Internal electric field densities of metal nanoshells

The internal field patterns for gold shells filled with the same material as the surrounding medium are calculated with Mie theory and in the quasistatic approximation and their properties compared to the response of homogeneous spheres and metallic rings. One major difference between the sphere and shell case is that the areas of highest field enhancement in metallic shells are located perpendicular to the incident polarization, whereas for metallic spheres they are along the polarization direction. Recent results based on the discrete dipole approximation (DDA) are shown to be misleading, which might be due to the use of a too coarse grid size. We also show that the type of resonance and the associated internal field pattern (low or high energy) has a strong impact on the external fields.     

Upper bounds to atomic electron densities in position and momentum spaces

Modified functions r ^–(r) and p ^–(p) of the spherically averaged electron densities (r) in position space and (p) in momentum space are found to be convex (i.e., the second derivatives are nonnegative everywhere) for all the 103 ground-state atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103), if the parameters are chosen to be 0.6 and 1.4. The convex property of r ^–(r) and p ^–(p) is used to derive upper bounds to the density functions (r) and (p) in terms of their radial moments r ^s and p ^s or frequency moments ^t and ^t . In most cases, the present bounds are shown to be more general and more accurate than those reported in the literature.     

Convergence of electric field and electric field gradient versus atomic basis sets in all-siliceous and Mg substituted phillipsites

Electrostatic potential (EP), electric field (EF), and electric field gradient (EFG) values are calculated in periodic models of magnesium substituted phillipsite (MgPHI) zeolite forms using periodic DFT (PDFT) hybrid B3LYP level with fourteen different basis sets. Relative root mean square differences between the EP, EF, or EFG values estimated between different basis sets are evaluated in several spatial domains available for adsorbate molecules in the zeolite. In these areas, the EF increase in MgPHI is evaluated relative to all-siliceous PHI types. The EP is interpreted in terms of framework ionicity for MgPHI and all-siliceous PHI models. Angular Si-O-Si dependence of the EFG asymmetry at (17)O atoms in all-siliceous zeolites is discussed.     

Bond orders and atomic properties of the highly deformed halogenated fullerenes C60F18 and C60Cl30 derived from their charge densities

The experimental charge densities of the halogenated C(60) fullerenes C(60)F(18) and C(60)Cl(30) were determined from high-resolution X-ray data sets measured with conventional Mo(Kalpha) radiation at 20 K for C(60)Cl(30) and with synchrotron radiation at 92 K for the fluorine compound. Bond topological and atomic properties were analyzed by using Bader's AIM theory. For the different C--C bonds, which vary in lengths between 1.35 and 1.70 A bond orders n between n=2 and significantly below n=1 were calculated from the bond topological properties at the bond critical points (BCP's). The low bond orders are seen for 5/6 bonds with each contributing carbon carrying a halogen atom. By integration over Bader's zero flux basins in the electron density gradient vector field atomic properties were also obtained. In contrast to free C(60), in which all carbon atoms have a uniform volume of 11 A(3) and zero charge, atomic volumes vary roughly between 5 and 10 A(3) in the halogenated compounds. Almost zero atomic charges are also found in the Cl derivative but a charge separation up to +/-0.8 e exists between C and F in C(60)F(18) due to the higher fluorine electronegativity, which is also seen in the electrostatic potential for which the electronegativity difference between carbon and fluorine, and the addition to one hemisphere of the fullerene cage leads to a strong potential gradient along the C(60)F(18) molecule. From the summation over all atomic volumes it follows that the halogen addition does not only lead to a dramatic distortion of the C(60) cage but also to a significant shrinkage of its volume.     

A semi-empirical extrapolation technique for atomic and molecular properties derived from correlated wavefunctions

A semi-empirical extrapolation technique is suggested for recovering the correlation defect remaining in atomic and molecular properties calculated from highly correlated wavefunctions. These procedures are applied to PNO-CEPA and PNO-IPPA calculations on F, F⁺, F^?, and HF in order to obtain “exact” estimates of the ionization potential, electron affinity, and dissociation energy.     

