Coulomb Energy Terms Research Articles

Nucleation behavior of cage structure of carbon in the presence of charge

The charge is produced in abundance in the processing condition of the cage structure of carbon. Considering low ionization energy and high electron affinity of carbon clusters compared with those of single atom or molecule, the carbon clusters are expected to be charged in such ionizing conditions. The charge is suggested to affect the nucleation behavior of a cage structure of carbon at least in two respects. First, the Coulomb energy term, which is newly introduced by charge, can make the energy well in the curve of the free energy versus number of atoms. In combination with the suitable driving force for precipitation of condensed carbon, the energy well will make stable the carbon clusters containing certain number of atoms with respect to both shrinking and growing, increasing the lifetime of the cluster of constant size. Second, the minimization of Coulomb energy favors the loose structure of carbon while that of the surface energy favors the compact structure. In terms of Coulomb energy, the cage structure is favored over the compact one as the cage structure of soap bubble is favored by the electrical double layer on the water surface. These effects of charge were examined based on the classical Thomson equation.

An approximate formula for the intermolecular Pauli repulsion between closed shell molecules. II. Application to the effective fragment potential method

The accuracy and efficiency of an approximate formula for the intermolecular Pauli repulsion between closed shell molecules, derived earlier [Mol. Phys. 89, 1313 (1996)], is demonstrated for dimers of H2O, CH3OH, CH2Cl2, CH3CN, (CH3)2CO, and (CH3)2SO. The energy derivative with respect to a Cartesian coordinate and rigid rotation about the center-of-mass (torques) are presented. The Pauli repulsion energy term is then combined with the Coulomb and classical induction energy terms of the effective fragment potential method [J. Chem. Phys. 105, 1968, 11081 (1996)] to give a general intermolecular interaction potential. This potential is applied to water and methanol clusters.

Nuclear Fragmentation Reactions at Relativistic Energies

Fragmentation reaction cross sections at relativistic energies are investigated using a phenomenological approach. Equations are obtained by a geometrical treatment in the framework of classical dynamics, in which the impact parameter is introduced. A numerical solution is obtained for the 56 Fe + 12 C system at 600 MeV/nucleon incident energy. It is shown that the predicted mass number distribution of fragments reproduces well the experimental data. The Coulomb energy term in the mass formula affects the nuclide dependence of cross sections to a favorable direction.

Nucleation behavior in the presence of charge in the CVD diamond process

The CVD diamond process adopts gas activation by plasma or hot filament, which produce abundant charges. In the presence of these charges, the nuclei are expected to be multiply charged. The nucleation behavior in the presence of these charges is studied. The effect of charge is suggested to be twofold: one is the formation of an electrical double layer on the surface of the nuclei cluster and the other is to reduce the nucleation barrier by introducing a Coulomb energy term, which is known as charge-induced nucleation. By the electrical double layer, the surface energy of the dielectric diamond can be reduced more effectively than that of the conducting graphite. This reduction of the surface energy favors the stability of the diamond nuclei over that of the graphite nuclei and can result in the dominant nucleation of diamond over graphite. The reduction of the surface energy and the Coulomb energy term can reduce the nucleation barrier markedly when the nuclei are multiply charged. However, the estimated absolute nucleation rate can barely explain the experimentally observed nucleation rate especially for a gas mixture of low methane concentration.

Nonparabolicity of the conduction band in CdSe and CdS xSe 1−x semiconductor microcrystallites

Nonparabolicity of the conduction band in CdSe and CdS xSe 1−x microcrystallites is shown to have an important role in the size dependent lowest exciton energy. The Haken potential, which gives the size dependent dielectric constant, is used in the calculation of the Coulomb interaction. Comparison with experiments is made for CdS xSe 1−x microcrystallites, and good agreement is obtained. The Coulomb energy term is compared for calculations using a parabolic band and a nonparabolic band, and using the Haken potential and the constant dielectric constant, and conventional calculations without nonparabolicity and the size dependent dielectric constant are found to underestimate the Coulomb interaction.

