One-electron Wave Research Articles

Continuous approximation for linear combination coefficients: Exploring a neglected concept

An alternative approach is introduced for accurately describe atomic orbitals using an integral transform of Gaussian-type basis functions (GTO) combined with continuous and analytical weight functions. The functional form of these weight functions was optimized using the variational criterion, achieving μHartree-level precision in energy calculations for atoms, monovalent ions up to the third period of the periodic table, and the H2 molecule. However, errors increased for heavier atoms, such as sulfur and chlorine, indicating the need for further refinement of the weight functions. This approach enhances the accuracy of electronic structure calculations, offering a rigorous alternative for deriving one-electron wave functions from discrete basis sets and vice-versa for atoms and molecules.

Semiempirical molecular-orbital calculations of dissociation energies of small molecules containing light elements

A semiempirical molecular-orbital approach has been developed to calculate the dissociation energies of 57 second-row neutral and charged diatomic molecules. One-electron energies and wave functions were used. The 2s and 2p electrons have separate energies and separate values of Z 2S and Z 2P . Calculations were made with a CNDO/INDO FORTRAN programme modified to a level of approximation that is more similar to extended Hückel calculations than to either CNDO or INDO. The correlation between calculated and experimental dissociation energies was favourable with a relative standard deviation of 15%. Additionally, dipole moments for the molecules were calculated concurrently with the same parameters. The correlation between calculated and experimental dipole moments was favourable for seventeen molecules with a relative standard deviation of 19%. The correlation between calculated and experimental ionisation potentials for fourteen molecules was also favourable with a relative standard deviation of 11%. Also, a repulsion work function was formulated and used in this work between pairs of atoms. For 90% of the molecules studied, the maximum calculated dissociation energy occurred within ±0.1 Å of the experimental bond distance. The semiempirical methods used in the present work could be used for future studies of larger molecules, including organic molecules.

Квантовая проводимость в одиночных и связанных квантово-размерных частицах узкозонных полупроводников

An organo-modified ordered layered structure with three-dimensional close packing based on colloidal quantum-sized particles (QP) of InSb, PbS, CdSe semiconductors and Langmuir-Blodgett films has been fabricated and studied. According to the current-voltage characteristics (CVC) of single-electron transport in the model of a nanocell with a linear chain QP across the layers, the processes limiting conductivity were established: emission-injection tunneling from a probe into a nanoparticle, motion in a nanoparticle determined by the establishment of an electronic wave process in it, and tunneling through a nanogap between nanoparticles. Quasi-periodic oscillations of the current and resonant peaks of quantum conductivity are observed on the I–V characteristics, which were estimated in the quantum wire model. For an even number of layers (QP, 2, or 4), the I–V characteristics were used to determine the attenuation of size quantization and the decrease in current due to the weak interaction of nanoparticles. With an odd number (3 or 5), the nanochain acts as a single quantum thread with manifestations on the CVC similar to the cases of one QP. In this case, the motion of an electron can be considered as a one-electron charge wave.

Ab Initio Calculations of Transport and Optical Properties of Dense Zr Plasma Near Melting

The dynamic electrical conductivity of dense Zr plasma near melting is calculated using ab initio molecular dynamics and the Kubo–Greenwood formula. The antisymmetrization of the electronic wave function is considered with the determinant of one-electron wave functions; exchange and correlation effects are treated via an exchange–correlation functional. Optical properties are restored using the Kramers–Kronig transformation. The influence of computational parameters and inner shell electrons on the results is thoroughly investigated. We demonstrate the convergence of our computations and analyze comparison with experimental data.

Semiclassical theory of electronic states in multilayer semiconductors. Part 1

States of electrons in multilayer semiconductor structures are theoretically investigated in the semiclassical approximation, where one-electron wave functions of the stationary Schrödinger equation are calculated in the presence of various types of potential, which is a slowly varying function of the coordinate. It is determined that the energy spectrum of electrons in the potential in the quadratic approximation takes discrete values and the steepness of the energy spectrum depends on the parameters of the expansion of the potential in coordinates.

Effect of the Donor/Acceptor Size on the Rate of Photo-Induced Electron Transfer

The photo-induced electron transfer has been under intensive investigation for a few decades already, and a good understanding of the reaction was developed based on thorough study of the molecular donor–acceptor (DA) system. The recent shift to hybrid DA systems opens the question of transferring the knowledge to analyze and design these new materials. One of the apparent differences is the size increase of the donor or acceptor entities. The electronic wave functions of larger entities occupy a larger volume, but since these are still one-electron wave functions, their amplitudes are lower. A simple analysis proposed here demonstrates that this leads to roughly inverse third power dependence of the electron transfer rate constant on the donor or acceptor size, kET∝R−3. This dependence can be observed upon switching from molecular to quantum dot donor in DA systems with a fullerene acceptor.

