Huckel Theory Research Articles

Simulation of electrical rectification effect in two-dimensional MoSe2/WSe2 lateral heterostructures

Two-dimensional (2D) transition metal dichalcogenides lateral heterostructures exhibit excellent performance in electrics and optics. The electron transport of the heterostructures can be effectively regulated by ingenious design. In this study, we construct a monolayer MoSe2/WSe2 lateral heterostructure, covalently connecting monolayer MoSe2 and monolayer WSe2. Using the Extended Huckel Theory method, we explored current-voltage characteristics under varied conditions, including altering carrier density, atomic replacement and interface angles. Calculations demonstrate a significant electrical rectification ratio (ERR) ranging from 200 to 800. Additionally, Employing Density Functional Theory with non-equilibrium Green’s function method, we investigated electronic properties, attributing the rectification effect to electronic state distribution differences, asymmetric transmission coefficients and band bending of projected local density of states. The expandability of the interfacial energy barrier enhances the rectification effect through adjustments in carrier concentration, atomic replacements and interface size. However, these enhancements introduce challenges such as increased electron-boundary scattering and reduced ambipolarity, resulting in a lower ERR. This study provides valuable theoretical insights for optimizing 2D electronic diode devices, offering avenues for precise control of the rectification effect.

Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding.

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.

A state-of-the-art theoretical method for estimating ultrasonic velocity in ionic liquid mixtures: An extension of McAllister's interaction model

McAllister’s Interaction Model has been extended to predict ultrasonic velocities in eight binary mixtures of ionic liquids and water at temperatures T = 288.15 K, 298.15 K, and 308.15 K.The ionic liquids chosen for the current study are [BMim][TfO], [BMpyr][TfO], [BMpy][TfO], [BMim][dca], [HMim][dca], [BMpyr][dca], [Mpy][MSO4], and [EEpy][ESO4]. The interactions considered in present cases have been investigated for a range of variations from three-body interactions to nine-body interactions. The experimental values of ultrasonic velocities for all the mixturesat temperatures T = 288.15 K, 298.15 K, and 308.15 Kare compared with the computed values. The differences between the experimental and theoretically predicted velocities are determined in terms of absolute percentage deviation. It is worth mentioning that McAllister’s Model of interactions has been extended, for consideration, from three-body interactions to nine-body interactions among constituent molecules of binary mixtures and applied for the prediction of ultrasonic velocities in binary mixtures of water and ionic liquids for the first time. The extended Huckel theory (EHT) is used to calculate the charge distributions in eight ionic liquids and water molecules to understand the active sites available for interactions on each constituting molecule of the binary mixtures under investigation. The results we obtained complemented our decision to extend McAllister’s interactions model (MAIM) to higher orders (four-body to nine-body interactions). The results obtained (using extended MAIM) report an excellent agreement with experimental velocity values for nine-body interactions for all the systems under study. It is also pointed out that McAllister’s assumption that the free energies of activation are the additive quantity for viscosity investigation in organic liquid mixtures is also valid in the case of ultrasonic velocity studies for ionic liquids and water mixtures. Considering McAllister’s conjecture that rather than a planar system of interactions among solvent-solute molecules, a three-dimensional approach to intermolecular interactions can be more appropriate, authors have confirmed the validity of McAlliter’s conjecture by successfully investigating three-dimensional multi-body (in the present case: 9-body) interactions in the binary mixtures of ionic liquids and water.

Effects of Non-Thermal Plasma on the Transition from Nano-Crystalline to Amorphous Structure in Water and Subsequent Effects on Viscosity

Recent studies have demonstrated that the physical properties of water treated with non-thermal plasma, or plasma-activated water (PAW), significantly differ from those of distilled water. For example, contrary to expectation, the viscosity of PAW becomes lower than that of distilled water at certain temperatures. This study developed a model to explain these differences by combining the two-state model of ordinary water, which describes water as a combination of nano-crystalline clusters and amorphous, free-floating molecules, using the Debye–Huckel theory for a fluid containing ions. A model for the viscosity of PAW was then developed from the general model. It explains how PAW has a lower viscosity than distilled water as the temperature decreases and why this effect is stronger than the colligative effect for ideal solutions. Finally, the viscosity model is compared to the experimental measurements of PAW treated with gliding arc plasma, showing that the data match the predicted values quite well. The model of PAW developed here can be used to understand other physical properties beyond viscosity, such as the surface tension, contact angle, electric conductivity, heat capacity, isothermal compressibility, and density, potentially facilitating new applications of PAW.

A single molecule diode based on gold electrodes and benzene molecule: conductivity and coupling analysis.

