CM frame kinetic energy for a molecule

In summary, the formula for the kinetic energy of a molecule in its center of mass frame includes three terms: the kinetic energy of the center of mass with respect to the lab frame, the kinetic energy associated with the distance between the nuclei, and the kinetic energy of the electrons with respect to the center of mass. The third term takes into account all rotational motions and can be further developed to include the rotational energy and a Coriolis term. The i and j indices in the third term represent the electrons in the molecule.
  • #1
kelly0303
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Hello! When the kinetic energy of a molecule is written in its CM frame we get the formula attached. The first term is the kinetic energy of the CM frame with respect to the lab frame, the second term is the kinetic energy associated with the distance between the nuclei and the last term is the kinetic energy of the electrons with respect to the CM. Can someone help me understand what the 3rd term is? It seems like all the possible motions are taken into account so I am not sure what that is (it comes out naturally from the mathematical derivation, but I am not sure what it is physically). Thank you!
 

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  • #2
Are you sure about the significance of the last term? What to the indices ##i## and ##j## sum over?

The 3rd term contains all the rotational terms. Further development of this term will lead to the rotational energy (rotational of the molecular frame wrt the lab frame) and a Coriolis term.
 
  • #3
DrClaude said:
Are you sure about the significance of the last term? What to the indices ##i## and ##j## sum over?

The 3rd term contains all the rotational terms. Further development of this term will lead to the rotational energy (rotational of the molecular frame wrt the lab frame) and a Coriolis term.
The last term is the kinetic energy of the electrons with respect to the molecule center of mass and the i and j indices are over the electrons. Actually the rotation of the molecule comes from the second term where R is the internuclear distance.
 

1. What is the CM frame kinetic energy for a molecule?

The CM frame kinetic energy for a molecule is the amount of energy that the molecule possesses due to its overall motion in the center of mass frame. It is a measure of the molecule's translational motion and is related to its mass and velocity.

2. How is the CM frame kinetic energy calculated?

The CM frame kinetic energy for a molecule can be calculated using the equation KE = 1/2 * M * V^2, where KE is the kinetic energy, M is the mass of the molecule, and V is the velocity in the center of mass frame.

3. Why is the CM frame kinetic energy important in studying molecules?

The CM frame kinetic energy is important in studying molecules because it provides information about their translational motion, which can affect their interactions with other molecules and their overall behavior in chemical reactions. It also helps in understanding the distribution of kinetic energy within a molecule.

4. How does the CM frame kinetic energy change with temperature?

The CM frame kinetic energy of a molecule is directly proportional to its temperature. As the temperature increases, the average kinetic energy of the molecules also increases, resulting in a higher CM frame kinetic energy. This is because temperature is a measure of the average kinetic energy of the molecules in a substance.

5. Can the CM frame kinetic energy be converted into other forms of energy?

Yes, the CM frame kinetic energy can be converted into other forms of energy, such as potential energy or heat energy, through various processes such as collisions or chemical reactions. This conversion is governed by the laws of thermodynamics.

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