Selectivity and efficiency of nitrite electroreduction catalyzed by a series of Keggin polyoxometalates

In this paper we have studied the influence of the charge and redox potential for a series of polyoxometalates (POMs) belonging to the Keggin family on the electrochemical reduction of nitrite or nitrous acid (NO2– or HNO2). We have focused on the correlation of gaseous products and the redox properties of the POMs. Analysis by differential electrochemical mass spectrometry (DEMS) showed that the gaseous products (NO and N2O) are formed at pH 2 and 5 by reaction of HNO2 or NO2– with the reduced POM. Only NO is detected when the POM ([PW12O40]3- , [SiW12O40]4-, [BW12O40]5-) undergoes the first one-electron reduction wave. However, N2O is obtained along with NO as soon as the POM undergoes two-electron reduction. The potential of the first reduction wave of the POM is correlated with its charge. Consequently NO and/or N2O appear at lower overpotential for [PW12O40]3- and [SiW12O40]4- followed by [BW12O40]5- and [H2W12O40]6-. Microkinetic simulations of the experimental current–potential curves were used to estimate the rate constant kc of the reaction between the reduced POM and HNO2 or NO2– in solution and the turnover frequency (TOF). At low overpotentials, the values of TOF are decreasing in a trend following the redox potential of the POM: [PW12O40]3- > [SiW12O40]4- > [BW12O40]5- while at high overpotentials the TOFs are dominated by kc following the reverse order. At pH 5 kc values are about 70 times lower than at pH 2. This is attributed to the decrease in the proton concentration and to the electrostatic repulsion between the negatively charged POMn- and NO2–.

Calculation of One-Electron Wave Functions and Energy Levels of N-Butane Molecule on the Basis of Slater Atomic Orbitals

Abstract It is known that the application of the group theory greatly simplifies the problems of polyatomic systems possessing to any space symmetry. The symmetry properties of such systems are their most important characteristics. In such systems, the Hamilton operator is invariant under unitary symmetry transformations and rearrangements of identical particles in the coordinate system. This allows to obtain information about the character of one-electron wave functions — molecular orbitals — the considered system, i.e. to symmetrise the original wave functions without solving the Schrödinger equation.

Analytical estimate of effective charge and ground-state energy of beryllium atom utilizing variational method

In this paper, we present an analytical procedure to determine the effective charge and ground-state energy of a four-electron beryllium atom. The procedure followed is based on a variant of variational technique using modified hydrogenic one-electron wave function to calculate effective charge in 1s and 2s states of beryllium atom. The effective charge in 1s state is 3.68609 and in 2s state is 1.82362. Further, we have used these values in non-relativistic Hamiltonian with interaction terms to calculate the ground-state energy of beryllium atom. The estimated value of ground-state energy (− 14.3423 au) is in good agreement with the experimental results and with other theoretically obtained values. The calculated results without using any computationally intensive technique are the essence of this research work.

Intersubband transitions in spherical quantum dot quantum well nanoparticle

In this paper, we present results about electronic spectra and optical properties of one-electron spherical quantum dot-quantum well (QDQW) structure. Investigated structure consists of CdSe core surrounded by ZnS shell and caped by infinitely high electron potential barrier which can be a good model for any high enough potential barriers. This specific QDQW structure is determined by CdSe and ZnS properties (effective masses and conductive band offset) and the core size and the shell thickness. We present calculation results for one-electron ground (1s) state and the first excited (1p) state transition. For this transition we have calculated oscillator strengths and linear and third-order nonlinear intersubband optical absorption coefficients for various core and shell size i.e. different CdSe core radii and ZnS barrier thickness. Change in core and shell dimensions induces change in one-electron wave function i.e. electron energy states and localization for both 1s and 1p states. As a result, intersubband 1s–1p transition of this system is greatly dependent on the core and shell size. For very small core radii, less than 0.7 nm, and core radii over 1.5 nm the most probable intersubband transition is 1s–1p, but in the region between 0.7 and 1.5 nm core radii, transitions from 1s to other p states dominates. Investigated properties depend mostly on the core radius. These results connect the dot structure and the optical properties of this particular structure. This behavior is than an illustration of similar systems.

