Electrostatic Potential Gradient Research Articles

Auxiliary functions for molecular integrals with Slater-type orbitals. II. Gauss transform methods

The Gauss transform of Slater-type orbitals is used to express several types of molecular integrals involving these functions in terms of simple auxiliary functions. After reviewing this transform and the way it can be combined with the shift operator technique, a master formula for overlap integrals is derived and used to obtain multipolar moments associated to fragments of two-center distributions and overlaps of derivatives of Slater functions. Moreover, it is proved that integrals involving two-center distributions and irregular harmonics placed at arbitrary points (which determine the electrostatic potential, field and field gradient, as well as higher order derivatives of the potential) can be expressed in terms of auxiliary functions of the same type as those appearing in the overlap. The recurrence relations and series expansions of these functions are thoroughly studied, and algorithms for their calculation are presented. The usefulness and efficiency of this procedure are tested by developing two independent codes: one for the derivatives of the overlap integrals with respect to the centers of the functions, and another for derivatives of the potential (electrostatic field, field gradient, and so forth) at arbitrary points. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model

Accurate, yet simple and efficient, formulae are presented for calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) from the aspherical Hansen-Coppens pseudoatom model of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909-921]. They are based on the expansion of |r' - r|(-1) in spherical harmonics and the incomplete gamma function for a Slater-type function of the form R(l)(r) = r(n) exp(-alpha ). The formulae are valid for 0 < or = r < or = infinity and are easily extended to higher values of l. Special treatment of integrals is needed only for functions with n = l and n = l + 1 at r = 0. The method is tested using theoretical pseudoatom parameters of the formamide molecule obtained via reciprocal-space fitting of PBE/6-31G** densities and experimental X-ray data of Fe(CO)(5). The ESP, EF and EFG values at the nuclear positions in formamide are in very good agreement with those directly evaluated from density-functional PBE calculations with 6-31G**, aug-cc-pVDZ and aug-cc-pVTZ basis sets. The small observed discrepancies are attributed to the different behavior of Gaussian- and Slater-type functions near the nuclei and to imperfections of the reciprocal-space fit. An EF map is displayed which allows useful visualization of the lattice EF effects in the crystal structure of formamide. Analysis of experimental 100 K X-ray data of Fe(CO)(5) yields the value of the nuclear quadrupole moment Q((57)Fe(m)) = 0.12 x 10(-28) m(2) after taking into account Sternheimer shielding/antishielding effects of the core. This value is in excellent agreement with that reported by Su & Coppens [Acta Cryst. (1996), A52, 748-756] but slightly smaller than the generally accepted value of 0.16 +/- 5% x 10(-28) m(2) obtained from combined theoretical/spectroscopic studies [Dufek, Blaha & Schwarz (1995). Phys. Rev. Lett. 25, 3545-3548].

Transport in polymer-gel composites: theoretical methodology and response to an electric field

A theoretical model of electromigrative, diffusive and convectivetransport polymer-gel composites is presented. Bulk properties are derived from the standard electrokinetic model with an impenetrable charged sphere embedded in an electrolyte-saturated Brinkman medium. Because the microstructure can be carefully controlled, these materials are promising candidates for enhanced gel-electrophoresis, chemical sensing, drug delivery, and microfluidic pumping technologies. The methodology provides `exact' solutions for situations where perturbations from equilibrium are induced by gradients of electrostatic potential, concentration and pressure. While the volume fraction of the inclusions should be small, Maxwell's well-known theory of conduction suggests that the theory may also be accurate at moderate volume fractions. In this work, the model is used to compute ion fluxes, electrical current density, and convective flow induced by an applied electric field. The electric-field-induced (electro-osmotic) flow is a sensitive indicator of the inclusion zeta-potential and size, electrolyte concentration, and Darcy permeability of the gel, while the electrical conductivity increment is most often independent of the polymer gel, and is much less sensitive to particle and electrolyte characteristics.

