vibrational degree of freedom, regardless of temperature.

You may have mean something else, which is related to degrees of freedom and temperature, but but you will have to formulate your question correctly.

Khashishi
Are you referring to rotational and vibrational degrees of freedom?

ehild
Homework Helper
Are you referring to rotational and vibrational degrees of freedom?

The diatomic molecule can perform only one kind of vibration: the interatomic distance change sinusoidally in time.

But the general SHM motion of angular frequency ω is of the form x=Asin(ωt+θ). Two data are needed to know the energy of the vibrating body : for example, the position and the velocity at the same time.
In Kinetic Theory, the Equipartition Principle assigns two (1/2 kT) average energy to a single vibration.

ehild

the Equipartition Principle assigns two (1/2 kT) average energy to a single vibration.
But not two degrees of freedom, as stated in the original message.

For diatomic molecule, why is the vibrational degree of freedom equal to two at high temperature?
Why not just one?
Thank you very much.
A number of sources refer to "libration" as a separate degree of freedom. This is described as a flexing or bending of the inter-atomic axis. Other sources do not mention libration.

ehild
Homework Helper
A number of sources refer to "libration" as a separate degree of freedom. This is described as a flexing or bending of the inter-atomic axis. Other sources do not mention libration.
Libration is restricted rotation. It does not exist for free diatomic molecules. Libration can happen in some external force field, or a diatomic part of a molecule can librate with respect to the other part.
http://en.wikipedia.org/wiki/Libration_(molecule)
ehild

A number of sources refer to "libration" as a separate degree of freedom.
The total number of degrees of freedom in a system of particles cannot be greater than the sum of the degrees of freedom of all the particles assumed unconstrained. The latter is 6 for a diatomic molecule. The nomenclature of the degrees of freedom commonly used in this case - 3 for the motion of CoM, two rotational and one vibrational - is thus maximal and any other degree freedom will not be independent.