Stereoselective electron transfer between chiral substrates and metal chelates anchored to polypeptides

Electron transfer from ortho-dihydroxy substrates, such as L(+)-ascorbic acid, L-adrenaline, and L-dopa, to iron(III) in [Fe(tetpy)(OH)2]+ ions anchored to sodium poly(L-glutamate) (FeTL) or poly(D-glutamate) (FeTD) was found to proceed stereoselectively when structurally ordered and partially shielded active sites prevent easy approach for redox partner. Oxidant-reductant interactions are then mediated by the polypeptide, whose conformational asymmetry ensures an efficient sterically discriminating environment. Evidence is produced that stereoselectivity chiefly arises from transition state effects, while thermodynamic discrimination is of minor importance. Theoretical models of the diastereomeric electron-transfer complexes were constructed by conformational energy calculations based on Coulombic, nonbonded, and hydrogen-bonded energy terms. The molecular parameters of the models enabled "differential" thermodynamic functions of the diastereomeric pairs and stereoselectivity to be evaluated and satisfactorily compared with those experimentally determined. The models give good insight into the observed topochemical phenomena and support the idea that stereoselectivity is coupled with a remote attack mechanism on the central metal ion where the peripheral tetpy ligand of the active sites acts as an electron-transfer agent.

Electrical properties of BaTiO 3 with a new parameterization for repulsion effects

The well-known simple polarizable point-ion model was modified by taking into account the effect of the nearest neighbour repulsion on the electronic polarization. This was done in such a way that the customary division of atoms into cores and shells was avoided. The parameters of the model were adjusted against the experimental spontaneous polarization and the refractive indices for the tetragonal phase. The calculated spontaneous polarizations for the orthorhombic and rhombohedral phases are in excellent agreement with the experiment. The variation of the calculated spontaneous polarization, coulombic energy terms and electric fields were studied as functions of volume and the depolarization factor. The anisotropy of the dipole-dipole interactions is too small to explain the experimentally observed birefringence. Therefore, the model was further modified by allowing the polarizabilities of the oxygen ions to depend quadratically on the polarizing field. In this manner, the model also explains the observed birefringence.

Vacuum polarization and the nuclear mass formula

The effect of vacuum polarization on the ground-state mass systematics of nuclei is considered. Its contribution to the ground-state energy of heavy nuclei is found to be a few MeV and can be simulated by using an effective nuclear radius in the Coulomb energy term of the mass formula. Its effect on the fission barriers seems to be small. The sub-barrier heavy-ion fusion cross section is found to be reduced at most by an order of magnitude with the inclusion of vacuum polarization in the interaction potential.

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr 0. It is observed from the behaviour ofr 0 that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr 0 is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E exp−E cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.

Electrostatics of the ferroelectric phases of BaTiO 3

Extensive theoretical calculations are reported here on the electrostatics of the three ferroelectric phases of BaTiO 3 using the static polarizable point-ion model. For each structure the following quantities have been calculated: monopole and dipole fields at ionic sites, field gradients, spontaneous polarization, high frequency dielectric constant and the Coulomb energy terms. The parameters of the model have been fitted on the basis of the experimental information on the tetragonal structure and then treated as constants for all the studied structures. The use of the experimental positional parameters of the orthorhombic structure gives such exceptional behaviour for all the calculated quantities that a redetermination of the structural parameters for this phase is suggested. Numerical study of the changes in the Coulomb energy as a function of the macroscopic depolarization potential demonstrated that the most stable state is achieved with the value zero for the potential.

