Repulsive Core Research Articles

Two-electron quantum dot with soft-edge barrier

A variational formalism to calculate energies of 1s, 2 1p, and 2 3p levels of a spherical quantum dot containing two electrons is developed. We express correspondent wave functions as a product of combinations of exact one-particle orbitals and variationally determined envelope function that depends only on separation between particles. An Euler–Lagrange differential equation for this last function is solved by using the trigonometric sweep method. We present novel curves for 1s, 2 1p, and 2 3p energy states dependencies on the radius of the quantum dots with hard wall and soft-edge barrier potential shapes. The effect of the repulsive core on the energies of the low-lying states and the pair correlation function is also analyzed. It is shown that the probability distribution of the electron–electron separation in a quantum dot with repulsive core is modified essentially with the increase of the quantum dot dimension, making more probable the finding of two electrons on diametrically opposite sides of the repulsive core.

On the uniqueness of structure extracted from diffraction experiments on liquids andglasses

There is continued interest in the problem of extracting structures from x-ray and neutrondiffraction data on liquids and glasses. Traditional Fourier transform techniques, with theirinherent weakness of possible systematic and truncation artefacts being introduced into theestimated distribution functions, are increasingly being complemented by computersimulation methods. These allow three-dimensional models of the scattering system to bebuilt, at the correct atomic number density, which are consistent with both the diffractiondata themselves and with other known or estimated constraints such minimum particleseparations. Here the empirical potential structure refinement (EPSR) method isused to explore structure in supercooled liquid Ni, amorphous Ge and amorphousGeSe2, and to evaluate alternative versions of the radial distribution functions which areconsistent with the diffraction data. In the case of liquid Ni, it is found that thereis, based on the diffraction data, some uncertainty on the hardness and shapeof the repulsive core of the interatomic pair potential, and this may influencethe current debate about the existence of icosahedral order in this liquid. Foramorphous Ge two distinct radial distribution functions are generated, both consistentwith the diffraction data, one of which has strong tetrahedral local order withthe other having a predominantly triangular local coordination. For amorphousGeSe2 it is found the SeSe and GeSe radial distribution functions can be determined well from thedata, but the GeGe distribution is more uncertain, with the best fits implying both GeGeand SeSe homopolar bonds as originally proposed. The results are used to discuss theambiguities inherent in the structural interpretation of diffraction data, even for one- andtwo-component systems.

Anomalous transport in molecularly confined spaces

We develop a novel theory to predict the density dependence of the diffusivity of simple fluids in a molecularly sized nanopore with diffusely reflecting walls, incorporating nearest neighbor intermolecular interactions within the framework of the recent oscillator model of low density transport arising from this laboratory. It is shown that when the pore width is about two molecular diameters, at sufficiently high densities these interactions lead to a repulsive inner core, as a result of which the diffusing molecules undergo more frequent reflections at the wall. This leads to a reduction in diffusivity with increase in density, which is consistent with molecular dynamics simulation results, and contrasts with the behavior in larger pores where the transport coefficient has previously been shown to increase with increase in density due to viscouslike intermolecular interactions. At low densities the behavior is opposite, with the inner core becoming more attractive with increase in density, which can lead to an increase in diffusivity. The theory consistently explains molecular dynamics simulation results when the inhomogeneous pair distribution function of moving particles in the pore is axially periodic, suggesting concerted motion of neighboring molecules. It is also shown that a potential of mean force concept is inadequate for describing the influence of intermolecular interactions on transport.

Toy model of the repulsive core of the nucleon-nucleon potential

We study the simplest quark model assuming that the sea of gluons and quark-antiquark pairs can be treated as a part of a static force and proceeding to calculate the hadronic states by solving the Schrodinger equation for a static confining interaction. We refer to this model, starting from a system of six interacting constituent quarks, and examine how the picture of two structureless nucleons can change when the effects caused by the substructure of the nucleons are taken into account.

Nuclear Force from Lattice QCD

The nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32(4) [approximately (4.4 fm)(4)] lattice. A NN potential V(NN)(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the (1)S(0) and (3)S(1) channels, we show that the central part of V(NN)(r) has a strong repulsive core of a few hundred MeV at short distances (r approximately < 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.