Calculation of electrostatic and polarization energies from electron densities

We investigate procedures for calculating the electrostatic and polarization energies, Ees and Epol, associated with noncovalent interactions. The starting points are the electron densities of the isolated components and the complex; these could be obtained either computationally or experimentally. A slightly modified version of a scheme proposed by Gavezzotti is used to carry out numerical integrations over these electron densities. Our approach to estimating Epol is based upon partitioning the charge distributions of the components into overlapping and nonoverlapping regions. The effects of varying the integration parameters, computational techniques and basis sets are examined in detail for several noncovalently bound molecular dimers. Our results are in good agreement with the values of Ees and Epol produced by other methods, which require analytical integrations over interaction Hamiltonian matrix elements.     

Wave functions derived from experiment. V. Investigation of electron densities,electrostatic potentials,and electron localization functions for noncentrosymmetric crystals

The constrained Hartree-Fock method using experimental X-ray diffraction data is extended and applied to the case of noncentrosymmetric molecular crystals. A new way to estimate the errors in derived properties as a derivative with respect to added Gaussian noise is also described. Three molecular crystals are examined: ammonia [NH(3)], urea [CO(NH(2))(2)], and alloxan [(CO)(4)(NH)(2)]. The energetic and electrical properties of these molecules in the crystalline state are presented. In all cases, an enhancement of the dipole moment is observed upon application of the experimental constraint. It is found that the phases of the structure factors are robustly determined by the constrained Hartree-Fock model, even in the presence of simulated noise. Plots of the electron density, electrostatic potential, and the electron localization function for the molecules in the crystal are displayed. In general, relative to the Hartree-Fock model, there is a depletion of charge around hydrogen atoms and lone pair regions, and a build-up of charge within the molecular framework near nuclei, directed along the bonds. The electron localization function plots reveal an increase in the pair density between vicinal hydrogen atoms.     

Role of electric field on surface wetting of polystyrene surface

The role of surface charge in fluid flow in micro/nanofluidics systems as well as the role of electric field to create switchable hydrophobic surfaces is of interest. In this work, the contact angle (CA) and contact angle hysteresis (CAH) of a droplet of deionized (DI) water were measured with applied direct current (DC) and alternating current (AC) electric fields. The droplet was deposited on a polystyrene (PS) surface, commonly used in various nanotechnology applications, coated on a doped silicon (Si) wafer. With the DC field, CA decreased with an increase in voltage. Because of the presence of a silicon oxide layer and a space charge layer, the change of the CA was found to be lower than with a metal substrate. The CAH had no obvious change with a DC field. An AC field with a positive value was applied to the droplet to study its effect on CA and CAH. At low frequency (lower than 10 Hz), the droplet was visibly oscillating. The CA was found to increase when the frequency of the applied AC field increased from 1 Hz to 10 kHz. On the other hand, the CA decreased with an increasing peak-peak voltage at or lower than 10 kHz. The CAH in the AC field was found to be lower than in the DC field and had a similar trend to static CA with increasing frequency. A model is presented to explain the data.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Bound-state plus continuum electron densities,and Slater sum,in a bare Coulomb field

After reporting numerical studies based solely on s-states of total (s + p + d etc.) bound-state densities, which allow the range of validity of the simplest density functional theory of Thomas and Fermi to be critically assessed, two areas in which analytical progress proves possible are focused on. The first of these is the local density of states in the continuum, for which an exact formula is derived. The second concerns the Slater sum, for which an explicit differential equation is established. Prior to this, only the Bloch equation satisfied by the off-diagonal generalization of the Slater sum, namely the canonical density matrix, was available.     

Nonlinear response of aluminum surface to electric field

The static limit of the perpendicular second-harmonic response of the exposed single-crystal planes of aluminum to applied electric field is studied using the variant of stabilized-jellium model which allows to account for the anisotropy of surface potential. The self-consistently calculated linear and second-order induced charge density distributions are used to determine the normal component of the polarization vector. The surface structure is found to have a pronounced effect on the anisotropy of second-harmonic response. © 1997 John Wiley & Sons, Inc.     

Optimized effective potentials from electron densities in finite basis sets

The Wu-Yang method for determining the optimized effective potential (OEP) and implicit density functionals from a given electron density is revisited to account for its ill-posed nature, as recently done for the direct minimization method for OEP's from a given orbital functional [T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett. 98, 256401 (2007)]. To address the issues on the general validity and practical applicability of methods that determine the Kohn-Sham (local) multiplicative potential in a finite basis expansion, a new functional is introduced as a regularized version of the original work of Wu and Yang. It is shown that the unphysical, highly oscillatory potentials that can be obtained when unbalanced basis sets are used are the controllable manifestation of the ill-posed nature of the problem. The new method ensures that well behaved potentials are obtained for arbitrary basis sets.     