Experimental, quantum computational study and in vitro antidiabetic activity of oxidovanadium(IV) complexes incorporating 2,2’-bis(pyridylmethyl)amine and polypyridyl ligands

This article describes synthesis and characterization of three oxidovanadium(IV) complexes using BPA (BPA = 2,2’-bis(pyridylmethyl)amine), 2,2-bipyridyl and 1,10-phenanthroline. These complexes were characterized by elemental analysis, spectroscopic (UV-vis, IR and EPR) and electrochemical methods. Room temperature magnetic susceptibility data show the paramagnetic nature of the complexes. Complexes were also characterized by electron paramagnetic resonance (EPR) spectral techniques. The optimized molecular structures show the presence of N3O3/N5O donor atoms in six-coordinate geometry. These complexes were evaluated and compared using thermogravimetric analysis and powder X-ray diffraction techniques. The species exhibit only one-electron reduction wave at a more negative potential. The catalytic activity of these complexes was also explored to mimic α-glucosidase and α-amylase activity. Moderate α-glucosidase and α-amylase inhibitors are shown by all complexes. These observations are expected to expand the possibility of designing new oxidovanadium(IV) complexes with significant anti-diabetic properties.

Effect of Distortions on the Geometric and Electronic Structures of One-Electron Oxidized Vanadium(IV), Copper(II), and Cobalt(II)/(III) Salen Complexes.

The ligands N,N'-bis(3-tert-butyl-5-methoxysalicylidene)-1,2-ethanediamine and N,N'-bis(3-tert-butyl-5-methoxysalicylidene)-1,3-propanediamine were chelated to V(IV)═O (1, 2), Cu(II) (3, 4), Co(II) (5), and Co(III) (6). The X-ray crystal structures of 1-6 were solved. The vanadium center in 1-2 resides in square pyramidal geometry, with an axially bound oxo ligand, whereas the metal ion displays a tetrahedrally distorted square planar geometry in 3-5. The extent of distortion is correlated to the length of the diamine spacer: The longer the linker, the larger the tetrahedral distortions. Complex 6 is octahedral with a bidentate acetate molecule that completes the coordination sphere. All the complexes were characterized by UV-vis and EPR spectroscopies, as well as DFT calculations and electrochemistry. Complexes 1-6 exhibit a reversible one-electron oxidation wave in the range -0.11-0.26 V vs Fc+/Fc. The cations 1+ and 2+ were structurally characterized, showing an octahedral V(V) ion with one oxo and one water molecule coordinated in axial positions. Their vis-NIR spectra are dominated by a band at 727 and 815 nm, respectively, which is assigned to a phenolate-to-vanadium(V) charge transfer (CT) transition. The crystal structures of 3+ and 4+ are congruent with Cu(II)-radical species, wherein the metal center remains four-coordinated. Both feature a Class II (Robin-Day classification scale) IVCT transition at around 1200 nm (ε > 1 mM cm-1), indicative of partial localization of the radical. The structure of 5+ displays a square pyramidal cobalt ion, where the fifth (axial) coordination is occupied by a water molecule. It displays a NIR feature at 1244 nm and is described as intermediate between high spin Co(III) and Co(II) radical. In the presence of acetate the dimer [(5)2(μ-OAc)]+ forms, which was structurally characterized and shows a blue shift and lowering in intensity of the NIR absorption band in comparison to 5+. Complex 6+ is a genuine Co(III) radical complex, wherein the phenoxyl moiety is localized on one side of the molecule.

A Ru-bda Complex with a Dangling Carboxylate Group: Synthesis and Electrochemical Properties.

