Partition Function: Energy States & Force Constants

[DanPhysChem]

Hi All - If I have a potential energy surface with two energy states, one higher than the other, where I can make the assumption that both potential wells can be approximated via harmonic potentials with force constants kA and kB then would the partition function for the system be Z=e^(-hwA/2kT)+e^(-hwB/2kT) where wA=sqrt(kA/m) and wB=sqrt(kB/m)? Also, if the higher energy state was the more likely to be populated at some temperature T, how small would kB (the higher energy state) need to be in terms of kA?

 

[DanPhysChem]

Anyone? Maybe I should have posted this in Advanced Physics.

 

[charng]

I would say that your assumption of using harmonic potentials to approximate the potential wells is valid as long as the energy difference between the two states is small compared to other energy scales in the system. In that case, the partition function you have provided is correct, and the higher energy state would indeed be more likely to be populated at a given temperature.

In terms of the force constants, kB would need to be significantly smaller than kA in order for the higher energy state to be more likely to be populated. This is because the partition function is proportional to the Boltzmann factor, e^(-E/kT), where E is the energy of the state. So, a smaller kB would result in a larger Boltzmann factor for the higher energy state, making it more likely to be populated.

However, it is important to note that the partition function is a mathematical concept and does not necessarily reflect the physical reality of the system. It is a useful tool for calculating thermodynamic properties, but it does not provide information about the actual distribution of particles in the system. Therefore, it is important to consider other factors and experimental data when interpreting the results of the partition function.