Auxiliary functions for molecular integrals with Slater‐type orbitals. I. Translation methods

AbstractMany types of molecular integrals involving Slater functions can be expressed, with the ζ‐function method in terms of sets of one‐dimensional auxiliary integrals whose integrands contain two‐range functions. After reviewing the properties of these functions (including recurrence relations, derivatives, integral representations, and series expansions), we carry out a detailed study of the auxiliary integrals aimed to facilitate both the formal and computational applications of the ζ‐function method. The usefulness of this study in formal applications is illustrated with an example. The high performance in numerical applications is proved by the development of a very efficient program for the calculation of two‐center integrals with Slater functions corresponding to electrostatic potential, electric field, and electric field gradient. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Gyroresonant Surfing Acceleration

We discuss a new acceleration or energization mechanism of charged particles in space and astrophysical plasmas. In the presence of an electrostatic potential gradient and a circularly polarized electromagnetic monochromatic wave, particles are accelerated efficiently by keeping cyclotron resonance with the wave due to the electrostatic dragging force. In addition, particles can propagate against the electrostatic potential even if they have smaller parallel energy. This mechanism is potentially widely applicable, in terms of particle acceleration and transport, to various space and astrophysical phenomena, such as shock environment and short-large amplitude magnetic structures. We introduce the basic physical process of the acceleration or energization mechanism theoretically and numerically.

Cantilever effects on electrostatic force gradient microscopy

The effects of the cantilever on electrostatic force microscopy are discussed. Numerical calculations of the electrostatic potential distribution and force gradient for typical experimental geometries are presented. A simple analytical relation between the calculated force gradients with and without cantilever is found. The main effect of the cantilever is to reduce the electric field in the tip–sample gap and, as a consequence, the force gradient can be strongly reduced. This effect can be very important for dielectric films while it can be neglected for metallic samples.

Electrostatic vortices associated with ion-temperature-gradient driven drift modes in electron-positron-ion plasmas

A set of nonlinear equations governing the dynamics of low-frequency electrostatic waves in the presence of equilibrium density, temperature, magnetic field and electrostatic potential gradients has been derived. In the linear limit, it is shown that nonzero equilibrium ion-temperature-gradient and the presence of positrons modify the basic drift modes. On the other hand, in the nonlinear case, it is shown that under certain conditions possible stationary solutions of the same set of nonlinear equations are reduced in the form of various types of vortex patterns. The results of the present investigation should be useful to understand the wave phenomena in laboratory and astrophysical e-p-i plasmas.

Transport of multicomponent ionic solutions in membrane systems

In this paper a set of phenomenological equations are derived for the transport of ionic solution and ionic species in a multicomponent solution through a membrane. The present study shows that, in addition to the conventional hydrostatic and osmotic pressures, there is an additional driving force generated by the gradient of electrostatic potential which is caused due to different ionic species having different membrane coefficients. This electrical potential gradient vanishes when the membrane coefficients for each species are identical.

Molecular dynamics simulation studies of the transport and adsorption of a charged macromolecule onto a charged adsorbent solid surface immersed in an electrolytic solution.

Molecular dynamics simulations were performed in order to study the transport and adsorption of a charged macromolecule (desmopressin) onto a charged solid surface in an electrolytic solution. The strong Coulombic interaction from the charged solid surface represents the major force for accelerating, orienting, entrapping in the electrical double layer, and adsorbing the macromolecule onto the charged solid surface. The macromolecule is flattened as it approaches the charged surface, giving rise to a stronger surface exclusion effect that shields surface sites. When adsorbed, the macromolecule is restrained by a surface interaction more than one hundred times stronger than the thermal energy, of which 99.8% results from the strong dominant Coulombic interaction, and trapped by a hydration layer adjacent to the surface. This leads to zero lateral displacement of the adsorbed macromolecule and indicates that surface diffusion is a physically implausible mechanism in similar systems. Explicit solvent is required for realistic representation of the macromolecular structure and the surface interaction energy. The adsorbed macromolecule also decreased the electrostatic potential gradient perpendicular to the charged solid surface and introduced additional electrostatic potential gradients laterally. The results obtained from the molecular dynamics simulations confirm the importance of electrophoretic migration and support the physical mechanisms used in a macroscopic continuum model that predicts an overshoot in the concentration of a charged macromolecule in the adsorbed phase under certain conditions of pH and ionic strength.