Structure and energetics of alkali-metal halide dimer molecules

The energetics and geometries have been computed for alkali-metal halide dimer molecules employing parameters for alkali halide diatomic molecules (monomers) obtained by fitting the potential functions to the experimental data on bond dissociation energies, equilibrium interionic distances, vibrational frequencies and dipole moments. The potential function used for this purpose is the ionic Rittner model as applied to the dimer molecules. It includes the coulombic, polarization, repulsion and dispersion energy terms. Contrary to previous work, the Rittner model gives results which are in good agreement with experiment and other calculations without altering the model or the input parameters. This success in duplicating the energetics and geometries of the dimers with a simple potential indicates that experimental origin and consistency are more important than the presumed physical significance of the potential. The anion–cation separations in the dimers are ca. 0.2–0.3 A bigger than in the monomers and 0.2–0.3 A smaller than in the corresponding alkali-metal halide crystals. For larger alkali-metal halides the overall potential is almost equal to the coulombic term as the other terms cancel each other out. The potential parameters derived from the scattering experiments and other sources are not successful in reproducing the dimer potentials and the related equilibrium geometries.

Study of β- and β″-aluminas by means of potential energy calculations

Potential energy calculations using Coulomb, short-range repulsive, and polarization energy terms have been made to study the conduction mechanism, the mixed-ion effects and charge compensation mechanisms in β-aluminas, and the conduction mechanism and non-Arrhenian behavior in β″-aluminas. It is concluded that the interstitialcy cation pairs are important to properties of β-aluminas, while the interacting ‘nearly-free’ cation vacancies are important to properties of β″-aluminas.

Nondivergent retarded self-interaction of a classical point electron

The retarded Lienard-Wiechert field, on the world-line of a point charge, is defined to be the line e→0 of the average value of this field over the timelike pseudosphere (x−z)2=ɛ2. It is shown that the divergent Coulomb-energy term exactly vanishes in the averaging process, but the radiation-reaction term is not affected. The reaction of this field on the particle correctly leads to the renormalized Lorentz-Dirac equation.

Calculation of motional activation energies for interstitial ions in the rutile structure using a minimum energy path model

Motional activation enthalpies have been calculated for interstitial cations in the rutile structure, using a minimum energy path approach. Coulombic, overlap repulsion and polarization energy terms were included in the potential energy expression. Preexponential factors in the overlap repulsion terms were evaluated by minimizing of the total electrostatic energy, and permanent dipole moments of the anion by an iterative method. The most favorable diffusion path was found to be parallel to the c-axis in the 1 2 , 0, z direction in both TiO 2 and MgF 2. Motional activation enthalpies increased with increasing interstitial cation radius and were larger in TiO 2 than in MgF 2. The path was independent of radius and material. Strongly anisotropic conductivity was predicted for both compounds.

Two sphere model for the asymmetric division of electrically charged liquid drops

For the binary division of electrically charged liquid drops a (pseudo) saddle point configuration is considered consisting of two spheres of radii r1 and r2, a distance α(r1 + r2) apart.Computation of surface energy and Coulomb energy terms shows that an asymmetric configuration, i.e., r1 ≠ r2 is energetically favored for all values of the fissionability parameter [Formula: see text], where x is defined as x = Q2/16πR3γ for the original drop with charge Q, radius R, and surface tension γ. Minimization of the energy terms requires a charge transfer directed towards the smaller sphere.Uniform, but not necessarily equal, surface charge is assumed for the two-sphere configuration. A more exact solution involving image charges gives very similar results.The present results for sphere separations α = 1 to α = ∞ confirm previous work in which a value of α = ∞ only was considered.

