Thermal properties of anharmonic Eckart potential model using Euler-MacLaurin formula

By employing the asymptotic iteration method (AIM), we solved the three-dimensional time-independent Schrodinger equation with the anharmonic Eckart potential model. The expression for the eigensolution of the anharmonic Eckart potential was obtained. With the help of the ro-vibrational energy spectra obtained, we derived the expressions for the ro-vibrational partition function and other thermodynamic functions, via the Euler MacLaurin formula. Effects of temperature and upper bound vibration quantum number on the thermodynamic functions of anharmonic Eckart potential were discussed for some diatomic molecular systems. It has been established that unique critical temperatures of ro-vibrational entropy and ro-vibrational specific heat capacity exist for the selected diatomic molecules.