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energy E0 as given by (5.21) and  is a parameter to be determined. The energy eigenvalues, of the Morse potential,
                              1
contain only two terms in (v + 1) (51).


             __ __ __ _1      hi
Ev   hc     h/2c    (v + 1   8c     (v + 1        (5.23)
   YD h    eLvh/2        2c1 8 Tr2CP    2



Equating the coefficients of (v + i) from (5.21) and (5.23) gives


                      = =21f0cu/Deh We            (5.24)


The vibrational energy levels are now expressed as



          Ev = hc  e(V + 1) - WeXe(V + 1 )j       (5.25)


The vibrational partition function is calculated according to

                          Vc
                       v I    Ev/kT               (5.26)
                         v=0

where E  is given by (5.25) using experimentally determined
       v
values of we and w xe (50). Note that (5.26) is a finite sum whereas (5.19) is based on the formula for the sum of an infinite geometric series, which is equivalent to the incorrect assumption that an infinite number of vibrational states exists below the dissociation limit. Only a finite