In this paper, we simulate a single-molecule diode to calculate the effective coupling and investigate the conductivity, as well as the effect of the electric field on these two parameters. First, we obtain the molecule states and energies at 0 V. The next step is to calculate the electrode/molecule coupling using the obtained electrode and molecule Hamiltonian. The electrode/molecule coupling depends on distance. By increasing the distance from 5 to 5.5 angstroms, the coupling decreases from 0.004 to 0.0002 eV. After calculating the electrode/molecule coupling, which is the most significant parameter in electron transfer, the results can be used to obtain the current-voltage and conductivity curves of the device. Simulation results demonstrate that externally applied electric field to the benzene molecule (isolated molecule) can cause a reduction in the effective coupling between the Au electrode and benzene, leading to decreased current and conductivity. Additionally, the applied electric field narrows the gap between the HOMO and LUMO energy levels. We conducted this computational work using Gaussian 09 software and a MATLAB code, both of which are based on the density functional theory (DFT) approach and the self-consistent field (SCF) method. For DFT calculations, we employed the three-parameter Beck hybrid exchange functional (B3), hybridized with the nonlocal correlation functional developed by Lee, Yang, and Parr (LYP). All optimizations were performed with triple-zeta polarized (TZP) split-valence 6-311G basis sets. The final step involved calculating the electrode/molecule coupling using the Huckel method and integrating the site-to-state transformation with Huckel parameters and the Fermi golden rule. After this calculation, we obtained the current-voltage and conductivity curves using MATLAB software.

Application of Debye–Huckel and Bronsted-Bjerrum theory to mass transfer rate in supported liquid membrane; effect of ionic strength on separation factor, an analysis through case studies

ABSTRACT The Debye–Huckel and Bronsted-Bjerrum theory has been applied to supported liquid membrane process to understand the effect of ionic strength on separation factor. The effect of ionic strength due to different salts and their concentration on the separation factor of Cu(II) and Zn(II) by supported liquid membrane using Di-2 ethyl-hexyl phosphoric acid (D2EHPA) as a mobile carrier has been studied. For those studies, different salts, i.e., NaCl, NaNO3, NaClO3, Na2SO4, and CH3COONa, have been used. A mathematical model for the dependency of separation factor of Cu(II) and Zn(II) on ionic strength considering Debye–Huckel theory and Bronsted–Bjerrum theory has been developed. Experiments were carried out using a batch-type permeator of micro-porous polypropylene thin sheet as the solid support for the liquid membrane in the presence of different ionic strength of anions. The calculated separation factor is well agreed with the obtained results within 95% confidence interval.

Thermodynamic Properties of Electrolyte Solutions, Derived from Fluctuation Correlations: A Methodological Review

This article presents a review of an approach for studying solution thermodynamics, which is based the on hydrodynamic fluctuation correlations analysis method suggested by Landau and Lifshitz. We show that the method is very general, and its applicability goes beyond hydrodynamics. It starts with examining the entropy production and fluctuating transport fluxes, which are related to concentration fluctuations and molecular interactions. The approach can be successfully applied to compute a wide range of thermodynamic properties such as the osmotic pressure (i.e., equation of state) and provides information about the interactions between the dissolved species. Using dilute electrolyte solutions as a case study, we reproduce results from the Debye and Huckel theory while starting from a very different physical perspective.

Electronic Properties of Aldehyde Complexes Using DFT for Electrooptical Activity

Characterization of materials infer for physical and chemical properties that depend on its molecular structure. Structure of molecule has its dependence on respective electrons of molecule under consideration occupying their positions that correspond to changes in density of electrons. Many theories of its kind were developed to study density of electrons with roots from wavefunction method and electron density method. Wavefunction method has its dependence with linear combination of atomic orbitals, Born approximation, variational principle ,potential energy surfaces for development of Huckel theory, Hartree fock self-consistent theory. Electron density method includes Ab-intio method and density functional theory is possible with Kohenberbg-Kohn existence theorem and Kohn Sham formalism. Density functional studies has diverted attention of researches for properties dependent on structure with use of quantum mechanical descriptors that influence chemical reactivity of molecule forming complexes with properties responsible for electrooptical activity. In the present work complexes with p-anisaldehyde were studied with set of anilines using Gaussian 16 package with B3LYP method. Studies in present work were analyzed from computed infrared spectra responsible for formation of complexes with shifts in wavenumbers; quantum mechanical descriptors for electronic properties. A feature of study is that complexes with p-nitroaniline have greater tendency influence on electronic properties responsible for electrooptical activity due to electrophilic nature.