Formation of quadrupolar vortices in ion-temperature-gradient modes

Nonlinear equations which govern the dynamics of low-frequency (ω≪ωci), ion-temperature gradient modes in the presence of equilibrium density, temperature, magnetic field, and electrostatic potential gradients are derived. For some specific profiles of the equilibrium flow velocity, number density, temperature, and magnetic field, new type of solutions in the form of quadrupole vortices are found for a nondissipative plasma. The results can have relevance to the understanding of the salient features of anomalous ion thermal transport and coherent vortex structure formation in magnetically confined plasmas, such as in tokamaks.

Bohm's particle on an interatomic surface: a brief note

In preceding work (Phys. Lett. A 286 (2001) 61; Europhys. Lett. 57 (2002) 20) we investigated the statistical meaning of Bader's interatomic surface under different Thomas–Fermi levels of approximation. In particular within Thomas–Fermi–Dirac–Weizsacker model we showed that at an interatomic surface, as defined by Bader, the normal component of the gradient of electrostatic plus Bohm's potential is equal to zero (Eur. Phys. Lett. 57 (2002) 20). In this communication we show the consequences of this result in terms of single quantum particle trajectory. The results show that Bader's surface is a surface of statistical equilibrium. Although in our preceding work we have already shown that the interatomic surface expresses equilibrium between statistical subsystems, the procedure adopted here considers electrons as explicit quantum particles with associated wavefunction, thus directly connects the quantum nature of the single particle with the statistical properties of the whole system. This picture is indeed very interesting since provide, within the framework of Bader's theory, an intriguing link between the quantum behavior of single particles, the statistical properties of the system they belong to and the chemical idea of atoms.

Structural basis of polyamine-DNA recognition: spermidine and spermine interactions with genomic B-DNAs of different GC content probed by Raman spectroscopy.

Four genomic DNAs of differing GC content (Micrococcus luteus, 72% GC; Escherichia coli, 50% GC; calf thymus, 42% GC; Clostridium perfringens, 27% GC) have been employed as targets of interaction by the cationic polyamines spermidine ([H(3)N(CH(2))(3)NH(2)(CH(2))(4)NH(3)](3+)) and spermine ([(CH(2))(4)(NH(2)(CH(2))(3)NH(3))(2)](4+)). In solutions containing 60 mM DNA phosphate (approximately 20 mg DNA/ml) and either 1, 5 or 60 mM polyamine, only Raman bands associated with the phosphates exhibit large spectral changes, demonstrating that B-DNA phosphates are the primary targets of interaction. Phosphate perturbations, which are independent of base composition, are consistent with a model of non-specific cation binding in which delocalized polyamines diffuse along DNA while confined by the strong electrostatic potential gradient perpendicular to the helix axis. This finding provides experimental support for models in which polyamine-induced DNA condensation is driven by non-specific electrostatic binding. The Raman spectra also demonstrate that major groove sites (guanine N7 and thymine C5H(3)) are less affected than phosphates by polyamine-DNA interactions. Modest dependence of polyamine binding on genome base composition suggests that sequence context plays only a secondary role in recognition. Importantly, the results demonstrate that polyamine binding has a negligible effect on the native B-form secondary structure. The capability of spermidine or spermine to bind and condense genomic B-DNA without disrupting the native structure must be taken into account when considering DNA organization within bacterial nucleoids or cell nuclei.

Purification, characterization and molecular modelling of two toxin-like proteins from the Androctonus australis Hector venom.

