Why Harmonic Oscillator?

I have a presentation which I sometimes give when asked to talk at schools science fairs called ‘From atoms to climate change’. It’s designed to engage with young chemists, physicists, biologists, geographers and geologists. In the talk I try to show how we can move from the fundamental properties of molecules at the quantum level to using variations in the abundance of stable isotopes of the light elements in nature to determine past climate change. We then look at the climate throughout the Phanerozoic from 560 Ma to the present. One of the take home messages from the talk is that our interpretation of the data has to be grounded in a thorough understanding of the underlying physics and chemistry.  The other one is that you are never too young to start playing with springs and balls (as models of molecules) and having fun with science. Which brings us to the harmonic oscillator. 

Equilibrium isotope partitioning between molecules is driven mainly by the Zero Point Energy (ZPE), that is the quantum mechanical requirement that molecules vibrate with a half quantum of energy even when they are in their ground states at absolute zero. This is a consequence of Heisenberg’s uncertainty principle. Close to the equilibrium inter-atomic distance in a molecule the potential energy, usually represented by a Morse potential, can be approximated by a harmonic function and the vibrational modes by a harmonic oscillator.  If we substitute one of the atoms of the molecule with an isotope of the same element we change the zero point energy of the molecule and thus the vibrational frequency of the bond. The difference in zero point energies between the isotopically substituted and non-substituted molecules is small, typically a few ten’s of joules per mol, but enough to drive measurable isotope partitioning between molecules in nature.

Hence the blog is called Harmonic Oscillator as it provides the fundamental link between physics and the effect of temperature on isotope partitioning and thus our ability to use isotopes to measure past earth surface temperatures.

Convoluted I know but an illustration of how my mind works.

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