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