Structural properties and optical response of Na clusters in Ne, Ar, and Kr matrices

We discuss the structural properties and optical response of a small Na cluster inside rare-gas (RG) matrices of Ne, Ar, or Kr atoms. The mixed systems are described with a hierarchical model, treating the cluster at a quantum-mechanical level and the matrix atoms classically in terms of their positions and polarizations. We pay special attention to the differences caused by the different matrix types. These differences can be explained by the interplay of core repulsion and dipole attraction in the interaction between the cluster electrons and the RG atoms.

Translation-Invariance of Two-Dimensional Gibbsian Point Processes

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.

Folding description of the fine structure of α decay to2+vibrational and transitional states

We analyze \ensuremath{\alpha}-decays to ground and ${2}^{+}$ vibrational states in even-even nuclei by using a coupled channels formalism. The \ensuremath{\alpha}-nucleus interaction is simulated by a double folding procedure using M3Y plus Coulomb two-body forces. Collective excitations are described by vibrations of the nuclear surface. We use a repulsive potential, with one independent parameter, in order to simulate Pauli principle and to adjust the energy of the resonant state to the experimental $Q$-value. The decaying state is identified with the zero nodes resonance inside the resulting pocket-like potential. We have found that the fine structure is very sensitive to the strength of the repulsive core and the vibrational parameter of the \ensuremath{\alpha}-nucleus potential. A satisfactory agreement with existing experimental data was obtained by using the vibrational strength as a free parameter. It turns out that the inverse of this parameter is proportional to the logarithm of the hindrance factor squared. Based on this fact we have made predictions for 15 vibrational \ensuremath{\alpha}-emitters.

The BCS-BEC Crossover and Superconductivity in a Lattice Fermion Model with Hard Core Repulsion

We considered the BCS{BEC crossover at T = 0 in the framework of a lattice fermion model (the extended Hubbard model). We analyzed the case of on-site hard core repulsion (U = 1) and intersite attraction (W < 0) in a 3D system with extended s-wave pairing symmetry. The mechanisms of density-driven and attraction-strength-driven crossover were analyzed. We obtained the ground state phase diagram. The analyzed quantities are: chemical potential, order parameter, coherence length, and fraction of condensed particles.

Temperature Effect on the Absorption Spectrum of the Hydrated Electron Paired with a Lithium Cation in Deuterated Water

The absorption spectra of the hydrated electron in 1.0 to 4.0 M LiCl or LiClO4 deuterated water solutions were measured by pulse radiolysis techniques from room temperature to 300 degrees C at a constant pressure of 25 MPa. The results show that when the temperature is increased and the density is decreased, the absorption spectrum of the electron in the presence of a lithium cation is shifted to lower energies. Quantum classical molecular dynamics (QCMD) simulations of an excess electron in bulk water and in the presence of a lithium cation have been performed to compare with the experimental results. According to the QCMD simulations, the change in the shape of the spectrum is due to one of the three p-like excited states of the solvated electron destabilized by core repulsion. The study of s --> p transition energies for the three p-excited states reveals that for temperatures higher than room temperature, there is a broadening of each individual s --> p absorption band due to a less structured water solvation shell.

Hydrodynamic tensor density functional theory with correct susceptibility

In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.

Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions

Using inverse statistical-mechanical optimization techniques, we have discovered isotropic pair interaction potentials with strongly repulsive cores that cause the tetrahedrally coordinated diamond and wurtzite lattices to stabilize, as evidenced by lattice sums, phonon spectra, positive-energy defects, and self-assembly in classical molecular dynamics simulations. These results challenge conventional thinking that such open lattices can only be created via directional covalent interactions observed in nature. Thus, our discovery adds to fundamental understanding of the nature of the solid state by showing that isotropic interactions enable the self-assembly of open crystal structures with a broader range of coordination number than previously thought. Our work is important technologically because of its direct relevance generally to the science of self-assembly and specifically to photonic crystal fabrication.

Semiempirical Molecular Orbital Scheme To Study Lanthanide(III) Complexes: PM3 Parameters for Europium, Gadolinium, and Ytterbium.

