External Point Charge Research Articles

Quantum microscopic vs. classical macroscopic calculations on the phenomenon of electrostatic influence

In order to compare microscopic and macroscopic approaches to the phenomenon of electrostatic influence, we have studied the atomic charges of an electric conductor, obtained either from macroscopic classical electrostatics, or microscopic quantum ab initio calculations. A torus was chosen as conducting material, built from valence monoelectronic atoms and influenced by an external point charge. The classical electric charges are obtained by integrating the macroscopic density over “atomic" sectors. This density is determined from a numerical integration of linearized electrostatic equations. The quantum charges are defined from Natural Orbitals in MP2/6-31G* calculations on clusters of different sizes. The overall agreement is good, with reasonable discrepancies due (i) to the continuity of the macroscopic model, which ignores the oscillations on atomic distances; and (ii) to the linearity constraint in the macroscopic equations.

Electric potential due to an infinite conducting cylinder with internal or external point charge

We utilize the Green's function method in order to calculate the electric potential due to an infinite conducting cylinder held at zero potential and a point charge inside and outside it. We calculate and plot the net force upon the point charge as a function of its distance to the axis of the cylinder. We show that this force goes to zero when the radius of the cylinder goes to zero, no matter the distance of the external point charge to the conducting line.

Nonlinear screening and stopping power in two-dimensional electron gases

We have used density-functional theory to study the nonlinear screening properties of a two-dimensional (2D) electron gas. In particular, we consider the screening of an external static point charge of magnitude $Z$ as a function of the distance of the charge from the plane of the gas. The self-consistent screening potentials are then used to determine the 2D stopping power in the low-velocity limit based on the momentum transfer cross section. Calculations as a function of $Z$ establish the limits of validity of linear and quadratic response theory calculations, and show that nonlinear screening theory already provides significant corrections in the case of protons. In contrast to the 3D situation, we find that the nonlinearly screened potential supports a bound state even in the high-density limit. This behavior is elucidated with the derivation of a high-density screening theorem which proves that the screening charge can be calculated perturbatively in the high-density limit for arbitrary dimensions. However, the theorem has particularly interesting implications in 2D where, contrary to expectations, we find that perturbation theory remains valid even when the perturbing potential supports bound states.

Ramo-Shockley relation for a series RCL circuit

The current induced by the passage of an external point charge through a plane vacuum capacitor in an RCL circuit free of current (voltage) sources is calculated. The case is also analyzed when an internal point charge is emitted by one of the capacitor plates, moves to the other plate, and is absorbed by it. A technique is proposed to measure the internal charge and its velocity component perpendicular to the capacitor plates in a passive RCL circuit.

Finite-Size Effect and Wall Polarization in a Carbon Nanotube Channel

The electronic structure and dielectric screening of finite-length armchair carbon nanotubes are studied in view of their technical applications. For this purpose, a self-consistent tight-binding method, which captures the periodic oscillation pattern of the finite band gap as a function of tube length, is applied. We find the parallel screening constant E| to grow nearly linearly with the length L and to show little dependence on the band gap. In contrast, the perpendicular screening constant E┴ is strongly related to the band gap and converges for L >1 0 R (radius) to its bulk value. Our description is employed to study the wall polarization in a short (6,6) nanotube filled with six water molecules, a situation that arises with technical uses of carbon nanotubes as channels. Single-walled carbon nanotubes (SWNTs) can be classified as metallic, quasi-metallic, or semiconducting, depending on how they are wrapped up from graphene layers. 1 When SWNTs are shortened, their energy levels become quantized, which makes them suitable for applications such as quantum dots and single-electron transistors. 2 It has also been proposed that the small size and stable structure make short SWNTs good candidates for artificial nanoscale channels for transport of water, 3-6 protons, 7,8 ions, 9 or polymers. 10 Recent experiments using X-ray diffraction 11 and neutron scattering 12 provided insight into the properties of nanotube-confined water. The observations revealed a chain of water molecules wrapped by a shell of water, all encapsulated inside SWNTs with diameter around 1.4 nm. 12 These experiments confirm an earlier prediction that water can enter the hydrophobic interior of narrow SWNTs. 3-6 From the modeling point of view, artificial SWNT channels have been studied by means of molecular dynamics (MD) simulations, focusing on both filling and transport properties. 3-6 In the previous simulations, the interaction between water and the SWNT was usually treated through a short-range van der Waals potential, and little attention was paid to the polarizable nature of the SWNT. Unlike many biological channels, SWNTs are highly polarizable due to their delocalized ﷿-electrons, which respond strongly to external fields. A study of screening effects of infinitely long SWNTs to an external point charge impurity has revealed that metallic nanotubes can effectively screen out the longrange Coulomb potential along the axial direction, while screening effects in semiconducting tubes are weaker. 13 Neglecting the polarization of SWNTs could be misleading because the filling and transport properties of water are sensitive to the water-SWNT interaction. 3 Therefore, knowl

