Comparative analysis of modified reverse degree topological indices for certain carbon nanosheets using entropy measures and multi criteria decision-making analysis

The diverse applications of various carbon nanostructures have sparked significant research interest. The potential significance of carbon nanosheets lies in their exceptional mechanical, electrical, and thermal properties, enabling advancements in various technological applications such as energy storage, electronics, and engineering, playing important roles in material science and nanotechnology. In the field of mathematical chemistry, topological indices play a crucial role by providing numerical insights into molecular structures. These insights facilitate predictive correlations with chemical properties and reactivity, ultimately finding utility in areas like drug design and material sciences. Expanding on this, the study delves into the application of entropy-based methodologies that originates from the arrangement of chemical structures. By assessing the complexity and other features of these structures, graph entropies are translated into information-theoretic metrics. This article examines modified reverse degree-based topological indices with its universal applicability to all degree-based indices. The standout feature is the adaptable parameter “ $k$” effectively shaping the molecular graphs degree sequence to best fit each dataset with their unique physicochemical properties, distinguishing it from conventional fixed degree methodologies. Additionally, we investigate graph entropies and examine the impact of varying the parameter “ $k$” on entropy measures across a range of nanosheet structures. The research focuses on characterizing carbon nanosheets, employing effective (MCDM) multiple criteria decision-making methods like VIKOR, TOPSIS, and SAW. Through these techniques, a comprehensive comparative analysis of the nanosheets is conducted with the aim of establishing optimized rankings for each type based on their unique attributes and characteristics.     

The confined helium atom: An information–theoretic approach

In this article, we study the helium atom confined in a spherical impenetrable cavity by using informational measures. We use the Ritz variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius $r_0$. As trial wave functions we use one uncorrelated function and five explicitly correlated basis sets in Hylleraas coordinates with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback–Leibler entropy, Tsallis entropy, disequilibrium and Fisher–Shannon complexity, as a function of $r_0$. We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. As expected these entropic measures are less sensitive to electron correlation in the strong confinement regime ( a.u.).     

Topological defects on the energy spectra of diatomic molecules embedded with shifted Deng–Fan oscillator potential under AB flux field

A study on the effect of point like global monopole topological defects on the energy eigenvalues of the diatomic molecules $H_2$, $LiH$, $CO$, $HCl$ embedded with Shifted Deng–Fan Oscillator Potential under the influence of Aharonov–Bohm flux field has been made here. Asymptotic Iteration Method (AIM) is used to find out the bound state solutions for arbitrary $l$ states by solving the non-relativistic Schrödinger equation. A Pekeris-type approximation has been used to approximate the centrifugal barrier term. It is observed that, energy levels of the diatomic molecules is significantly affected by the global effects of the point like global monopole, flux field and effective potential field.     

A DFT calculation of electronic structures,magnetic, and thermoelectric properties of the new equiatomic quaternary Heusler alloy RuTiCrSi

The stabilities, mechanical, electronic, and magnetic properties of the new equiatomic quaternary Heusler alloy (EQHA) RuTiCrSi were investigated using the Kohn-Sham DFT (KS-DFT) calculations within the generalized gradient approach (GGA), the modified version of the exchange potential introduced by Becke and Johnson in addition to the GGA (mBJ-GGA), and Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. The ground-state equilibrium energy reveals that the ferromagnetic with type 2 structure is the more stable. The RuTiCrSi is energetically, mechanically, and dynamically stable. The calculated self-consistent total magnetic moment is 2 μB and agrees well with the Slater-Pauling rule of $M_{\mathrm{t}}=\left|Z_{\mathrm{t}}-24\right|$. The electronic structure results from mBJ-GGA and HSE06 functionals show a half-metallic behavior. A high Curie temperature is obtained using the mean-field approximation. The thermoelectric response was calculated using the semi-classical Boltzmann transport equation under constant relaxation time. The maximum value of Seebeck coefficient is observed at the ambient temperature of $741\mathrm{\mu V}{\mathrm{K}}^{-1}$. It was also observed that the power factor increases significantly as temperature rises. Therefore, the new EQHA RuTiCrSi seems to be a potential candidate for spintronic thermoelectric applications.     

Modeling of a linear ion trap with driving rectangular waveforms

We consider the operation of a digital linear ion trap with resonant radial ejection. A sequence of rectangular voltage pulses with a dipole resonance signal is applied to the trap electrodes. The periodic waveform is piecewise constant, has zero mean, and is determined by an asymmetry parameter $d$: one value is taken on interval $\left(0,\mathit{dT}\right)$ and another on $\left(\mathit{dT},T\right)$, where $T$ is the RF period. Ion mass scanning is performed by varying the asymmetry parameter $d$ and amplitude of the negative pulse part with time. The ion oscillation frequencies and acceptance of the linear trap are calculated. The dependence of the ion mass to charge ratio $m/z$ on the parameter $d$ is $m/z~d^2$. The maximum value is about $m/z=30$ kDa for typical parameters of the linear trap: frequency 0.5 MHz, rod radius 4 mm, and negative pulse amplitude 1 kV. The dipolar excitation frequency is 0.125 MHz at which the LIT acceptance is maximal.     

