Morse potential specific heat with applications: an integral equations theory based

Morse potential specific bond volume: a simple formula with applications to dimers and soft-hard slab slider

Morse potential interaction is an important type of the vibrational potentials, especially, in the quantum mechanics which is used for the describing of general vibrational cases rather than the harmonic one. Morse potential has three fitting parameters, the depth of the Morse interaction, the distance of equilibrium bond and the range parameter which determines the range of the well. The Morse interaction specific bond volume is a three dimensional image of the bond length in its molar case, and this specific volume is the generalisation in three dimensions. In this study, the integral equation theory of the simple fluids has been applied for deriving a novel formula of the specific bond volume for Morse potential based on one of the approaches in the theory and based on the boundary conditions. We find that the specific bond volume of Morse potential depends on the absolute temperature via logarithmic function and square root function, besides, the specific bond volume of Morse potential decreases when the temperature decreases for different values of the molar volume and for different values of the depth of Morse well. In addition to that, the specific bond volume of Morse potential increases when the depth of the well decreases for different temperature values. Also, it is found from the formula which we derive that the specific bond volume of Morse potential increases via linear function with the molar volume of the system for different values of temperatures. We apply the formula of the specific bond volume of Morse potential for finding this specific volume for two molecules of the hydrogen halogens, which are the hydrogen chloride, and hydrogen fluoride. We find that the specific bond volume of the hydrogen chloride is greater than the one of the hydrogen fluoride. Also, we apply the formula for the two simple molecules gases which are the hydrogen molecules, and the nitrogen molecules. Besides, we apply the formula for the slab-slider system in two cases: hard and soft materials, and we concluded that the changes of the specific bond volume of the soft materials is faster than the hard materials. We believe that the formula which is found of the specific bond volume of Morse potential is general and can be applied for multiple materials.

Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms

A number of interaction energy types are employed in the vibrations studies, especially in the spectroscopic analysis, such as the harmonic oscillator and Morse oscillator. In this research, a derivation of an analytical formula of equation of state of Morse oscillator is considered by employing the approximations used in the simple fluids theory. The compressibility formula of the pressure and the virial expansion formula of the pressure using the solutions of the main equation of the simple fluids theory with one of the approximations of the theory are employed for the purpose of the derivation. The virial coefficients of the total Morse oscillator pressure (the first order one, and the second order one) are found for Morse oscillator with respect to the fractional volume of the components, where we conclude that the first order term is proportional to the absolute temperature directly and depends on the diameter of the particles, while we concluded that the second order coefficient term is more complicated than the first order one with temperature, and also, depends on the three Morse oscillator parameters and the diameter of the particles. Besides, we conclude that the total pressure of Morse oscillator, generally, depends on the minimum energy of the well of Morse oscillator, the width parameter of Morse oscillator, and the equilibrium bond distance of the oscillator, in addition to their dependence on the absolute temperature of the components, and the diameter of the particles. The formula of the Morse oscillator equation of state which is found in this research can be applied to multiple materials described using Morse oscillator such as lots of dimers in the vibrations spectroscopy.