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

A molecular potential model is proposed and the solutions of the radial Schrӧdinger 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.

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

A molecular potential model is proposed and the solutions of the radial Schrӧdinger 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.

A Liquid-Metal-Based Freestanding Triboelectric Generator for Low-Frequency and Multidirectional Vibration

There are a lot of vibrational energies, which are low frequency, multidirectional, and broadband, in the nature. This creates difficulties for devices that aim at harvesting vibration energy. Here, we present a liquid-metal-based freestanding triboelectric generator (LM-FTG) for vibration energy harvesting. In this device, the fluidity of liquid is used to increase sensitivity to vibration for better low-frequency response and multidirectional vibration energy harvesting capability. The freestanding power generation mode is able to increase power generation stability. Experiments show that the bandwidth of LM-FTG can almost cover the entire sweep frequency range, and a 10 μF capacitor can be charged to 6.46 V at 7.5 Hz in 60 s by LM-FTG. In particular, 100 LEDs are illuminated in the low-frequency environmental experiment successfully. The proposed LM-FTG can work in low frequency with large working bandwidth, which provides an effective method for energy harvesting of low-frequency and multidirectional vibrations.

A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation

This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the potential functions within the framework of the semi-classical approximation. The performance of the approximation was investigated as a function of the molecular mass. In this approximation, the nuclei were assumed to move in a classical potential. The Bohr-Sommerfeld quantization rule was then applied to calculate the vibrational energies of the molecules numerically. The results indicated that the first vibrational transition frequencies (v1ß0) of all hydrogen isotopes were consistent with the experimental ones, with a minimum percentage error of 0.02% for ditritium (T2) molecule using the Modified-Rosen-Morse potential. It was also demonstrated that, in general, the Rosen-Morse and the Modified-Rosen-Morse potential functions were better in terms of calculating the vibrational energies of the molecules than Morse potential. Interestingly, the Morse potential was found to be better than the Manning-Rosen potential. Finally, the semi-classical approximation was found to perform better for heavier isotopes for all potentials applied in this study.

Ab initio adiabatic study of the AgH system

In the framework of the Born–Oppenheimer (BO) method, we illustrate our ab-initio spectroscopic study of the of silver hydride molecule. The calculation of 48 electrons for this system is very difficult, so we have been employed a pseudo-potential (P.P) to reduce the big number of electrons to two electrons of valence, which is proposed by Barthelat and Durant. This allowed us to make a configuration interaction (CI). The potential energy curves (PECs) and the spectroscopic constants of AgH have been investigated for Σ+, Π and Δ symmetries. We have been determined the permanent and transition dipole moments (PDM and TDM), the vibrational energies levels and their spacing. We compared our results with the available experimental and theoretical results in the literature. We found a good accordance with the experimental and theoretical data that builds a validation of the choice of our approach.

Ro-vibrational energies of cesium dimer and lithium dimer with molecular attractive potential

An approximate solution of the Schrӧdinger equation for a molecular attractive potential was obtained using the parametric Nikiforov–Uvarov method. The energy equation and the corresponding radial wave functions were calculated. The effects of the potential parameters on the energy eigenvalues were examined. The thermal properties under the molecular attractive potential were calculated and the behaviour of the thermal properties with the maximum quantum state (λ) and the temperature parameter (β) respectively, were studied. Using the molecular spectroscopic parameters, the Rydberg–Klein–Rees (RKR) of cesium dimer and lithium dimer were both obtained and compared with the experimental values. The RKR values of both cesium dimer and lithium dimer calculated aligned with the observed values. The deviation and average deviation of the RKR for each molecule were also calculated.

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.

Spectroscopic study of the Electronic Properties of AgH

In this study, we describe our ab-initio study of the molecule of silver hydride AgH in the framework of the Born-Oppenheimer (BO) approximation.This molecule is composed of 48 electrons so the calculation of all electrons is very difficult. To solve this problem, we have been used a pseudo-potential (P.P),which is proposed by Barthelat and Durant allow reducing the number of electrons to two electrons of valence. This allowed usto perform a configuration interaction (CI). We have been determined the potential energy curves (PECs) and the spectroscopic constants for all symmetries Σ+, Π and Δ of AgH. The permanent and transition dipole moments (PDM and TDM), the vibrational energies levels and their spacing have been determined.We compared our results with the available theoretical and experimental studies in the literature. We found a good agreement with the theoretical and experimental results, which builds a validation of the choice of our method.

Diatomic molecules energy spectra for the generalized Mobius square potential model

The modified version of the generalized Mobius square (GMS) potential has been obtained by employing the dissociation energy and equilibrium bond length as explicit parameters. The potential parameters have been defined in terms of the molecular parameters. The modified GMS potential has also been used to model internuclear interaction potential curves for different states of diatomic molecules. Also, we have obtained the rotational–vibrational energy spectra of the new GMS potential model, both analytically and numerically for the different diatomic molecules. This was done by employing a Pekeris-type approximation scheme and an appropriate coordinate transformation to solve the Schrodinger equation. Our results have been compared with the experimental Rydberg–Klein–Rees (RKR) data and its corresponding average absolute deviations in terms of the dissociation energy computed. The effects of the vibrational and rotational quantum numbers on the rotational–vibrational energies for the different states of the various diatomic molecules have also been discussed. This paper has shown to be highly relevant to the studies of thermodynamic and thermochemical functions of diatomic molecules.