On physical analysis of entropy measures for sodium oxide via statistical models

This study delves into a comprehensive physical analysis of entropy measures applied to sodium oxide ${\text{Na}}_2\text{O}$. A key idea in information theory and thermodynamics, entropy is essential to comprehending the stability of a system. The study clarifies the intricate relationships and physical properties of ${\text{Na}}_2\text{O}$ by combining theoretical analysis with statistical methods, providing important knowledge for material design and industrial operations. In a chemical graph, atoms are shown by vertices while their bonding are illustrated by edges. Sodium oxide is a major contributor to manufacture glass, it also has potential applications in ${\text{CO}}_2$ sequestration, transparent materials, biomedical devices and nano grating glass. A topological index is a relationship between the molecular graph and its topology. We have computed various graph entropies based on different topological indices of chemical graph of sodium oxide. Further we have integrated these graph entropies with distinct thermodynamical measures of sodium oxide by developing mathematical models between both quantities. We have developed these mathematical frameworks in MATLAB. All the models are selected relying on the least mean squared error or sum of squared error.     

Cn,CnH and their anions: Quest for linearity with n≤8 even versus odd,and beyond

Using the concept of quasi-molecule (“tile”) and the database of quasi-molecules embedded on a parent molecule, it is discussed whether the latter can attain linear form or otherwise. Besides anew accurate optimization of all tiles (quasi-triatomics) at various levels of ab initio theory and basis-sets, the nature of the predicted stationary points for the title parent molecules is probed through a priori calculations here too reported. Also discussed is the common rule that even- $n$ ${\text{C}}_n{\text{H}}^{-}$ anions are linear while odd-numbered ones tend to have nonlinear isomers. The reported quasi-molecule approach is general, and allow the prediction of linearity or otherwise of the parent systems prior to calculations on them. When based on an extension of the bisection method (Varandas, Int. J. Quantum Chem. 2023 , 123, e27036.), it is easy to use even for large parent molecules, as illustrated for neutral and anionic carbon clusters with $n\ge 9$.     

Spherically confined hydrogenic atoms under classical non-ideal plasmas: Scaling law for the critical cage size

An elegant calculation is carried out to investigate the effects of the non-ideality of classical plasma on the energy levels of the hydrogenic atoms held in a spherical cage. Organized effect of the non-ideal classical plasma is described by an analytical pseudopotential which contains the Debye length $D$ and non-ideality parameter $\gamma$ as parameters. Convergent results for the bound states are obtained variationally by utilizing a large trail function containing cosine term which automatically takes care of the requisite boundary conditions. For the plasma-free case, our results are in excellent agreement with the most accurate results available in the literature. An inclusive study is made to explore the changes emerging in the energy levels due to the variation of the plasma parameters and cage size. Special emphasis is made on the determination of critical cage size precisely. The present study specifically reveals that the increasing plasma non-ideality leads to the elongation of the critical cage size. Moreover, it is empirically found that the critical cage size for a given hydrogenic atom can be obtained from a scaling law.     

Physical versus non-physical effective nuclear masses for non-adiabatic corrections to molecular spectra

Two types of developments for very accurate non-adiabatic corrections to rovibrational molecular energy levels, one of a formal nature and the other of a heuristic nature, lead to fundamentally different approaches for effective nuclear masses. The former yields effective masses that have non-physical interpretation at some ranges of nuclear distances. The later uses physical masses obtained from electronic structure calculations. This paper contains a brief review of the subject and proposes procedures to improve and generalize the heuristic approach. Comparisons are made of the results obtained by the two approaches for the H ${}_2$ molecule, since no further calculations were found with the proper accuracy, but some issues involving the HeH ${}^{+}$ ion and the water molecule are discussed. The conclusion is that the heuristic approach has many advantages over the formal one, namely, equivalent accuracy and physically grounded qualitative interpretation. But, moreover, it seems to be presently the only method that allows non-adiabatic calculations for well isolated states of larger molecules.     

Theoretical investigation of the weak interactions of rare gas atoms with silver clusters by resonance Raman spectroscopy modeling

The interactions of rare gas atoms (Rg = Ar, Kr, and Xe) with small neutral and cationic silver clusters have been investigated by density functional methods and the effect of these weak interactions on the resonance Raman spectra of the complexes has been evaluated. The resonance Raman technique that depends on the properties of ground and excited state, seems deeply sensitive to the weak rare gas–metal cluster interactions, and the use of inert gases has been proven to be an excellent approach to recognize the ability of this technique to detect extremely weak interactions. In this work, for , and complexes the IR, normal and resonance Raman spectra have been calculated and the effect of rare gas–cluster stretching vibration ( ) on the pattern and the relative intensities of different spectra have been investigated. The resonance Raman spectra for the weakly interacted complexes (with the interaction energies less than ?2.0 kcal/mol) exhibit the vibration with the detectable intensity that its intensity increases by going from Ag₆–Ar to Ag₆–Xe complex. Moreover, the resonance Raman spectra (based on the excited state gradient approximation) for high intensity nearly degenerate excited states, proved the effect of accumulation of the excited state charge density on the relative intensity of vibration.     