Two toxin-like proteins (AahTL1 and AahTL3) were purified from the venom of the scorpion Androctonus australis Hector (Aah). AahTL1 and AahTL3 are the first non toxic proteins cross-reacting with AahI toxins group which indicates that these proteins can be used as a model of vaccins. In order to study structure-function relationships, their complete amino-acid sequences (66 residues) were determined, by automated Edman degradation. They show more than 50% of similarity with both AahI and AahIII antimammal toxins. Three-dimensional structural models of AahTL1 and AahTL3 constructed by homology suggest that the two proteins are structurally similar to antimammal scorpion alpha-toxins specific to voltage dependent Na+ channels. The models showed also that amino-acid changes between potent Aah toxins and both AahTL1 and AahTL3 disrupt the electrostatic potential gradient at their surface preventing their interaction with the receptor, which may explain their non toxicity.

Experimental, Hartree−Fock, and Density Functional Theory Investigations of the Charge Density, Dipole Moment, Electrostatic Potential, and Electric Field Gradients inl-Asparagine Monohydrate

We have investigated the charge density, ρ(r), its curvature, ∂2ρ/∂rij, the dipole moment, μ, and the electrostatic potential, Φ(r), in l-asparagine monohydrate by using high-resolution single-crystal X-ray crystallography and quantum chemistry. In addition, we have compared electric field gradient, ∇E, results obtained from crystallography and quantum chemistry with those obtained from single-crystal 14N nuclear magnetic resonance spectroscopy. A multipole model of the X-ray ρ(r) is compared to Hartree−Fock and density functional theory predictions, using two different large basis sets. The quality of the calculated charge densities is evaluated from a simultaneous comparison of eight Hessian-of-ρ(r) tensors at bond critical points between non-hydrogen atoms. These tensors are expressed in an icosahedral representation, which includes information on both tensor magnitude and orientation. The best theory-versus-experiment correlation is found at the B3LYP/6-311++G(2d,2p) level, which yields a slope of 1.0...

The role of the electrostatic potential, electric field and electric field gradient on the acidity of AFI and CHA zeotypes

We consider the role of short- and long-range interactions in determining the acidity of microporous solids. Within the context of an interatomic forcefield approach and a correct treatment of long-range electrostatics we demonstrate the role of the electrostatic potential, electric field and electric field gradient in determining the vibrational frequency of a Bronsted acid centre. We demonstrate the applicability of these concepts for AlPO4-5, AlPO4-34, SSZ-24 and SSZ-13, in whose unit cells a single Bronsted acid site was introduced in the four different oxygens. Furthermore, we show, by using the energy required to elongate the OH bond—essentially the first stage of proton transfer—as a measure of acidity, how the vibrational frequency is related to the acid strength.

Nonlinear dynamics and anomalous energy transport in an electrostatic ion-temperature-gradient driven drift-dissipative mode

By using Braginskii transport equations for ions and Boltzmann distribution for electrons, a new system of nonlinear equations governing the dynamics of low-frequency, short-wavelength electrostatic waves in the presence of equilibrium density, temperature, magnetic field, and electrostatic potential gradients has been derived. New ion-temperature-gradient (ITG) driven drift-dissipative modes are shown to exist. An expression for anomalous ion energy transport caused by nonthermal electrostatic fluctuations is also derived. Furthermore, possible stationary solutions of the nonlinear system are obtained in the form of double vortex. On the other hand, the temporal behavior of newly derived nonlinear dissipative systems can be described by the generalized Lorenz–Stenflo equations which admit chaotic solutions. The results of the present investigation should be helpful for understanding the wave phenomena in space and tokamak plasmas.

Electrostatics and reactivity of surface defects on Si(111)-(2×1)

We calculated the electrostatic field (the gradient of the molecular electrostatic potential) near steps and corners on the Si(111)-(2×1) surface using the semiempirical AM1 molecular orbital method. Calculations on appropriate models, derived from the experimental surface structure, indicate that the magnitude of the electrostatic field increases considerably in the vicinity of discontinuities. While the field near the unreconstructed perfect surface is less than 2 V/nm, it becomes larger by a factor of 2 to 4 near steps and corners. Semiempirical AM1 molecular orbital calculations on models with ammonia and methane molecules adsorbed near surface defects indicate that NH and CH bond lengths increase, the corresponding bond orders decrease, compared with the gas phase. This means that the enhanced electrostatic field weakens covalent bonds, promoting dissociation. On this basis we suggest that the electrostatic field is a determining factor of the enhanced catalytic activity near surface discontinuities.