Modeling Fermi Level Effects in Atomistic Simulations

AbstractIn this work, variations in electron potential are incorporated into a Kinetic Lattice Monte Carlo (KLMC) simulator and applied to dopant diffusion in silicon. To account for the effect of dopants, the charge redistribution induced by an external point charge immersed in an electron (hole) sea is solved numerically using the quantum perturbation method. The local carrier concentrations are then determined by summing contributions from all ionized dopant atoms and charged point defects, from which the Fermi level of the system is derived by the Boltzmann equation. KLMC simulations with incorporated Fermi level effects are demonstrated for charged point defect concentration as a function of Fermi level, coupled diffusion phenomenon and field effect on doping fluctuations.

Surface response of a conductor: static and dynamic, electric and magnetic

The response of a flat metal surface to an external point charge or monopole moving parallel to it is analyzed for a variety of cases. The same basic formalism of matching partial wave expansions is used for each case with slight adaptations in order to emphasize the common physics as one determines the induced forces. The point disturbance is either stationary or moving at constant speed (and height) or suddenly appearing. The metal’s response is first treated via electrostatics and then generalized to electrodynamics. The influence of the metal’s thickness is studied in separate calculations wherein it ranges from semi-infinite down to much less than the penetration depth of the induced fields. The latter limit allows considerable analytic progress and an alternate description in terms of receding images.

Screening of a point charge by an anisotropic medium: Anamorphoses in the method of images

We extend the classical dielectric image problem for an external point charge interacting with a semi-infinite medium to the case of an anisotropic dielectric. We show that the exterior potential is a solution to an unconventional image problem. By contrast the interior potential is not a solution to any simple image system; instead it can be obtained through an anamorphic transformation of an image solution. We calculate the volume bound charge density that is induced within the anisotropic dielectric and distinguishes it from an isotropic medium where the volume density vanishes. This solution provides a very simple and physically relevant example in which the physics of the surface and volume bound charge densities in a polarized dielectric can be analyzed.

Image charges revisited: Beyond classical electrostatics

The method of images in electrostatics seems to lead to a paradox: The charges induced on the surface of a grounded conductor by an external point charge do not spread out although the electrostatic field is normal to the surface. This effect can be understood if one takes into account the spreading of the charges inside the conductor due to the kinetic energy (either thermal or quantum mechanical) of the electrons. Corrections to the usual electrostatics of images are then calculated (in particular, it is shown that the conductor surface is not an exact equipotential) when the distance of the point charge to the surface is much larger than the screening length. Applications are discussed.