Thixotropic hydrogel derived from a product of an organic solid-state synthesis: properties and densities of metal-organic nanoparticles

Metallogels form from Cu(II) ions and tetratopic ligand rctt-1,2-bis(3-pyridyl)-3,4-bis(4-pyridyl)cyclobutane. The tetrapyridyl cyclobutane has been synthesized in the organic solid state. The gel forms with a variety of counteranions and gels water. The hydrogel is thixotropic and is composed of nanoscale metal-organic particles (NMOPs), a high surface area of which likely accounts for the gelation of the polar aqueous medium. A shear stress profile of the thixotropic hydrogel gave a yield value of 8.33 Pa. A novel combination of atomic force microscopy (AFM) and scanning transmission X-ray microscopy (STXM) is used to assess the densities of individual NMOPs. A density of 1.37 g/cm(3) has been determined. A single-crystal X-ray diffraction study demonstrates the ability of the unsymmetrical cyclobutane 3,4'-tpcb to self-assemble with Cu(II) ions in [Cu(2)(hfac)(4)(3,4'-tpcb)](∞) (where hfac is hexafluoroacetylacetonate) to form a solvated 1D coordination polymer.     

Measures of distance for atomic charge and momentum densities and their relationship to physical properties

Atomic charge and momentum densities of 91 atoms (He? U) are classified in terms of their L₁, L₂, and entropic measures of distance from the densities of the preceding atoms. The relationship between these distances and the first ionization energies is also considered. © 1995 John Wiley & Sons, Inc.     

Extracting atoms from molecular electron densities via integral equations

The observation that a molecular electron density is close to the superposition of its constituent atoms leads naturally to the idea of modeling a density by a sum of nuclear-centered, spherically symmetric functions. The functions that are optimal in a least-squares sense are known as Stewart atoms. Previous attempts to construct Stewart atoms by expanding them in an auxiliary basis have been thwarted by slow convergence with respect to the size of the auxiliary basis used. We present a method for constructing Stewart atoms via convolution integrals which bypasses the need for an auxiliary basis, and is able to produce highly accurate approximations to Stewart atoms.     

Influence of transport properties in electric field gradient focusing

Miniaturized devices for electric field gradient focusing (EFGF) were developed that consist of a cylindrical separation channel surrounded by an acrylic-based polymer hydrogel. The ionic transport properties of the hydrogel enable the manipulation of the electric field inside the separation channel. A changing cross-section design was used in which the hydrogel is shaped such that an electric field gradient is established in the separation channel. One of the challenges with this type of EFGF device has been that experimental resolution between protein analytes is lower than theoretically predicted. In order to investigate this phenomenon, a mathematical transport model was developed using FEMLAB. Model results and experimental observations showed that the reduced performance was caused by concentration gradients formed in the EFGF channel, and that these concentration gradients were the result of an imbalance in cation transport between the open separation channel and the hydrogel. Removing acidic impurities from the monomers that form the hydrogel reduced this tendency and improved the resolution. These transport-induced concentration gradients can be used to establish electric field gradients that may be useful for sample pre-concentration. Both the results of simulation and experiments demonstrate how transport-induced concentration gradients lead to the establishment of electric field gradients.     

Deformation of water droplets on solid surface in electric field

The purpose of this paper is to analyze the deformation of water droplets on a solid surface under electric stress. A mathematical model making it possible to simulate the axisymmetric as well as non-axisymmetric deformations of droplets is developed. According to this model, the droplet deformation depends on several parameters such as the volume and the number of droplets, the conductivity and the permittivity of droplets, their proximity to one another, the surface of the solid material, and the location of each droplet on the dielectric surface. The results of the simulation show the disturbance of the background field through the presence of a single or multiple droplets. An experimental study is also achieved by considering one to three droplets aligned simultaneously on a dielectric smooth surface between two electrodes subjected to AC voltages. The influence of the background field and the droplet location regarding the electrodes on the deformation of water droplets are evidenced.     

Refinement of electron momentum densities of ionic solids using an experimental energy constraint

It is demonstrated how one can refine a given approximate momentum density distribution using a constraint of the experimental electronic energy. The technique developed is based on the calculus of variations. This technique has been applied to ionic solids such as LiF, LiCIl NaF, NACl, MgO, KF and KCl.