Ruthenium complexes containing the tetradentate 2,2'-bipyridine-6,6'-dicarboxylato (bda2-) equatorial ligand and ortho-subsituted pyridines in the axial position have been prepared and characterized using spectroscopic, crystallographic and electrochemical techniques. Complexes [Ru(Hbda)(DMSO)(pyC)] (1) and [Ru(bda)(DMSO)(pyA)] (2) (where pyC is 2-pyridinecarboxylate, pyA is pyridine-2-ylmethanol and DMSO is dimethyl sulfoxide) have been isolated in moderate to high yields. The solid state structures of (1-H)- and 2 reveal the strong chelate effect of the axial pyridine ligand that coordinates in a bidentate fashion leaving the bda2- equatorial ligand coordinating in a tridentate mode. In solution, compound 2 shows a dynamic equilibrium between different coordination modes of the bda2- and pyA ligands. This phenomenon does not occur for 1 because the carboxylate binds stronger than the labile alcohol in 2. Cyclic voltammetry analysis of 1 reveals a complex behavior with a pH-independent wave at E1/2 = 1.12 V that is tentatively associated with the two-electron RuIV/II couple. In sharp contrast, complex 2 shows a pH-dependent one-electron wave at E1/2 = 0.83 V (pH 1), assigned to the proton-coupled electron transfer process of the RuIII/II couple and a pH-independent wave at E1/2 = 1.06 V assigned to the RuIV/III couple. Compound 2 is used to prepare complex [Ru(bda)(pic)(pyA)] (4). This complex is air sensitive and converts to complex [Ru(bda)(pic)(pyE)] (5) (where pyE is methyl 2-pyridine carboxylate) in the presence of methanol. This oxidation also occurs by applying a positive potential to an aqueous solution of 4, producing the derivative [Ru(bda)(pic)(pyC)] (3). Cyclic voltammetry of 3 shows two pH-independent one-electron oxidation waves at E1/2 = 0.64 V and E1/2 = 1.0 V, corresponding to the RuIII/II and RuIV/III couples, respectively. In addition, a water oxidation catalytic wave appears at Eonset ≈ 1.4 V. Foot-of-the-wave analysis of this catalytic wave based on a water nucleophilic attack accounts for a TOFmax = 0.63-0.74 s-1.

Redox-Active Glycol Nucleic Acid (GNA) Components: Synthesis and Properties of the Ferrocenyl-GNA Nucleoside, Phosphoramidite, and Semicanonical Dinucleoside Phosphate

Ferrocenylated glycol nucleic acid (Fc-GNA) components are rarely studied in the field of xeno nucleic acid (XNA) chemistry. As an attempt to contribute to XNA chemistry, in the present article we report a seven-step synthesis of the first semicanonical dinucleoside containing the Fc-GNA nucleoside linked to the adenosine nucleoside with a phosphodiester bond. First, the nucleoside-bearing ethynylferrocenyl moiety in the C5 position of the uracil nucleobase was obtained. In the following steps, the nucleoside was transformed into the phosphoramidite intermediate that in turn was reacted with N6-benzoyl-2′,3′-O-isopropylideneadenosine to afford the target dinucleoside phosphate with 47% yield. The newly obtained Fc-GNA nucleoside is redox-active, and on the basis of this property (function), it belongs to a new class of functional GNA (fun-GNA) nucleosides. The electrochemistry of the Fc-GNA nucleoside, dinucleoside phosphate, and ferrocenyl furanopyrimidone nucleoside that was obtained as an undesired byproduct of Fc-GNA nucleoside synthesis was investigated by cyclic voltammetry (CV). The CV result showed the presence of a one-electron ferrocenyl-centered redox wave in each case. The half-wave potentials of the Fc-GNA nucleoside and dinucleoside phosphate were 89 and 99 mV, respectively, against the FcH/FcH+ couple. Finally, the activity of the newly obtained Fc-GNA components was studied against the nontumorigenic mouse L929 and human cervix adenocarcinoma HeLa cells. The synthesized compounds showed no cytotoxic activity against the tested cell lines.

Highly conjugated donor-acceptor dyad based on monotetrathiafulvalene covalently attached to a magnesium norphthalocyanine unit

A novel highly conjugated donor–acceptor dyad composed of a tetrathiafulvalene (TTF) moiety covalently attached to a magnesium norphthalocyanine (NPc) unit (1) has been synthesized and full characterized. Ultraviolet–visible spectroscopy and electron paramagnetic resonance data reveal that 1 forms an electron transfer complex with 2,3,5,6-tetrafluoro-7,7,8,8-tetra-cyanoquinodimethane (F4TCNQ). Detailed electrochemical investigations show one irreversible one-electron oxidation wave, two quasi-reversible one-electron oxidation waves, and two irreversible one-electron reduction waves, indicating that 1 is a good π-electron donor. Compound 1 shows clear intramolecular charge transfer (ICT) interactions from the tetrathiafulvalene fragments to the norphthalocyanine core. This phenomenon can be explained by density functional theory (DFT).

Visualizing the 30-Dimensional Antisymmetrized Electronic Structure of Water: The Emergence of Lone Pairs.