Semiempirical parameters for europium, gadolinium, and ytterbium have been developed for use in the PM3 method to allow the structure and energetics of complexes containing lanthanide(III) ions to be accurately modeled. At the semiempirical level, the lanthanide(III) ion is represented by a +3 core and has a minimal basis of 6s5d6p (9 atomic orbitals), the 4f electrons being included within the electronic core. Training sets containing up to 19 lanthanide complexes, with data computed at the density functional theory (DFT) level, have been employed for each lanthanide(III) ion. A gradient-based optimization algorithm has been used, and important modifications of the core repulsion function have been highlighted. The derived parameters lead in general to good predictions of the structure of the complexes and demonstrate improvements in the prediction of water binding energies compared to the AM1/sparkle model. For the 28 Eu(III), 28 Gd(III), and 29 Yb(III) complexes optimized at the DFT level, the PM3 average unsigned mean errors for all interatomic distances between the lanthanide(III) ion and the ligand atoms of the first coordination sphere are 0.04, 0.03, and 0.03 Å, respectively. The derived parameters are shown to be comparable to small-basis set DFT calculations in predicting the experimental structures of various lanthanide(III) complexes. The derived parameter sets provide a starting point should greater accuracy for a more restricted range of compounds be required.

Phase Structure in a Quark Mass Density-and-Temperature-DependentModel

The phase diagram of bulk quark matter in equilibrium with a finitehadronic gas is studied. Different from previous investigations, wetreat the quark phase with the quark mass density-and-temperature-dependentmodel to take the strong quark interaction into account,while the hadron phase is treated by hard core repulsion factor. Itis found that the phase diagram in this model is, in severalaspects, different from those in the conventional MIT bag model,especially at high temperature. The new phase diagram also hasstrong effects on the mass-radius relation of compact hybrid stars.

Compatibility of Exotic States with Neutron Star Observation

We consider the effect of hard core repulsion in the baryon-baryon interaction at short distance to the properties of a neutron star. We obtain that, even with hyperons in the interior of a neutron star, the neutron star mass can be as large as $\sim 2 M_\odot$.

Collisions of ideal gas molecules with a rough/fractal surface. A computational study

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).

Molecular dynamics study of the equilibrium flux of gas molecules to a fractal/rough surface: Effects of gas atom diameter

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using the random deposition technique. By applying various depositions the surface roughness was controlled and, as a measure of irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in ideal gas and the numbers of collisions with these surfaces were counted. The calculations were carried out using the simplified molecular dynamics simulation technique (only hard core repulsions were assumed). The calculations were performed for various ratios of gas phase atoms diameter to the surface substrate atoms diameter. The results obtained showed that the size of a gas phase atom has crucial influence on the relation between the frequency of collision and the surface fractal dimension

Computer Simulation of the Ionic Atmosphere around Z-DNA

We describe a coarse-grained model for Z-DNA that mimics the DNA shape with a relatively small number of repulsive interaction sites. In addition, negative charges are placed at the phosphate positions. The ionic atmosphere around this grooved Z-DNA model is then investigated with Monte Carlo simulation. Cylindrically averaged concentration profiles as well as the spatial distribution of ions have been calculated. The results are compared to those for other DNA models differing in the repulsive core. This allows the examination of the effect of the DNA shape in the ionic distribution. It is seen that the penetrability of the ions to the DNA groove plays an important role in the ionic distribution. The results are also compared with those reported for B-DNA. In both conformers the ions are structured in alternating layers of positive and negative charge. In Z-DNA the layers are more or less concentric to the molecular axis. Besides, no coions enter into the single groove of this conformer. On the contrary, the alternating layers of B-DNA are also structured along the axial coordinate with some coions penetrating into the major groove. In both cases we have found five preferred locations of the counterions and two for the coions. The concentration of counterions reaches its absolute maximum at the narrow Z-DNA groove and at the minor groove of B-DNA, the value of the maximum being higher in the Z conformer.

Spatial correlation of two particles in semiconductor quantum ring

We analyze the effect of the spatial correlation on the ground state energy of two particles (two electrons and exciton–hole pair) confined in quantum ring (QR) with a soft-edge-barrier confinement potential. Starting from the Schrödinger variational principle we derive a one-dimensional differential equation for the spatial pair correlation function (SPCF), which we solve numerically by using the shooting method. The effect of the repulsive core in a self-assembled GaAs/InAs QR on the two-electron and exciton SPCF is analyzed. A comparative analysis of the dependencies of the two-particle ground state energies on the inner and outer radii of GaAs/InAs QRs with different confinement potential shapes is presented.

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction.