The molecular partition function
- a sum of the boltzman factors of each energy level
- is a measure of the number of thermally active energy levels at said temperature (flats that are having parties)
- determines how particles distribute
- has a value independent upon the number of particles
- is a function per molecule
The lowest level e
The loweste level, e, contributes E to the power 0 which equals 1, so contributes 1 to the sum
The more accessilbe energy levels
the closer the contribution to the sum is to 1, thus partition function measures the number of thermally active enrgy levels.
States share the same energy
They are degenerate (g)
Translation
movement of molecule through 3D space
Rotational partition function
energy levels that arise from rotation of the molecules about an axis
Molecular rotation - symmetry
Homonuclear diatomics
- quantum mechanical properties of nuclei cause the occupation of only certain rotational states.
- given by sigma (2 for hetero, 1 for homo)
Bosons
particles with integer spin
fermions
particles with half integer spin
anti-symmetry and symmetry
when two identicle particles are interchanged, the total wave function MUST change sign for FERMIONS and remain unchanged for bosons (OMG FERMIONS are so dramatic)
Ortho and Para 1H2
- High temps dominating factor ortho has a nuclear spin degeneracy of 3. mixture 3:1 ortho:para
- low temps dominating factor is the lowest rotational state is only available to para. mixture is pure para
Vibrational partition function
describes energy levels arising from vibrationn of molecules
the harmonic oscillator
small displacements, stretching and compressing, obey Hooke’s law
Electronic partition function
- This describes the consequence of energy levels available to be occupied by electrons in molecules.
- only a small number of electronic energy levels lie within a few kT of the ground state
- no way to caluclate the energy levels of a multi-electron atom/ molecule
- calculate the electronic partition function as an explicit sum of terms over electronic levels i:
The electronic ground state
very often the electronic ground state lies much more thank kT below any excited state
degeneracy of atomic electronic level
the degeneracy of an atomic electronic energy level can be found easily from its term symbol
The overall molecular partition function
- for a closed shell molecule, the electronic degeneracy of the ground state is generally 1
- for a molecule like O2 with two electrons singly occupying degenerate orbitals, the electronic degeneracy is 3
- multiply the component partition functions together
The overall molecular energy
- add the component energies together
what does qtrans with large numbers mean
that there are many translational energy levels thermally available
