  The Deng-Fan-Eckart (DFE) potential is as good as the Morse potential in
studying atomic interaction in diatomic molecules. By using the improved
Pekeris-type approximation, to deal with the centrifugal term, we obtain the
bound-state solutions of the radial Schr\"odinger equation with this adopted
molecular model via the Factorization Method. With the energy equation
obtained, the thermodynamic properties of some selected diatomic molecules(H2 ,
CO , and ScN ) were obtained using Poisson summation method.. The unnormalized
wave function is also derived. The energy spectrum for a set of diatomic
molecules for different values of the vibrational n and rotational l are
obtained. To show the accuracy of our results, we discuss some special cases by
adjusting some potential parameters and also compute the numerical eigenvalue
of the Deng-Fan potential for comparison sake. However, it was found out that
our results agree excellently with the results obtained via other methods.
