Nonperiodic Systems Research Articles

Direct Approach to Density Functional Theory: Heaviside−Fermi Level Operator Using a Pseudopotential Treatment

A new method is presented for calculating electron densities in nonperiodic, polyatomic systems using Cartesian coordinates in three dimensions. The method blends a direct approach to spin-density-functional theory and uses (1) the “Heaviside−Fermi level operator” h(EF − Ĥ) rather than solving Schrodinger eigenvalue problems, (2) the distributed approximating functional for discretization and interpolation, (3) a multigrid iteration procedure for accelerating the convergence, (4) a separable, nonlocal form of pseudopotential, and (5) a fast method for solving Poisson's equation in nonperiodic systems. Example calculations of the electronic structure for the Ne atom and the C2 and O2 dimers are presented.

Calculating Electrostatic Interactions Using the Particle−Particle Particle−Mesh Method with Nonperiodic Long-Range Interactions

The particle−particle particle−mesh (PPPM) method is an accurate and computationally efficient method for calculating interactions in molecular simulations. The PPPM method is based on separating the total interaction between particles into the sum of short-range interactions, which are computed by direct particle−particle summation, and long-range interactions, which are calculated by solving Poisson's equation using periodic boundary conditions (PBCs). For nonperiodic systems there is a concern that use of PBCs may introduce an artificial periodicity into the system. In this article we propose, and test, the use of boundary conditions for the long-range interactions which mimic surrounding the explicit system by high dielectric material such as water.

High-efficiency beam-wave interaction in quasiperiodic structures.

A semianalytical method for the design and analysis of high-efficienty ({gt}50%) generation of radiation in traveling output structures is presented. No {ital a} priori assumption about the functional form of the electromagnetic field is required. The concept of scalar interaction impedance used in periodic structures is generalized to a matrix in the case of a nonperiodic system. Its eigenvalue is shown to be directly related to the beam-wave interaction efficiency. The method is demonstrated with the design and analysis of a 70% efficiency system.

Electron dynamics in graded nanostructures

In this paper I describe recent work, jointly with M. Geller, treating the dynamics of electrons in semiconducting alloys, such as Al c Ga 1− c As, whose compositions, characterized by c, is a slowly varying function of position: | ▿ c( r)| b ⪡ 1, where b is a characteristic lattice spacing. The mathematical framework is provided by the so-called generalized Wannier functions (GWF) a n, l ( r) where n and l are band and site labels (for composite bands an additional label v is needed). The GWFs are generalizations to non-periodic systems of the traditional Wannier functions for periodic systems. We show that the eigenstates and frequency-dependent electric response functions can be completely described in terms of two quantities, ε n ( k; c) and p nn′ ( k; c), the energy and momentum matrix elements of the uniform alloys of concentrations c, ranging over the values of c in the non-uniform system under consideration.

Theoretical investigations of the magnetic behaviour of Cr monolayers deposited on a Fe(001) substrate: Role of a mono-atomic step

In this paper we present a theoretical study of the magnetic properties of n Cr monolayers (ML) deposited on a Fe(001) substrate. We use the real space recursion method in a tight binding framework to determine the electronic structure of non-periodic systems involving a large number of inequivalent atoms. The aim of this work is to investigate the possibility to obtain a magnetic defect in the Cr layer by frustrating the plane to plane antiferromagnetic (AF) order. First, we study the magnetism of n perfect Cr monolayers (1 ≤ n ≤ 10) deposited on a perfect (001) Fe substrate and we show that a magnetic defect can be obtained for n ≥ 6 ML but it is clearly less stable than the solution without defect. We show also that, after the deposition of 3 Fe monolayers onto the Cr, the magnetic defect is obtained for much smaller Cr thicknesses ( n ≥ 2). Then, we consider a Fe substrate presenting a mono-atomic step. We study the magnetic moments distributions during the growth process of Cr monolayers assuming that the growth starts at the step. We show that (i) the perturbation due to the step is limited to the vicinity of the step and has a small extension in the plane of the Cr layers, and (ii) a wall is generated in the Cr layer by the step and splits clearly the Cr layer into two domains. Finally, we determine the structure of collinear walls in chromium and we discuss their role on the magnetic properties.

Dynamical localization for nonperiodic systems

We consider two nonlinear kicked systems modulated according to sequences with different degrees of randomness: periodic, Fibonacci, Thue-Morse, Rudin-Shapiro and random. We have numerically found dynamical localization in the Fibonacci case for the two considered models and in the Thue-Morse case for just one of the models. We have also found examples of ballistic delocalization in the Fibonacci and Thue-Morse cases. The dynamical behaviors generated from Rudin-Shapiro and random sequences were found to be essentially equivalent.

Electronic structures of large, extended, nonperiodic systems by using the elongation method: Model calculations for the cluster series of a polymer and the molecular stacking on a surface

AbstractThe elongation method based on the molecular orbital (MO) theory, which enables us to extend a polymer with any molecular fragments theoretically, has recently been developed by our group. As the next step, we introduced an approach based on the crystal orbital (CO) theory into above treatment. In the present work, the elongation method was developed at the Hartree–Fock level with CNDO/2 parameters and applied to model systems composed of the cluster series of a polymer and the molecular stacking on a surface. In the cluster‐series calculations, the hydrogen molecule [(H2)n], hydrogen fluoride [(HF)n], polyethylene, and polyacetylene were created successively to approximate their one‐dimensional periodic polymers by using the MO‐based elongation method. In the molecular‐stacking models, we described the hypothetical surface of crystal as periodically arranged hydrogen molecules by the COs, and several hydrogen molecules were stacked up on the surface one after another with the elongation procedure. Furthermore, the lattice defect on surface in which a part of stacked layer is lacking was dealt with by our approach. We also treated carbon monoxide chemisorption on a periodic magnesium chain as a more realistic model. Results for these systems support the applicability of our method for nonperiodic interactions in one‐ and two‐dimensional large systems. © 1995 John Wiley & Sons, Inc.

