Physical Chemistry , 1st ed.

levels are so large, it would take millions or billions of degrees or atmospheres
to have any significant change in qnuc. Since chemistry typically doesn’t con-
sider such extremes, the effect ofqnuccan be safely ignored. Furthermore, for
state functions that are directly related to ln qor q, having qnucas a simple
whole number translates to a small additive correction to the overall value of
the state function, especially when compared to the contributions of the other
qvalues. Since the correction is relatively small, it can easily be ignored. Also,
for changes in state functions, nuclear states are usually not changed, so this
very small correction cancels in the final-minus-initial value determination. As
such, it never even shows up.
For all these reasons,qnucis justifiably ignored in chemistry. This reinforces
the minimal influence nuclei have on chemistry, which is more the domain of
electrons. (However, we will soon consider an interesting—and surprising—
effect of nuclear states on chemistry.)
The electronic part of the partition function for an atom (we consider mol-
ecules later) is considered similarly to the nuclear partition function, as an ex-
plicit summation over the negative exponentials of the electronic energy levels:

qelect 



ifirst

giei/kT (18.5)

electronic level

Again, if we define the zero point for electronic energy as the ground electronic
state, equation 18.5 becomes

qelectg 1 



isecond

giei/kT (18.6)

electronic level

In many cases, the terms of the summation can be ignored because, like
excited nuclear levels, excited electronic states are so high in energy compared
to kTthat the negative exponential is a negligible number compared to g 1 , the
degeneracy of the ground state.
However, this is not always the case. Many systems have low-lying electronic
excited states, whose energies above the ground state are not high with respect
to kT. Therefore, the negative exponential is not negligible, especially with de-
generacy of the electronic state (gi) as part of that term in the summation.
Strictly speaking, electronic partition functions must be considered on an in-
dividual basis and term-by-term. Only when additional terms become so small
that they are negligible can the summation be stopped, or truncated.The fol-
lowing examples illustrate.

Example 18.1

The first five electronic states of the carbon atom are:

State Energy (cm^1 ) Energy (J) Degeneracy

1 0 0 1

2 16.4 3.26 

10 ^223

3 43.5 8.64 

10 ^225

4 10,194 2.0249 

10 ^191

5 21,648 4.3001 

10 ^191

Determine the value of the electronic partition function qelectusing only

the first energy level, then by successively including the second, third, fourth,

18.2 Separating q: The Nuclear and Electronic Partition Functions 619