Modeling of Adsorption Properties of Zeolites: Correlation with the Structure

The adsorption of N2 and CO in Na X-zeolites has been studied for different framework structures and extraframework cation distributions. To this aim, the cation-molecule system modeling one site has been embedded in a set of external point charges which simulate the zeolite environment of the site and has been treated quantum chemically, using a method based on density functional theory. This procedure has been applied to the 64 cationic sites accessible for adsorption in a crystal unit cell of an ideal X-zeolite with a Si/Al ratio equal to 1. These calculations have shown that only a few cations are favorable for initial adsorption and that those cations are always of type III(III ′). Their efficiency depends both on the framework geometry and on their location in the supercages. The analysis of the quantum chemical results in terms of a classical description involving electrostatic and induction interaction energies with the framework has led to the conclusion that the direction of the electric field vector created by the zeolite in the supercages is an important factor determining the zeolite adsorption properties. Zeolites are aluminosilicate materials that are widely used for size and shape catalysis, hydrocarbon conversion, and sorbing processes. Their physicochemical properties are based on the ability of these open crystalline structures to enclose charged and neutral species within cavities. Their properties are thus strongly related to the structure of the framework and also to the distribution among cages and channels of the cations that are associated with the Al centers. Indeed, those extraframework cations are the active sites for adsorption processes, whereas their neighboring oxygens are involved in base catalysis. Adsorption and desorption studies of small probe molecules like N2 and CO are used to provide information about cations and basic sites. Those experiments show that the adsorption of molecules within the cages varies with the number and nature of occupied cationic sites. 1-3 However, there is presently no real understanding of how adsorption properties of zeolites depend on the cation distribution. The major difficulty encountered in the study of such a correlation arises from the incomplete information provided by experimental structure determinations about cationic sites. First, very few structures are known for low-silica zeolites, i.e. for those including a large number of cations. 4 Moreover, the studies concerned with zeolites containing a single type of cations are even more scarce, due to the difficulty of full cationic exchange. Crystal and powder structure determinations provide positions for the cations associated with the probabilities of occupying the various sites, which, very often, do not sum up to the total number of cations. Cation positions vary also with their chemical nature and with the extent of dehydration. Lithium cations are hardly detectable by X-ray diffraction, and sodium cations may not be well differentiated from water molecules. Finally, experimental conditions of preparation and dehydration may induce differences in the solids, leading to different structures and thus different adsorption properties. For all these reasons, we think that modeling may be an appropriate tool to analyze the relations between adsorption properties and zeolite structures. Although a large variety of modeling techniques have already been used for the prediction and analysis of zeolite structures and properties, only a very few studies have been devoted to systems including cations other than protons. During the last decade, the main effort has been devoted to H-zeolites, mainly due to their widespread applications in acid catalysis. 5-7 Only recently have some dynamical studies of Na and Ca A-zeolite, 8-10 Na Y-zeolite, 11 and Na and K offretite 12 proposed detailed structures including cation positions. In recent papers, we have shown that the nature of the cation and its location in the framework are essential factors for N2 and O2 adsorption. 13,14 In these studies, it was shown that short-range interactions between incoming molecules and

Molecular-orbital study of Li and LiOH adsorption on a Cu(001) surface. II. Cluster-model calculations with image charges

Hartree-Fock and configuration-interaction calculations were performed for ${\mathrm{Cu}}_{4}$ Li and ${\mathrm{Cu}}_{4}$ LiOH, as models of Li/Cu(001) and LiOH/Cu(001), respectively. To take into account the dielectric-response effect of the metal surface to external point charges, we used cluster models with image charges. For ${\mathrm{Cu}}_{4}$ Li, the calculated vibrational frequency was almost the same as that given by a cluster model without image charges, and both values agreed well with the experimental value. Image charges improved the Li-OH vibrational frequency for ${\mathrm{Cu}}_{4}$ LiOH. On the other hand, simple cluster calculations without image charges gave poor results for work-function changes upon Li and LiOH adsorption; however, by considering image charges, we obtained excellent results, were comparable to the observed values.

