In this work, we have solved the radial part of the Schrödinger equation with Tietz potential to obtain explicit expressions for bound state ro-vibrational energies and radial eigenfunctions. The proper quantization rule and ansatz solution technique were used to arrive at the solutions. In modeling the pseudo-spin–orbit term of the effective potential, the Pekeris-like and the Greene-Aldrich approximation recipes were applied. Using our equation for eigen energies, we have deduced expression for bound state energy eigenvalues of Deng-Fan oscillator. The result obtained agrees with available literature data for this potential. Also, for arbitrary values of rotational and vibrational quantum numbers, we have calculated bound state energies for the Tietz oscillator. Our computed results are in excellent agreement with those in the literature. Furthermore, the result showed that unlike Greene-Aldrich approximation, energies computed based on Pekeris-like approximation are better and almost indistinguishable from numerically obtained energies of the Tietz oscillator in the literature. With the help of our formula for ro-vibrational energy, analytical expressions for some important thermodynamic relations were also derived for the Tietz oscillator. The derived thermal functions which include ro-vibrational: partition function, free energy, mean energy, entropy and specific heat capacity were subsequently applied to the spectroscopic data of KI diatomic molecule. Studies of the thermal functions indicated that the partition function decreases monotonically as the temperature is raised and increases linearly for increase in the upper bound vibrational quantum number. On the other hand, increase in either temperature or upper bound vibrational quantum number amounts to monotonic rise in the entropy of the KI molecules

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In this paper, a total of fourteen dye extracts from different plants’ parts (flowers and fruits) were extracted. Absorbance of light by dye extracts with 5%, 10% and 20%concentrationsweremeasured using a UV-Vis spectrophotometer at different wavelengths. A system of linear equations in terms of wavelength and absorbance without film thickness was developed and solved using MATLAB software. Also, optical energy bandgap (Eg) obtained experimentally are at range of 1.77- 2.76 eV. From the solutions of the system of equations, the (Eg) of the natural dyes were obtained. The results show all the dye extracts have (Eg) in the range 1.34-2.09 eV which falls within the range of UV and IR portions of the electromagnetic spectrum. Also, the results reveal that sunflower (Helianthus) dye has the smallest (Eg) of 1.34 eV and guava (Guajava) peel dye with the higher (Eg) of 2.09 eV. This means Helianthus dye absorbs more light over a wider part of the electromagnetic spectrum and the easier electron transfer from its valence band to the conduction band. The values obtained via matrix method are in agreement with the experimental values with slight deviation, hence this validates the matrix method of obtaining optical energy bandgaps.

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In this paper, a simple strategy to select and grade efficient natural dye-sensitizers for photo-absorption is developed. The selection criteria help to choose efficient dye for construction of solar cell. On the other hand, the dye-grade technique based on light and matter interaction parameters (absorbance, anthocyanin, and light harvesting efficiency) further reduce the number of dyes for efficient dye-sensitized solar cell (DSSC) production. The result shows that the dyes extracted from witch seed flower (Striga hermonthica), flamboyant flower (Delonix regia), and bitter gourd (Momordica charantia) have dye-grade 1, are the most efficient photo-absorber for enhanced DSSC fabrication while guava peel dye has grade 10 being the least efficient dye. The selection criteria and dye-grade techniques provide surer way of getting promising dyes for effiective DSSC production than choosing the dyes randomly based on some features like their colors and abundance.

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