Information theory and thermodynamic properties of diatomic molecules using molecular potential.

Owing to the devise applications of molecules in industries, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for the position and momentum spaces were obtained to verify the Heisenberg's uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF) using Maple 18 software. The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

Theoretic measure and thermal properties of a standard Morse potential model.

Since the proposition of the standard form of Morse potential [Formula: see text] model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H2), lithium molecule (Li2), and potassium molecule (K2). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.

Non-relativistic molecular modified shifted Morse potential system.

A shifted Morse potential model is modified to fit the study of the vibrational energies of some molecules. Using a traditional technique/methodology, the vibrational energy and the un-normalized radial wave functions were calculated for the modified shifted Morse potential model. The condition that fits the modified potential for molecular description were deduced together with the expression for the screening parameter. The vibrational energies of SiC, NbO, CP, PH, SiF, NH and Cs2 molecules were computed by inserting their respective spectroscopic constants into the calculated energy equation. It was shown that the calculated results for all the molecules agreement perfectly with the experimental RKR values. The present potential performs better than Improved Morse and Morse potentials for cesium dimer. Finally, the real Morse potential model was obtained as a special case of the modified shifted potential.

Eigen-solutions and thermal properties of multi-parameter exponential potential.

In this work, we determined an approximate eigen solutions of Modified multi-parameter exponential potential using supersymmetric quantum mechanics approach (SUSY) with improved Greene-Aldrich approximation to the centrifugal term. The energy equation and its corresponding normalised radial wave function were fully obtained. The proposed potential reduces to other useful potentials like Rosen-Morse, Hellmann, Yukawa and Coulomb potential as special cases. The thermodynamic properties like the vibrational mean energy ( U ß , V ), Vibrational heat capacity ( C ß , V ), vibrational entropy ( S ß , V ) and vibrational free energy ( F ß , V ) of the interacting potential were studied via partition function ( Z ß , V ) obtained from the resulting energy equation. This study was applied to three diatomic molecules: Chromium hydride (CrH), Titanium Hydride (TiH) and Thiocynate (ScN). To ascertain the high degree of our analytical mathematical accuracy, we compared the results of special cases with an existing results. These were found to be in excellent agreement with the existing results.

Vibrational energies of some diatomic molecules for a modified and deformed potential.

A molecular potential model is proposed and the solutions of the radial SchrÓ§dinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov-Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Solutions of the Schrödinger equation and thermodynamic properties of a combined potential.

The solution of the radial Schrödinger equation was obtained using the methodology of supersymmetric approach with a combination of modified generalized Pöschl-Teller potential and inversely quadratic Yukawa potential model. The non-relativistic ro-vibrational energy spectra and the corresponding wave functions were obtained and numerical results were generated for some states. The variation of energy of the combined potential and the subsets potentials with the screening parameter for various quantum number were graphically studied. The effect of the potential parameters on the energy for different states was also studied numerically. For more usefulness and applications of the work, the vibrational partition function and the various thermal properties like mean energy, Helmholtz energy, heat capacity and entropy were calculated. The behaviour of the thermodynamic properties with respect to temperature change for various quantum number and maximum quantum states were examined in detail. The temperature has positive effect on all the thermal properties except the free energy.

Bound-state solutions and thermal properties of the modified Tietz-Hua potential.

An approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz-Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz-Hua potential and the actual Tietz-Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz-Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz-Hua potential and that of the actual Tietz-Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.

Eigensolution techniques, expectation values and Fisher information of Wei potential function.

An approximate solution of the one-dimensional relativistic Klein-Gordon equation was obtained under the interaction of an improved expression for Wei potential energy function. The solution of the non-relativistic Schrödinger equation was obtained from the solution of the relativistic Klein-Gordon equation by certain mappings. We have calculated Fisher information for position space and momentum space via the computation of expectation values. The effects of some parameters of the Wei potential energy function on the Fisher information were fully examined graphically. We have also examined the effects of the quantum number n and the angular momentum quantum number ℓ on the expectation values and Fisher information respectively for some selected molecules. Our results revealed that the variation of most of the parameters of the Wei potential energy function against the Fisher information does not obey the Heisenberg uncertainty relation for Fisher information while that of the quantum number and angular momentum quantum number on Fisher information obeyed the relation.

Analytical determination of theoretic quantities for multiple potential.

The approximate analytical solutions of the three-dimensional radial Schrödinger wave equation with a multiple potential function has been studied using a suitable approximation scheme to the centrifugal term in the framework of parametric Nikiforov-Uvarov method. The energy equation and the wave function were obtained. The calculated wave function was used to study Shannon entropy and variance via expectation values. The behaviour of Shannon entropy and variance respectively with the equilibrium bond length were examined in detail. A special case of the multiple potential (pseudoharmonic-like potential) was equally examined under Shannon entropy and variance. For further application of the study, some diatomic molecules were examined under variance and Shannon entropy. Finally, some variance inequalities were derived using Cramer-Rao uncertainty relation and these were justified by numerical results.