Density functional study of the relationship between energy, hardness, and polarizability of molecules in nonequilibrium situations

We have studied the variation of hardness, polarizability, and electronic and nuclear repulsion energy components of molecules in different nonequilibrium situations obtained by bond distortion and also by placing external point charges on the symmetry axis of the molecules. The above quantities are calculated through Kohn-Sham version of spin-polarized density functional theory with nonlocal exchange correlation functional. Interesting correlations have been found to exist between different energy components, hardness, and polarizability. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 917–926, 1997

Electrostatic problem of a point charge in the presence of a semi-infinite semiconductor

The space-charge region that is induced in a semiconductor half-space by an external point charge is analyzed. The mathematical model gives rise to a free-boundary problem, since the edge of the space-charge region [a surface z=z(d) in cylindrical coordinates] is unknown. From the formal solution of Poisson’s equation, an integral equation for z(d) is derived and approximately solved. The solution describes the depletion region in dependence of the magnitude of the point charge, the charge-semiconductor distance, and the doping and dielectric constant of the semiconductor. Approximate expressions are derived for the force acting on the point charge and are used to estimate the electrostatic force between the tip and a silicon sample in a scanning force microscope. The limitations of the model are discussed and its generalization to the case of a semiconductor coated by a dielectric film is outlined.

The interaction of a point charge with a metal surface: theory and calculations for (111), (100) and (110) aluminium surfaces

The asymptotic form of the image interaction is derived for a classical external point charge at a distance z1 outside a periodic metallic surface, generalizing to real metals the analytical result of Lang and Kohn (1973) for jellium. The centre of gravity zc of the induced charge coincides with the position of the image plane z0 in the limit of linear response. However, whereas zc is shown to depend through non-linear response on the magnitude of the external charge q, z0 is independent of q. We show that surface periodicity does not modulate z0, but adds to the image interaction a periodic component decaying exponentially with z. In addition, the long-ranged effect of non-linearity on the interaction energy is a term attractive to a positive external charge and proportional to q3/(z1-z0)4. We report first-principles pseudopotential calculations of the interaction energy with three aluminium surfaces: (111), (100) and (110). A supercell geometry is used. A discrete classical model without adjustable parameters reproduces the effect of the surface periodicity on the image interaction at each of the three surfaces.

Nonlinear hydrodynamic theory of electronic stopping power

We have formulated a fully nonlinear hydrodynamic theory of the electronic stopping power of charged particles in matter. In the zero velocity limit, our theory reduces to a Thomas-Fermi-Dirac-von Weiszäcker description of the electronic screening around an external point charge. With increasing velocity, the dynamic screening charge is obtained from a numerical solution of the hydrodynamic equations. We also introduce a fluid viscosity which allows one to simulate the single-particle excitations responsible for the low velocity stopping power. A comparison of our results for protons and antiprotons with linear response theory shows that nonlinearities in the screening are important for all velocities up to the stopping power maximum. In addition, comparison with earlier nonlinear quantum-mechanical calculations at low velocities shows that the hydrodynamic theory provides a realistic and accurate description of the stopping power phenomenon.

A variational approach to charged polymer chains: Polymer mediated interactions

A variational approach, based on a quadratic trial Hamiltonian is used to determine the configurational as well as the mechanical properties of a system composed of two point charges plus a neutralizing charged polymer, considered as a model of polyelectrolyte–macroion interactions. The quadratic variational ansatz used in the context of charged polymers presents a variant of the Feynman–Kleinert approach properly generalized to include polymer self-interactions. Conditions for chain localization in the field of a point charge are derived and its consequences for polymer-mediated forces between two point charges are analyzed. It is established that in three dimensions the polymer can confer long range attraction to nominally equally charged point ions. At small separations, the polymer mediated force is elastic in origin, stemming from the soft electrostatic anchoring of the chain to both point charges, but with a force constant much stronger than expected from entropic elasticity alone. At large separations, the polymer mediated interactions are of long range and are due to polymer-induced charge reversal on one of the external point charges.