The electronic structure of water is typically thought of as exhibiting lone pairs of electrons, described by some as "rabbit ears". This is not the universal view, and it does not mesh with an interpretation based on the one-electron wave functions that emerge from molecular orbital theory. Here, we show, by analyzing the 30-dimensional antisymmetrized wave function (Slater determinant) rather than the Hartree product, that the water wave function indeed exhibits equivalent lone pairs. The observed photoelectron spectrum is reconciled with this view, in terms of a relaxation of this structure upon the loss of an electron. Therefore, the lone-pair viewpoint is shown to be completely consistent with both the experimental results and the calculated wave function.

Impurity-modulated optical response of a disc-shaped quantum dot subjected to laser radiation

We report the optical properties of a laser-driven two-dimensional quantum dot with a hydrogenic impurity exposed to a magnetic field. The effective mass approximation is used to bring out the effect of an intense laser field, resulting in dressed Coulomb and confinement potentials, on the one-electron energy levels and wave functions. The results obtained suggest that the action of the laser field leads to crucial changes in the energy spectra of the system and the impurity binding energy. Furthermore, the position and the height of the resonant peaks of the absorption coefficients and refractive index changes depend strongly not only on the geometrical confinement strength but also on the magnetic field and laser radiation through the “laser-dressed” potential.

Bis(tetraphenylarsonium) hexafluoridotechnetate(IV) dihydrate: preparation, structure and spectroscopic analysis.

Reports of quadrivalent transition-metal fluoride salts containing bulky organic cations are limited. In this context, we prepared the bis(tetraphenylarsonium) hexafluoridotechnetate(IV) dihydrate salt, (C24H20As)2[TcF6]·2H2O, by a cation metathesis reaction of (NH4)2[TcF6] in water. This is the first report of an arsonium salt of the hexafluoridotechnetate(IV) dianion. (AsPh4)2[TcF6]·2H2O crystallizes in the triclinic space group P-1. The [TcF6]2- anion adopts a slightly distorted octahedral geometry with an average Tc-F bond length of 1.933 Å. The cyclic voltammogram of (AsPh4)2[TcF6]·2H2O in CH3CN shows a one-electron reversible oxidation wave at 1.496 V.

Assessment of the exact-exchange-only Kohn-Sham method for the calculation of band structures for transition metal oxide and metal halide perovskites

In the present paper we assess the performance of the exact-exchange-only (EXX) Kohn-Sham method to predict band structures of transition metal oxide and metal halide perovskites with the main emphasis on band gaps. For the considered set of prototypical systems with cubic structure, the performance of the EXX method for the prediction of band gaps is comparable with other popular methods for this purpose like density-functional calculations with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and one-shot $GW$ (${G}_{0}{W}_{0}$). Comparison with experimental values suggests that in the case of perovskites the EXX method, like HSE and $GW$ methods, should be supplemented by a treatment of electron-phonon effects. The EXX method is computationally more efficient than ${G}_{0}{W}_{0}$ and also provides post-self-consistent access to one-electron wave functions and band structures within the complete Brillouin zone with much lower computational effort than both ${G}_{0}{W}_{0}$ and hybrid DFT methods. We confirm the importance of including the higher-lying semicore shells within the explicitly treated states for halide perovskites which was already noted by earlier studies. Calculations taking into account only the valence space without the semicore states, however, remain still a reasonable option in practice. Spin-orbit coupling effects seem to be slightly underestimated in DFT calculations both with respect to $GW$ and experiment. The source of this underestimation can be of both technical and formal nature, and this point requires more critical consideration. For ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$, sizable Rashba spin splittings appear for the structure with the C-N bond of the methylammonium ion not lying along the long diagonal of the cubic unit cell.

Photoionization of Endohedrals with Account of Fullerenes Polarization

We have calculated photoionization cross-section of endohedral atoms A@CN. We took into account the polarizability of the fullerene electron shell CN that modifies the incoming photon beam and the one-electron wave functions of the caged atom A. We employ simplified versions of both static and dynamic polarization. The properly modified one-electron wave functions became a starting point of the account of the multi-electron correlations in the frame of the random phase approximation with exchange (RPAE). We treat atomic and fullerenes polarization that act upon photoelectron similarly, substituting them by static polarization potential. The photon beam polarizes the fullerene. This effect is accounted for introducing a polarization factor. As concrete objects, we have considered Ar and Xe atoms inside fullerene C60. Inclusion of polarization prominently increases the photoionization cross-section mainly close to the threshold.