Simulation of Carbon Nanotubes Using CNT Band Based on Extended Huckel Theory and Number of Pz Orbital theory to predict its density of state

Simulation of Carbon Nanotubes Using CNT Band Based on Extended Huckel Theory and Number of Pz Orbital theory to predict its density of state

A conversation on the quartic equation of the secular determinant of methylenecyclopropene

Abstract The Hückel method (HM) is based on quantum mechanics and it is used for calculating the energies of molecular orbitals of π electrons in conjugated systems. The HM involves the setting up of the secular determinant which is expanded to obtain a polynomial which is to be solved. In general, the polynomial is one which may be factorized. However, in May 2020, students brought to my attention that the secular determinant of methylenecyclopropene could not be factorized completely. As a result of this, we used a combination of online tools, technology and visualization to calculate the roots of the secular determinant. This write-up, in a playwriting format, describes the conversation between the facilitator and the students.

Analysis of Biphenylene and Benzo{3,4}cyclobuta{1,2-c}thiophene Molecular Orbital Structure using the Huckel Method

The Huckel method is an old fashion method to predict the molecular orbital and energies of  electrons in a conjugated molecule. Although Huckel`s theory`s approximations are relatively crude, its general results are still reasonable compared to the advanced computing method and experimental results for many molecules. This paper describes the Huckel calculation of biphenylene and benzo{3,4}cyclobuta{1,2-c}thiophene using the HuLis software. The benzo{3,4}cyclobuta{1,2-c}thiophene is a derivative of biphenylene, in which case one of the benzene rings is replaced by a thiophene ring. This change produces new electronic properties that are interesting to study. This work focused on calculating those molecules on energy levels diagrams, linear combination coefficient of molecular orbitals, molecular orbital shape, energy gap, resonance energy, bond-order, bond length, and charge distribution (π electron population). Besides, we calculate the harmonic oscillator measure of aromaticity (HOMA) parameter to study the Huckel method`s validity.

Color Energy of Some Cluster Graphs

Let $G$ be a simple connected graph. The energy of a graph $G$ is defined as sum of the absolute eigenvalues of an adjacency matrix of the graph $G$. It represents a proper generalization of a formula valid for the total $\pi$-electron energy of a conjugated hydrocarbon as calculated by the Huckel molecular orbital (HMO) method in quantum chemistry. A coloring of a graph $G$ is a coloring of its vertices such that no two adjacent vertices share the same color. The minimum number of colors needed for the coloring of a graph $G$ is called the chromatic number of $G$ and is denoted by $\chi(G)$. The color energy of a graph $G$ is defined as the sum of absolute values of the color eigenvalues of $G$. The graphs with large number of edges are referred as cluster graphs. Cluster graphs are graphs obtained from complete graphs by deleting few edges according to some criteria. It can be obtained on deleting some edges incident on a vertex, deletion of independent edges/triangles/cliques/path P3 etc. Bipartite cluster graphs are obtained by deleting few edges from complete bipartite graphs according to some rule. In this paper, the color energy of cluster graphs and bipartite cluster graphs are studied.

To inquire the effects of different geometric electrodes on current characteristics of C24 fullerene molecular junction.

Two different types of geometric electrode configurations were utilized to form C24 fullerene based molecular junction. The C24 molecule was intercalated in-between gold electrodes with two different shapes viz. knife edge and flat edge and the resultant molecular junctions (MJs) were simulated using nonequilibrium Green's function combined with semiempirical extended Huckel theory (EHT). Different transport parameters, namely projected device density of states, current-voltage curve, differential conductance curve, molecular orbitals, and transmission spectra were investigated at discrete bias voltages to gain insight about the various transport phenomena occurring in these molecular junctions. The results show that when the C24 fullerene is placed in between the flat-edged electrodes, current and conductance are higher in magnitude in comparison to the knife-edged configuration. These deductions give us a new perspective to design advanced molecular devices for electronics applications in the future.

Distribution of Electrons and Ions Near an Absorbing Spherical Body in a Nonequilibrium Plasma

The applicability of the collision kinetic model of point sinks, viz., the linearized theory of screening of the electric field produced by a charged dust particle, based on the Vlasov equations for electrons and ions in a nonequilibrium plasma, which are supplemented with collision terms in the Bhatnagar–Gross–Crook form and effective point sinks to dust particle, is analyzed. The criterion for the applicability of the collision kinetic model of point sinks is the smallness of the deviation of the electron and ion number densities near an absorbing spherical body from unperturbed values. The distributions of electron and ion number densities obtained using the collision kinetic model of point sinks and the orbit motion limited approach are compared. It is shown that the latter approach is applicable only in the low-pressure limit, and upon an increase in pressure, the Coulomb asymptotics of the potential, which is proportional to the frequency electron and ion collisions with neutral atoms (molecules), renders the orbit motion limited approach inapplicable for calculating the ion distribution. It is established that the domain of applicability of the collision kinetic model of point sinks is close to the applicability domain of the Debye–Huckel theory.