Applicability of the Marcus equation to proton transfer in symmetric and unsymmetric systems

The Marcus equation was tested, within the framework of ab initio calculations, in the simple proton transfer reaction within the pre-existing hydrogen bonds of complexes containing water and formic acid. Asymmetry was introduced into the transfer potential of (H 2O·H·OH 2) + by addition of multiple external ions (e.g. Na +, Cl − and Li +) and point charges or dipoles. The Marcus equation predicts transfer barriers in excellent agreement with quantum calculations, as is also true when the ion approaches the otherwise symmetric protonated formic acid dimer. The situation is less favorable when an external ion introduces a perturbation into an intrinsically asymmetric transfer potential, as in the proton-bound dimer pairing a water with a formic acid molecule. Excellent predictions are obtained when the asymmetry parameter is taken as the effect of the ion itself, damped by a factor of two.

RING OXIDIZED RETINALS FORM UNUSUAL BACTERIORHODOPSIN ANALOGUE PIGMENTS*

Three ring oxidized retinal analogues have been isolated from the exhaustive oxidation of all-trans retinal. All-trans 4-oxoretinal and 2,3-dehydro-4-oxoretinal have similar absorption maxima to that of all-trans retinal and have been shown to be in the 6-s-cis conformation in solution. Pigments formed with bacterioopsin exhibit absorption maxima (520 nm) blue-shifted from that of bacteriorhodopsin (bR), indicating a disturbance of the external point charge by the electronegative carbonyl moiety at the 4 position. The third analogue contains a ring contracted to a cyclopentenyl-alpha,beta-dione. Unlike the majority of retinals, this analogue displays a 6-s-trans conformation in solution and has a red-shifted absorption maximum at 435 nm. The resulting bR analogue pigment (515 nm) is formed five times faster than the other oxoretinal pigments. All three oxoretinal pigments show an irreversible 20 nm blue shift upon exposure to white light. The 4-oxo and 2,3-dehydro-4-oxoretinal pigments, after irradiation, undergo a small reversible blue shift (4-8 nm) on dark adaptation. These two pigments pump protons, although with slowed photocycle kinetics, demonstrating that these structural changes (addition of the carbonyl at the C-4 and insertion of a double bond in the ring) do not block the function of the pigment. Extraction of the C-15 tritiated analogue retinals from illuminated and non-illuminated pigments of all three oxoretinals yield identical results. Therefore, any crosslinking of these oxoretinals to the protein is by linkages which are unstable to the extraction procedures.

Theoretical study of alkali-metal-atom adsorption on transition-metal surfaces by a cluster approach: Finite-size effects.

Finite-size effects in the adsorption energy of alkali-metal atoms on transition-metal surfaces, calculated from a clusterlike model, are investigated. In a first step, the interaction of an external point charge with a metallic cluster of finite size is examined. The link with the usual imagelike behavior for the charge-metal interaction is made. It is shown that one must define a corrected interaction energy by removing a part of the interaction due to the variation of the Fermi level with respect to the value of the external charge. Then, when the external charge is sufficiently far from the metallic cluster, this charge-cluster-corrected interaction presents the usual imagelike behavior for the extended surface, multiplied by a factor which depends on the size of the cluster. From these results, a method to calculate the adsorption energy for alkali-metal atoms on transition-metal surfaces by using a cluster model for the metal surface is proposed. The induced dipole moment, which is related to the work-function change with adsorption at low coverge, is also examined. An application is done for K adsorbed on Pd.

String model for the rate constant of nonadiabatic solvation in the hydration reaction of carbon dioxide

AbstractPerturbation theory for the rate constant of nonadiabatic solvation is presented. Miller's treatment of the RRKM theory is used for the unperturbed rate constant, and thereby the “string model” of chemical reaction is used for the description of the perturbation of solvation. The reaction path under the influence of the external force field is defined as the intrinsic reaction coordinate (IRC) that is treated as a string. The string is thrown in the external static force field that acts as a nonadiabatic source of perturbation. As an application of the present treatment, the effect of the external point charge for hydration reaction of CO2 is calculated as a preliminary model for catalytic activity of the carbonic anhydrase in the tissues and lung capillary vessels.