Towards an Accurate Wave Function for Positronium Hydride

A variational wave function for the ground state of positronium hydride is presented. The wave function is considerably more accurate than any previously reported. The only simplifications used are (a) only kinetic and Coulombic potential energy terms are included in the Hamiltonian, (b) the motion of the proton is ignored, and (c) the nucleus-positron distance is excluded from the wave function. The last assumption is the major source of error, but it enables us to evaluate all integrals exactly. Several trial wave functions are examined, the one giving the lowest energy being an open-shell exponential function times a 12-term power series through second-degree terms in the five remaining interparticle coordinates. Positronium hydride is found to be stable with respect to separation into hydrogen and positronium by at least 0.657 eV. The annihilation rate for two-photon events is found to be 2.095 ${\mathrm{nsec}}^{\ensuremath{-}1}$ for the trial wave function giving the lowest energy, and 2.265 ${\mathrm{nsec}}^{\ensuremath{-}1}$ for the trial wave function which most nearly satisfies the positron-electron cusp condition. A search for bound excited states of PsH and a bound state for the system ${e}^{+}\mathrm{He}$ was unsuccessful.

Chemical binding in silicate minerals Part II. Computational methods and approximations for the binding energy of complex silicates

Methods have been generated and evaluated for the calculation of the electrostatic binding or partial binding energy of silicate minerals. Computational techniques used for finding the Coulomb energy and its derivatives are the Ewald method for lattice sums and differential Fourier synthesis. Computations are carried out for all symmetrically independent atoms in the unit cell. Repulsion energies and their derivatives are calculated using simple exponential repulsion terms. Covalency in the bonds is taken into account by reducing charges on ions for the Coulomb energy terms. By using differentials of energy terms, equations are given for shifting atoms to minimum energy positions.

On the theory of the low-temperature spontaneous magnetization of ferromagnetic metals

The temperature variation of the low-temperature spontaneous magnetization ξ of a ferromagnetic metal is obtained from assumptions that are consistent with the usual band theory. The second-quantized Hamiltonian for the system is taken to contain electronic energy band terms as well as Coulomb and exchange energy terms. The Green function method is used. It is shown that spin-wave excitations of small wave vector k exist with energies proportional to k 2 , from which it is deduced that ξ = ξ 0 {1— γ T 3/2 ), with ξ 0 dependent on the average number of electrons per band. An analytical expression is found for the constant γ which differs from that obtained in the Heisenberg model.

Generalized Atomic Mass Law

Least-squares analyses have been performed on a set of atomic masses using standard and generalized semiempirical mass laws. Presumably because of errors in the assumed form of the standard mass law, its least-squares coefficients can be determined at best to an accuracy of about 10%, and masses are predicted with an uncertainty of several ${\mathrm{M}\mathrm{e}\mathrm{v}/\mathit{c}}^{2}$. The standard mass law has been generalized by addition of shell effect and deformation terms. While the least-squares fitting of the generalized mass law is better than for the standard mass law, it is still not possible to predict atomic masses to an accuracy better than a few ${\mathrm{M}\mathrm{e}\mathrm{v}/\mathit{c}}^{2}$. The nuclear deformations and the well depth of the nuclear interaction obtained from the additional mass-law terms are in reasonable agreement with more accurate determinations by other methods. A similar statement applies to the nuclear radius constant as obtained from the least-squares coefficient of the Coulomb energy term. A study has also been made of the effects of additional terms propertional to the absolute value of the isotopic spin, exchange and surface corrections to the Coulomb energy, and the surface correction to the normal isotopic term.

RADIUS OF NUCLEAR CHARGE DISTRIBUTION AND NUCLEAR BINDING ENERGY

From the analysis of the experimental results (high energy electron scattering, X-ray spectra of μ-mesonic atoms), it is pointed out that the radius of nuclear charge distribution, Rp, is very nearly proportional to the cubic root of the atomic number z1/3, ins tead of the usually accepted relation Rp∝A1/3. Under this assumption, we have modified the semi-empirical mass formula. The Coulomb energy term is now assummed to be of the form 3/5 (z2e2)/ropz1/3).The aagreement of the nuclear binding energies calculated fromthe new fomula with the experimental data is definitely better than that of the old Bethe-Weizsacker formula. Also the mass numbers of the most beta-stable nuclei are very correctly predicated by the new formula.