Heme/Copper Terminal Oxidases.

Spatially well-organized electron-transfer reactions in a series of membrane-bound redox proteins form the basis for energy conservation in both photosynthesis and respiration. The membrane-bound nature of the electron-transfer processes is critical, as the free energy made available in exergonic redox chemistry is used to generate transmembrane proton concentration and electrostatic potential gradients. These gradients are subsequently used to drive ATP formation, which provides the immediate energy source for constructive cellular processes. The terminal heme/copper oxidases in respiratory electron-transfer chains illustrate a number of the thermodynamic and structural principles that have driven the development of respiration. This class of enzyme reduces dioxygen to water, thus clearing the respiratory system of low-energy electrons so that sustained electron transfer and free-energy transduction can occur. By using dioxygen as the oxidizing substrate, free-energy production per electron through the chain is substantial, owing to the high reduction potential of O{sub 2} (0.815 V at pH 7). 122 refs.

Statistical thermodynamic foundation for photovoltaic and photothermal conversion. I. Theory

We intend to cover the need for a general statistical foundation of the thermodynamic models of photovoltaic and/or photothermal conversion. The solid body receiving radiation is considered in considerable generality. This includes (1) nuclei of the lattice and their core electrons, (2) the electrons of the conduction band, (3) the electrons or holes of the valence band, (4) the traps in the forbidden gap. These components are subject to radiation and external fields (such as mechanical stress, gradients of electrostatic potential, or of temperature). The basis of the treatment is the Boltzmann transport equation. Different forms of this equation are considered, as the particles encountered in the body receiving radiation are both fermions (electrons and holes) and bosons (photons and phonons). Three main directions are followed. First, the continuity equations are derived in a rigorous manner. Second, the irreversibilities occurring during the conversion of radiation are emphasized. Third, the differences and similarities between photovoltaic and photothermal conversion are investigated.

Electrostatic analysis of TEM1 beta-lactamase: effect of substrate binding, steep potential gradients and consequences of site-directed mutations.

Escherichia coli TEM1 is a penicillinase and belongs to class A beta-lactamases. Its naturally occurring mutants are responsible for bacterial resistance to beta-lactamin-based antibiotics. X-ray structure determinations show that all class A beta-lactamases are similar, but, despite the numerous kinetic investigations, the reaction mechanism of these enzymes is still debated. We address the questions of what the molecular contexts during the acylation and deacylation steps are and how they contribute to the efficiency of these penicillinases. Electrostatic analysis of the 1.8 A resolution refined X-ray structure of the wild-type enzyme, and of its modelled Michaelis and acyl-enzyme complexes, showed that substrate binding induces an upward shift in the pKa of the unprotonated Lys73 by 6.4 pH units. The amine group of Lys73 can then abstract the Ser70 hydroxyl group proton and promote acylation. In the acyl-enzyme complex, the deacylating water is situated between the carboxylate group of Glu166, within the enzyme, and the estercarbonyl carbon of the acyl-enzyme complex, in an electrostatic potential gradient amounting to 30 kTe-1 A-1. Other residues, not directly involved in catalysis, also contribute to the formation of this gradient. The deacylation rate is related to the magnitude of the gradient. The kinetic behavior of site-directed mutants that affect the protonation state of residue 73 cannot be explained on the basis of the wild-type enzyme mechanism. In the wild-type enzyme, the very high rates of acylation and deacylation of class A beta-lactamases arise from an optimal chemical setup in which the acylation reaction seems triggered by substrate binding that changes the general base property of Lys73. In site-directed mutants where Lys73 is protonated, acylation may proceed through activation of a water molecule by Glu166, and Lys73 contributes as a proton shuffle partner in this pathway.