Compressed lithium atom under Debye screening

In the present paper, we introduced two approximation methods to investigate the spherically compressed lithium atom under the influence of Debye plasma. Specifically, the diffusion and the variational Monte Carlo methods are used for the first time to study this case. We incorporated an exponential screening into the nuclear Coulomb potential to account for the plasma influence. We focused our investigation on analyzing the combined effect of compression and plasma environment on the behavior of the lithium atom in its ground state. The resulting outcomes exhibited consistent pattern across various confinement radii $R_c$ and Debye plasma lengths $\mu$. Many of the results are novel contributions, as they have yet to be explored. Moreover, the findings from this study demonstrated reasonable agreement with the limited existing theoretical results.     

Dielectrophoresis microbial characterization and isolation of Staphylococcus aureus based on optimum crossover frequency

Characterization of antibiotic-resistant bacteria is a significant concern that persists for the rapid classification and analysis of the bacteria. A technology that utilizes the manipulation of antibiotic-resistant bacteria is key to solving the significant threat of these pathogenic bacteria by rapid characterization profile. Dielectrophoresis (DEP) can differentiate between antibiotic-resistant and susceptible bacteria based on their physical structure and polarization properties. In this work, the DEP response of two Gram-positive bacteria, namely, Methicillin-resistant Staphylococcus aureus (MRSA) and Methicillin-susceptible S. aureus (MSSA), was investigated and simulated. The DEP characterization was experimentally observed on the bacteria influenced by oxacillin and vancomycin antibiotics. MSSA control without antibiotics has crossover frequencies ($f_{x0}$) from 6 to 8 MHz, whereas MRSA control is from 2 to 3 MHz. The $f_{x0}$ changed when bacteria were exposed to the antibiotic. As for MSSA, the $f_{x0}$ decreased to 3.35 MHz compared to $f_{x0}$ MSSA control without antibiotics, MRSA, $f_{x0}$ increased to 7 MHz when compared to MRSA control. The changes in the DEP response of MSSA and MRSA with and without antibiotics were theoretically proven using MyDEP and COMSOL simulation and experimentally based on the modification to the bacteria cell walls. Thus, the DEP response can be employed as a label-free detectable method to sense and differentiate between resistant and susceptible strains with different antibiotic profiles. The developed method can be implemented on a single platform to analyze and identify bacteria for rapid, scalable, and accurate characterization.     

Numerical study supplemented with simplified model on electrophoresis of a hydrophobic colloid incorporating finite ion size effects and ion-solvent interactions

We consider a modified electrokinetic model to study the electrophoresis of a hydrophobic particle by considering the finite sized ions. The mathematical model adopted in this study incorporates the ion steric repulsion, ion-solvent interactions as well as Maxwell stress on the electrolyte. The dielectric permittivity and viscosity of the electrolyte is considered to vary with the local ionic volume fraction. Based on this modified model for the electrokinetics we have analyzed the electrophoresis in a single as well as mixture of electrolytes of monovalent and non-$z:z$ electrolytes. The dependence of viscosity on local ionic volume fraction modifies the hydrodynamic drag as well as diffusivity of ions, which are ignored in existing studies on electrophoresis. A simplified model for electrophoresis of a hydrophobic particle incorporating the ion steric repulsion and ion-solvent interactions is developed based on the first-order perturbation on applied electric field. This simplified model is established to be efficient for a Debye layer thinner than the particle size and a smaller range of slip length. This model can be implemented for any number of ionic species as well as non-$z:z$ electrolytes. It is established that the ion steric interactions and dielectric decrement creates a counterion saturation in the Debye layer leading to an enhanced mobility compared to the standard model. However, experimental data for non-dilute cases often under predicts the theoretically determined mobility. The present modified model fills this lacuna and demonstrate that the consideration of finite ion size modifies the medium viscosity and hence, ionic mobility, which in combination lowers the mobility value.     

The role of monomer geometry on the properties of polyolefins: A numerical study

We explore the role of monomer geometry on the structural, dynamic, and thermodynamic properties of polyolefis by employing all-atom molecular dynamic simulations. Specifically, we compare properties of atactic polyolefins in the molten state including polypropylene (aPP), a short-chain branched polymer: poy(1-hexene) (aPH), and a polymer having cyclic olefins: poly(vinyl cyclobutane) (aPVCB). We find polymers having the same chain mass and atom composition (hydrocarbon-based molecules), but having different monomer architecture differ strongly in material properties. In particular, the polymer glass transition ( $T_{\mathrm{g}}$) and bulk modulus ( $B$) show higher values for aPVCB in comparison to aPP and aPH. This increase is caused by having the carbon atoms in a cyclic structure, making aPVCB achieve higher mass and energy densities. By contrast, adding linear short side chains to polymer backbones causes a reduction in $T_{\mathrm{g}}$ and $B$, since side chains make backbones displace each other reducing their packing and thus their mass and energy densities. More broadly, our numerical results suggest that the incorporation of VCB monomers to linear polyolefins will enhance their properties, opening the possibility for designing a new set of materials.