The interacting boson model.

Discussion of the most important formulae and construction of plots for some functions of mathematical physics relevant to quantum mechanics. These functions are Hermite polynomials, Legendre polynomials and Legendre functions, spherical harmonics, Bessel functions and spherical Bessel functions and Laguerre polynomials. Directly related to some of these and also discussed are the eigenfunctions of the one-dimensional harmonic oscillator and the radial eigenfunctions of the harmonics oscillator in three dimensions and of the hydrogen atom.

Special Functions of Mathematical Physics

Highly effective mild steel corrosion inhibition in 1 M HCl solution by novel green aqueous Mustard seed extract: Experimental, electronic-scale DFT and atomic-scale MC/MD explorations

This chapter describes the three basic types of chemical bonds that join atoms and ions together. It discusses the properties associated with each type of bond those are metallic, ionic, and covalent. The chapter describes the weaker forces that act among molecules. It focuses on the properties of the bonds, bond energies, bond lengths, covalent, and ionic radii. The chapter illustrates the attraction between positive ions and surrounding freely mobile electrons. It discusses the geometry of molecules. The dipole moment of a polyatomic molecule is determined by both, the bond polarity and molecular geometry. The chapter provides an overview of intermolecular forces. It explains energy–distance relationship in bond formation. The most important determining factor in the geometry of covalently bonded molecules is the number of electron pairs in the valence shell of the atoms involved.

The chemical bond

Green/sustainable plant origin organic molecules with structures including polar functional groups, heteroatoms and aromatic rings play a vital role in the adsorption and inhibition effectiveness on metal substance in harsh acidic environments. The components like apigenin, eriodictyol, naringenin, taxifolin in Tamarindus indiaca extract can easily adsorb on the mild steel (MS) surface and sufficiently control its rate of corrosion in contact with aggressive acids. In this paper, the corrosion retardation potentiality of Tamarindus indiaca extract for MS in 1 M HCl was experimentally (EIS, potentiodynamic polarization, SEM, AFM and contact angle) and theoretically (basic atomic/electronic scale tools) explored. EIS outcomes proposed 93% numerical inhibition power for 800 ppm Tamarindus indiaca extract after 2.5 h steel immersion in aggressive media. Potentiodynamic polarization experiment results declared that Tamarindus indiaca extract operated as combined anodic/cathodic green inhibitor with cathodic inhibition prevalence. Final results demonstrated the icorr value reduction from 0.98 µA cm−2 (for bare sample) to 0.14 µA cm−2 (for 800 ppm inhibitor concentration), demonstrating 85% inhibition performance in acidic solution. Also, the weight loss measurements depicted 93% efficiency after 4 h steel exposure to 1 M HCl media (solution temperature = 25 °C). The temperature effect on the inhibitor properties was evaluated in the temperature range of 25 °C to 55 °C and outcomes showed endothermic reactions occurrence for protection. Based on the AFM micrographs it was shown that HCl solution combined with 800 ppm Tamarindus indiaca extract led to the most smoothened MS surface and the average roughness decreased to lower values (average roughness for uninhibited sample = 119 nm and for inhibited sample = 31 nm). Conclusions derived from different isotherms demonstrated that following Langmuir isotherm a mono inhibitive layer of Tamarindus indiaca extract molecules covered the iron substance. Molecular simulations strongly affirmed the preference of Tamarindus indiaca extract molecules for adsorption on the MS substrate. The DFT explorations highlighted that the aromatic rings and oxygen heteroatoms behaved as influential local sites for molecular adsorption.

Electronic/atomic level fundamental theoretical evaluations combined with electrochemical/surface examinations of Tamarindus indiaca aqueous extract as a new green inhibitor for mild steel in acidic solution (HCl 1 M)

Prostate cancer that is resistant to castration has been a prominent health challenge in the lives of men, particularly older men. This study looks at the spectroscopic properties, density functional theory (DFT) calculations, and molecular docking of the chemical N-(1H-pyrrol-2-yl) methylene)-4-methylaniline(PMMA) in order to see if it can be used as a chemotherapeutic medication for the treatment of castration-resistant prostate cancer(CRPC). The frontier molecular orbitals (FMO), Fukui reactivity functions, non-linear optics (NLO), and natural bond orbitals (NBO) were investigated further using DFT at the 6–311++G (d, p) with five different functional (B3LYP, B3PW91, ɷB97XD, PBEPBE, and M06–2X) for the investigation of the studied molecular structural properties. The experimental and theoretical vibration analysis of the synthesized molecule employing DFT investigations in different solvents at B3PW91/6–311++G (d, p) were found to be in good agreement. The docking results with three different proteins (4XVE, 1XF0, 5Y8Y) with PMMA showed good binding affinities when compared to the standard drug (Darolutamide) (DLA). The molecular docking results indicated that PMMA have an excellent chemotherapeutic potential for the treatment of CRPC. 

Structural Benchmarking, Density Functional Theory Simulation, Spectroscopic Investigation and Molecular Docking of N-(1H-pyrrol-2-yl) methylene)-4-methylaniline as Castration-Resistant Prostate Cancer Chemotherapeutic Agent.

Purpose




This paper aims to appraise the inhibitory effect of saponins extracted from Gongronema latifolium (SEGL) on mild steel in acid media. This is in a bid to conserve our environment and maintain the integrity of engineering structures and materials.




Design/methodology/approach




The corrosion inhibition of SEGL and ethanolic extracts of the leaves of G. latifolium (EEGL) on mild steel was studied by hydrogen evolution technique within a temperature range of 30-60°C in tetraoxosulphate (VI) acid solutions.




Findings




The extracts inhibit the corrosion of mild steel, and the inhibition efficiency depends on the concentration of the plant extract, temperature and the period of immersion. SEGL was comparatively more efficient than EEGL. Optimum values of the inhibition efficiency for both the EEGL and SEGL (93.7 and 96.5 per cent, respectively) were obtained at extract concentration of 10 g/L, whereas the least values were obtained at extract concentration of 0.5 g/L.




Originality/value




This paper provides new information on the possible application of isolated SEGL as an environmentally friendly corrosion inhibitor. The possible mechanism of the inhibitive action is also given.

A. I. Ikeuba

Papers

Structural Benchmarking, Density Functional Theory Simulation, Spectroscopic Investigation and Molecular Docking of N-(1H-pyrrol-2-yl) methylene)-4-methylaniline as Castration-Resistant Prostate Cancer Chemotherapeutic Agent.

Green corrosion protection for mild steel in acidic media: saponins and crude extracts of Gongronema latifolium

SVET and SIET Study of Galvanic Corrosion of Al/MgZn2in Aqueous Solutions at Different pH

Understanding the galvanic corrosion of the Q-phase/Al couple using SVET and SIET

Electrochemical, TOF-SIMS and XPS studies on the corrosion behavior of Q-phase in NaCl solutions as a function of pH