Real-space Representation Research Articles

Fullerene-like structure of activated carbons

The structure of the commercial activated carbons AX21 and BP71 has been studied using the high-energy X-ray diffraction and molecular dynamics techniques. The diffraction measurements were carried up to a maximum value of the scattering vector K max = 24 Å − 1 . The obtained diffraction data have been converted to a real space representation in the form of the radial distribution function. Structural models containing 2 and 4 graphene layers, approximately 16–20 Å in size, were computer generated and then relaxed using the reactive empirical bond order potential for carbon–carbon interactions and the Lennard–Jones potential with parameters for inter-layer interactions. The molecular dynamics simulations were performed at 300 K to account for the thermal oscillations. For such models the intensity and radial distribution functions were computed. The correctness of the models was verified by comparison of the simulations with the experimental data both in real and reciprocal space. The effects of hydrogen, saturating dangling bonds of edge atoms, the presence of non-six membered rings and the sp 3 defects on the resulting structure were investigated.

Diagrammatic content of the dynamical mean-field theory for the Holstein polaron problem in finite dimensions

In the context of the Holstein polaron problem, it is shown that the dynamical mean-field theory (DMFT) corresponds to the summation of a special class of local diagrams in the skeleton expansion of the self-energy. In the real space representation, these local diagrams are characterized by the absence of vertex corrections involving phonons at different lattice sites. Such corrections vanish in the limit of infinite dimensions, for which the DMFT provides the exact solution of the Holstein polaron problem. However, for finite dimensional systems, the accuracy of the DMFT is limited. In particular, it cannot describe correctly the adiabatic spreading of the polaron over multiple lattice sites. Arguments are given that the DMFT limitations on vertex corrections found for the Holstein polaron problem persist for finite electron densities and arbitrary phonon dispersion.

Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays

Recent demonstrations have shown that the transmission through a subwavelength aperture in metal film placed in a periodic lattice or an aperiodic structure is significantly increased relative to a bare aperture. Using terahertz time-domain spectroscopy, we analyze the enhanced transmission properties of aperiodic and corresponding random 2D aperture arrays perforated in metallic films, which include quasicrystals and quasicrystal approximates. We demonstrate that the transmission enhancement phenomenon occurs for aperture arrays having discrete Fourier components in the 2D geometrical structure factor. We further show that the phenomenon is valid for a larger class of 2D aperture array designs that can be tailored to exhibit desired resonances and hence is more general. The inherent relationship between various features observed in the measured time-domain electric field, calculated transmission spectra, and the real and reciprocal space representation of the aperture array is discussed in detail. The results are interpreted in terms of Fano-type interference mechanism. The importance of antiresonance features observed in the transmission spectra is also discussed.

Convergence stability and estimator in orbital free electronic structure calculation on a grid at finite temperature

The electronic charge density is the central quantity in density functional theory. It can be expressed as the diagonal elements of the density matrix in its real space representation, which can be computed by a recursion method based on the Trotter formula. This allows for an orbital free computation of the charge density in the Kohn Sham formalism at finite temperature whose numeric complexity increases linearly with the size of the system (that is, an order N method).No assessment of the numerical properties such an approach has been presented yet, and this paper aims to analyze its convergence properties.In particular, we wish to understand its convergence properties as a function of the number of recursion steps, to establish an error estimate in order to devise a stopping criterion, and to analyze the “locality properties” of the method which is necessary to make it an order N method. We illustrate the assessment with numerical tests performed for the free electron gas and for Helium at a density and high temperature relevant to shock physics.

The field theoretical study of chemical interaction in terms of the Rigged QED: new reactivity indices

How the mode of bonding affects stability and reactivity of molecule on the frame of nonrelativistic limit of the rigged quantum electrodynamics using new indices for description of bond properties related to bond orders have been characterized here. These indices are in close relation with tensorial interpretation of bond that among others allows discriminating covalent bonds using spindle structure concept. The real three-dimensional space representation of new interaction energy density utilized in this study contribute to better understanding of interaction phenomena between atoms and molecules. The differences in reactivity and stabilities of molecules have their root in the redistribution of interaction energy density.

A 5-1/2-dimensional theory for fast and accurate evaluation of the cyclotron resonance heating using a real-space wave representation

The cyclotron resonance heating rate in a plasma has been evaluated so far from a five-dimensional (5D) quasilinear model because the 6D evaluation is prohibitively expensive. However, the quasilinear approach as applied to the cyclotron resonance heating has fundamental difficulties in evaluating the net effect from a large number of coupled wave modes (leading to strong spatial wave inhomogeneity) since the theory is built on the Fourier space wave representation, and does not include the regular nonlinear particle dynamics within a resonance passing event since the theory is based on the unperturbed orbit theory. A new 5-1/2D theory is formulated for evaluation of a more accurate resonant particle dynamics using the real-space wave representation, which overcomes the shortcomings of the quasilinear cyclotron resonance heating theories by reproducing the 6D physics at the 5D computing speed.

