Kinetic Energy of Rotating Water Molecule

[dgreenheck]

When calculating the kinetic energy of a rotating water molecule (translational and vibrational motion not important here), am I correct in assuming that you do all the calculations from the center of mass and analyze each axis of rotation (x,y,z)? The bent geometry is throwing me off! Any molecule would rotate about its center of mass wouldn't it?

 

[Drakkith]

I BELIEVE you are correct. But I don't really know. I couldn't really see a molecule rotating around anything but it's center of mass.

 

[SpectraCat]

When calculating the kinetic energy of a rotating water molecule (translational and vibrational motion not important here), am I correct in assuming that you do all the calculations from the center of mass and analyze each axis of rotation (x,y,z)? The bent geometry is throwing me off! Any molecule would rotate about its center of mass wouldn't it?

Well, a single water molecule rotating in free space has only kinetic energy (if you ignore vibration), so the rotational kinetic energy is simply the energy of the quantum rotational state that the molecule happens to be in.

You are correct that you begin the analysis by using parameters from the vibrationally averaged structure (bond length of O-H bonds and H-O-H bond angle), and then calculate the elements of the inertial tensor. Diagonalizing the inertial tensor gives you the moments of inertia around the three principal axes, as you surmised. If you are lucky, one or more of the moments are the same, in which case you can just use a convenient analytical formula to calculate your energy. However, water is an asymmetric top (all three moments are different), so solving for its rotational energy levels is non-trivial, but fairly straightforward. See http://en.wikipedia.org/wiki/Rotational_spectroscopy" .

With a little searching, you can probably find highly-accurate tabulated values for the water rotational energy levels online (you can certainly find them in the academic literature). If you want to calculate the levels, and you have specific questions, I may be able to help you further. The simple model I laid out above is called the rigid rotor model, and is only an approximation .. several additional considerations (e.g. centrifugal distortion, Coriolis coupling, nuclear hyperfine coupling, etc.) may need to be accounted for in accurate work.