A Study on the Effect of Trust on the Delivery App. Service to Emotional & Rational Factor & User's Word of Mouth

The resonance parameter value between the saturated carbon and unsaturated carbon atom in cyclopentadiene has been evaluated. And then cyclopentadiene has been investigated on the correlations between it's electronic structures and reactivities by means of the extended Huckel method proposed by R. Hoffmann.

The Activity Coefficients of High-Charge Electrolytes in Aqueous Dilute Solutions

We examine in detail the activity coefficient of higher-charge electrolytes, which, in dilute solutions, can display negative deviations from the Debye–Huckel limiting law instead of the usual positive deviations typical of lower-charge electrolytes. This fact is of considerable relevance for scientists concerned with extrapolation to infinite dilution of thermodynamic and kinetic quantities. It is shown that this “strange” behavior originates merely from the electrostatic interactions between each ion and all other ions, with no necessity of hypothesizing the presence of chemical association; these negative deviations, indeed, are predicted even at the level of the “primitive model” (ions assumed as charged, unpolarizable, rigid spheres inside an unstructured, isotropic, dielectric fluid). Three different approximations for the behavior of the primitive model of low-charge and high-charge electrolytes are tested, in addition to the Debye–Huckel theory; i.e. IPBE (a numerical accurate integration of the Poisson–Boltzmann equation), the Mayer theory of the electrolytes in the so-called DHLL + B2 approximation, and the Bjerrum theory. In the Supporting Information, the fundamentals of the respective algorithms are reported, and the effects produced by the differences of size between cations and anions, are also examined.

Electrical doping in single walled carbon nanotube systems: A new technique

First report on electrically doped semiconducting carbon nanotube is presented using Extended Huckel Theory in combination with Non-equilibrium Green’s function formalism. The results show increase in current with the increasing electrical doping concentration. Electrical doping induces high charge concentration at small applied voltages and is far more superior because of its fault free approach overcoming the limitations of conventional doping. Furthermore, the device density of states confirms the sufficient number of peaks in the valence and conduction bands. The obtained results were compared with other theoretical results in the field in the form of a table. The results are very beneficial for the designing of high-performance CNT devices and enhancing their potential applications in the electronics industry.

Relationship of the Permittivity with the Activity Coefficients of Water and Ions in Aqueous Solutions of Lithium and Sodium Sulfates

The activity coefficients in aqueous solutions of lithium and sodium sulfates at 298 K were calculated by the generalized Debye–Huckel theory using the experimental values of the static permittivity of the solutions. The effect of the hydration and ion association on the dielectric and thermodynamic properties of the electrolyte solutions was considered.

Formation of Glycinate Complexes of Iron(II) in Solutions of Different Ionic Strengths

Processes of complexation in the Fe(0)–Fe(II)–glycine–Na(H)ClO4–H2O system at a temperature of 298.15 K, an ionic strength of solutions of 0.1–1.0 (NaClO4), СFe(II) = 1 × 10−3, and in the pH range of 0.8–8.0 are studied according to the Clark–Nikolsky oxidation potential. Experimental curves are obtained for the dependences of EMF on concentration, рН, pCFe(II), рСHL. Successive approximation of theoretical and experimental oxidative potential functions is used to calculate the constants of complexation. The dependence of the constant of complexation on the ionic strength of the solution is calculated on the basis of the Debye–Huckel theory. It is found that the formation constants of coordination compounds fall as the ionic strength of a solution rises.

Destructive-quantum-interference suppression in crown ether single molecule junction

The electronic transmission coefficient of X-crown ether-Y (X = 3Y ;Y = 4, 5, and 6) have been investigated using density functional theory and Green’s function approximation incorporated with the Huckel method. The results illustrate unexpected role of the oxygen atoms to highly enhance charge transport in the crown ether molecules by moving the destructive quantum interferences (QI) close to the Fermi level. Such slight shifting creates a beneficial peak-valley pattern in the transmission spectra that facilitates the ON/OFF variation. Moreover, the length of the crown ether rings offers an insignificant impact on electronic transmission. Hence, we believe that these findings would deepen our understanding of QI patterns and exploit crown ether molecules more practically and efficiently in molecular devices.