Real-space description of current-constrained molecular junctions

A current constrained approach is proposed for the calculation of characteristic current/voltage curves for molecular junctions described in a real space representation. A steady-state current is imposed on the molecule prepared in a nonequilibrium state, and the voltage drop is obtained from the electrical power spent on the molecule to sustain the current. The molecular resistance is related to relaxation phenomena that drive the molecule towards the equilibrium state. A phenomenological model, borrowed from the field of molecular spectroscopy, is adopted to describe relaxation, accounting for both depopulation and dephasing (inelastic and elastic scattering). The current is related to coherences, and the coherence lifetimes, with contributions from both depopulation and dephasing, enter the definition of the molecular resistance. For the specific case of a single electron in a two-site junction the standard result of conductivity quantization is regained, a result that holds for dispersionless as well as dispersive junctions. The proper implementation of the continuity constraint for steady-state dc transport requires the introduction of multiple Lagrange multipliers and results in nonlinear potential profiles across the molecule leading to the intriguing concept of bond resistance.

Comparison of the electronic structure of PPV and its derivative DIOXA-PPV

Electronic structure of two conjugated polymers, PPV and its derivative DIOXA-PPV, are studied by quantum-chemistry methods. Good agreement between the calculations and available experimental data validates the applied methods and enables us to draw conclusions about properties of excitons and polarons in these polymers. In particular, simultaneous use of different correlation plots in atomic site representation and transition densities in real space representation reveals electronic structure and spatial localization of the elementary excitations. The properties of the DIOXA-PPV are discussed in context of possible applications in molecular electronics devices.

A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction

A genetic algorithm is described that is suitable for determining the global minimum energy configurations of crystal structures and which can also be used as a polymorph search technique. This algorithm requires no prior assumptions about unit cell size, shape, or symmetry, nor about the ionic configuration within the unit cell. This therefore enables true ab initio crystal structure and polymorph prediction. Our algorithm uses a real-space representation of the population members, and makes use of a periodic cut for the crossover operation. Results on large Lennard-Jones systems with fcc- and hcp-commensurate cells show robust convergence to the bulk structure from a random initial assignment and an ability to successfully discriminate between competing low enthalpy configurations. Results from an ab initio carbon polymorph search show the spontaneous emergence of both Lonsdaleite and graphite-like structures.

Molecular dynamics simulation of carbon nanotube structure

Carbon nanotubes with the Stone-Wales defects were generated, and molecular dynamics simulations of the nanotubes have been performed at temperature of 300 K using the reactive empirical bond order potential and Lennard–Jones one. The carbon configurations obtained from the simulations were used to calculate the powder diffraction patterns, which have been converted to a real space representation, yielding a pair correlation function. The theoretical results are compared with the pulsed neutrons experimental data for the carbon nanotubes synthesised by catalytic chemical vapour deposition. These comparisons show important influence of the Stone-Wales defects on the simulated results and their best agreement with the experimental data is obtained for 0.87% concentration of the defects.

Helical Spin Order on the Move

Magnetic materials can be thought of as assemblies of billions of miniature magnets called spins. These tiny microscopic magnets can be arranged in several possible configurations, depending on how the spins line up. When all the spins are aligned with each other, they form ferromagnets, examples of which can be found on most refrigerator doors. Here, the prefix “ferro” refers to iron, which is magnetic and naturally displays this kind of parallel-spin order. Another type of magnetic order is antiferromagnetic, in which nearby spins are oriented opposite to each other. Spin arrangements more complex than these can occur, however. An example is helical spin order (see the first figure). As its name suggests, this is a helix-like arrangement of the spins distributed along chains. Like a tiny magnetic corkscrew, the spin direction rotates around the axis of the helix (1). These microscopic arrangements of spins can be measured by techniques such as neutron scattering. Such methods, however, yield data in reciprocal space, which requires conversion to a real-space representation.

Energy relaxation and pulsed neutrons diffraction studies of carbon nanotubes

Carbon nanotubes containing non-hexagonal rings have been computer generated and relaxed by minimization of the energy using the conjugate–gradient method. Then the powder diffraction patterns have been computed and converted to a real-space representation by the Fourier transform, yielding pair correlation functions which are compared with the pulsed neutrons experimental data for the single-wall carbon nanotubes produced by catalytic chemical vapour deposition. Effects of defective graphene cylinders on the interatomic distances and the resulting structures are discussed. The obtained results are also discussed in relation to previously reported paracrystalline behaviour of the nearest-neighbours distance fluctuations.

