By employing the asymptotic iteration method (AIM), we solved the three-dimensional time-independent Schrödinger 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.

通过采用渐近迭代法 (AIM)，我们用非谐 Eckart 势模型求解了三维时间无关的薛定谔方程。得到了非谐 Eckart 势的本征解的表达式。借助获得的旋转振动能谱，我们通过欧拉麦克劳林公式推导了旋转振动分配函数和其他热力学函数的表达式。讨论了温度和上限振动量子数对一些双原子分子系统非谐埃卡特势热力学函数的影响。已经确定，对于选定的双原子分子，存在独特的旋转振动熵和旋转振动比热容的临界温度。