Unrestricted TDHF studies of nuclear response in the continuum

The TDHF dynamics in the small-amplitude regime is studied in the real-space and real-time representation. The continuum is taken into account by introducing a suitable complex potential. This is equivalent to the continuum random-phase approximation and applicable to deformed nuclei.

Parity-projected Skyrme Hartree–Fock and angular momentum projection approach to Mg isotopes

We perform calculations of the variation after parity projection with Skyrme interaction for ground and excited states of even-even Mg isotopes. Using the 3D real-space representation, we can take into account any kind of deformation; e.g., cluster structure, γ-deformation. We also perform the full 3D angular momentum projection to obtained rotational spectra and B(E2). In 24Mg, the ground Kπ = 0+ and several odd-parity bands are calculated. In 30,32,34Mg, our calculation reproduces a breaking of the N = 20 magic number, so-called Island of inversion phenomena. Properties of both the ground and excited states are reasonably reproduced.

Time-dependent quasiparticle current-density-functional theory of x-ray nonlinear response functions

A real-space representation of the current response of many-electron systems with possible applications to x-ray nonlinear spectroscopy and magnetic susceptibilities is developed. Closed expressions for the linear, quadratic, and third-order response functions are derived by solving the adiabatic time dependent current density functional (TDCDFT) equations for the single-electron density matrix in Liouville space.

Optical Responses of Conjugated Polymers by TDDFT in Real-Space and Real-Time Approach

ABSTRACTThe time dependent density functional theory (TDDFT) has applied to study the optical responses of the conjugated polymers such as poly(p-phenylenevinylene) and poly(9, 9-dialkyl-fluorene). In our study, the real-space grid representation is used for the electron wavefunctions in contrast to a conventional basis set on each atom. In the calculations of the optical responses, the real-time approach is employed, where we follow the linear responses of the systems under externally applied perturbations in the real time. Since a real polymer is too large to handle, we have calculated the oligomers with different length and observed the spectrum peak is redshifted as the length of oligomer increases. The property of the polymer is extrapolated as the infinitely long oligomer. The estimated polymer spectra agree with the experiments reasonably well.

Dielectric Properties of Semiconductors by TDDFT in Real-Space and Real-Time Approach

ABSTRACTThe dielectric responses of semiconductors such as C, Ge, Si, and AlGaAs are studied by the time-dependent density-functional theory. In our study, the real-space grid representation of the electron wave functions is used and the real-time approach is employed for the dynamics of the system. Both the static and dynamic dielectric functions are calculated, and we yielded that the static dielectric constants ε(0) are especially in good agreement with the experimental values. The effect of Al-component in the compound semiconductor AlxGa1−xAs is also studied. The peaks of the imaginary part of the dielectric function change with the band separation as a function of the Al-component. Furthermore, the static dielectric constants show the expected change due to the band separation as a function of the Al-component.

On the computation of the demagnetization tensor for uniformly magnetized particles of arbitrary shape. Part II: numerical approach

In Part I, we described an analytical approach to the computation of the demagnetization tensor field for a uniformly magnetized particle with an arbitrary shape. In this paper, Part II, we introduce two methods for the numerical computation of the demagnetization tensor field. One method uses a Fourier space representation of the particle shape, the other starts from the real space representation. The accuracy of the methods is compared to theoretical results for the demagnetization tensor of the uniformly magnetized cylinder with arbitrary aspect ratio. Example computations are presented for the hexagonal plate, the truncated paraboloid, and a so-called “Pac-Man” shape, recently designed for MRAM applications. Finally, the magnetostatic self-energy of a uniformly magnetized regular polygonal disk of arbitrary order is analyzed. A linear relation is found between the order of the polygon and the critical aspect ratio for in-plane vs. axial magnetization states.

Local structure of saccharose- and anthracene-based carbons studied by wide-angle high-energy X-ray scattering

A series of porous carbon materials, produced by pyrolysis of saccharose and anthracene and heat treated at 1000, 1900 and 2300 °C have been studied by wide-angle X-ray scattering. The X-ray data were collected at European Synchrotron Radiation Facility (ESRF) in Grenoble on the ID15A beam line (high-energy X-ray diffraction) using a wavelength of E=116.2 keV, λ=0.1067 Å. The data were recorded in the scattering vector range from 0.5 to 24 Å −1 which enabled them be converted to a real-space representation via the Fourier transform. The structure of these carbons has been described in terms of a model based on disordered, graphite-like layers with very weak interlayer correlations. At higher temperatures the anthracene-based carbon transforms into graphite while the carbon produced from saccharose remains disordered. The graphitization process has been studied in detail by careful analysis of the diffraction data in real and reciprocal space.

On the computation of the demagnetization tensor field for an arbitrary particle shape using a Fourier space approach

A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given.