Reduced density matrix solution of the coupled coherent-incoherent exciton dynamics with the effects of quenching

An effective theoretical method for the study of excitation energy transfer dynamics in molecular aggregates, based on the formalism of the reduced density matrix, has been developed. The influence of a dissipative environment has been incorporated on the microscopic level, and the new established model is applicable also to nonperiodic systems and finite temperatures. An irreversible exciton removal out of the states of the reduced density matrix by the quencher molecules has been simulated via the introduction of sink parameters into the Hamiltonian, which simulates the finite lifetime of the excitation. The proposed method yields an equation for the site probability densities which comprises the basic information on the exciton dynamics. The procedure developed avoids the necessity of the calculation of memory functions. An illustration of the application of the method to a model of a hexamer aggregate with an additional quencher placed in the middle is presented.

SIMULATION PROCEDURES IN CONDENSED MATTER PHYSICS: AN ALGORITHM ALTERNATIVE TO THE STANDARD RANDOM NUMBER GENERATORS

Numerical simulation techniques play a very important role in solid state physics, in particular, as far as the determination of electronic and vibrational structure of non-periodic systems is concerned. The basis of these techniques is the construction of a random Hamiltonian and a random state of interest; to do that, standard congruential algorithms for the generation of pseudorandom numbers are commonly used. The aim of this paper is to propose a novel, alternative way for the generation of random operators and vectors. This technique, based on the concept of minimum correlation sequence, gives results equivalent to or better than the standard approach.

Massively parallel calculations of the electronic structure of non-periodic micro-crystallites of transition metal oxides

We report massively parallel computations of the electronic density of states of a non-periodic micro-crystalline of rutile TiO 2 with a sample of 491 520 atoms. Mathematically, the problem is equivalent to solving an n× n eigenvalue problem, where n ∼ 2 500 000. We used MasPar MP-1 and MasPar MP-2 autonomous SIMD computers with up to 16 384 processing elements (PEs) with the entire computing time ∼ 1.5 h (on 4K MasPar MP-2). We used the equation of motion method and the non-trivial tight binding model in our calculations and conclude that these methods when implemented on the massively parallel SIMD computer architectures, are very well suited for studying the electronic structure of complex non-periodic systems with both point and extended defects.

W-geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Pl\"ucker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding K\"ahler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Pl\"ucker embedding. These conditions are automatically fulfiled when Toda equations hold.

Existence of exponentially localized Wannier functions for nonperiodic systems.

For a large class of nonperiodic systems, exponentially localized Wannier functions, associated with isolated parts of the energy spectrum, are proved to exist.Received 15 October 1992DOI:https://doi.org/10.1103/PhysRevB.47.10112©1993 American Physical Society

Electron transport in non-periodic systems including amorphous metals and quasicrystals

Amorphous metals, quasicrystals, their related approximants and Si:P crystalline semiconductors are selected as non-periodic systems possessing different degrees and features in randomness of their atomic arrangements. Our aim is to discuss their electron transport mechanisms in as unified a picture as possible. The physical role of the electron diffusion coefficient D, defined as the ratio of the conductivity over the density of states at the Fermi level, is clarified by relating it to the g-factor originally introduced by Mott as a parameter to express the degree of electron localization. We claim that not only the extent of the Boltzmann-type transport mechanism but also the electronic structure dependent localization effects can be clearly envisaged on the D- ϱ diagram. The origin of a large resistivity observed in the AlMnSi 1 1 - approximant is also discussed with the help of the D- ϱ diagram.

An exact method to solve the diluted extended Hubbard model

In this paper, we report a new method to find an exact solution of the extended Hubbard Hamiltonian for systems with a low electronic density. This method is based on mapping the original problem onto a tight-binding case in a higher dimensional space, which can be solved exactly. For one- and two-dimensional systems, the local pairing problem of two electrons with anti-parallel spins is analyzed by looking at the binding energy and the coherence lenght for different interaction regimes. This method can be applied to study the electronic correlation in non-periodic systems.

Substitutions, Finite Automata and Number Systems

Recently, nonperiodic deterministic physical systems modeled on substitutional sequences generated by morphisms from A into A*, A being a finite alphabet, have been studied extensively. For morphisms A → A k , the resulting substitutional sequences (uniform tag sequences) have been known to be k-automatic. Here, the tag sequences are generalized, and all substitutional sequences are shown to be automatic in a certain sense

Substitutions, Finite Automata and Number Systems

Recently, nonperiodic deterministic physical systems modeled on substitutional sequences generated by morphisms from A into A*, A being a finite alphabet, have been studied extensively. For morphisms A →Ak, the resulting substitutional sequences (uniform tag sequences) have been known to be k-automatic. Here, the tag sequences are generalized, and all substitutional sequences are shown to be automatic in a certain sense.

Derivation of the sink model

Standard two-site Generalized (to nonperiodic systems and finite temperature) Stochastic Liouville Equation model is rigorously reduced, using a partitioning projector, to a single-site model with a sink. Under some additional restrictive assumptions, the usual single-site sink model is reproduced. Repeating the reasoning under the same assumptions for a more-site model, the resulting sink model is identified with that in the version by capek and Szocs. It is argued that the original sink model by Kenkre cannot be derived in this or any other rigorous way.

The application of reverse flow reactors to endothermic reactions

The concept of the reverse flow reactor traditionally used for mildly exothermic reactions has been extended to endothermic reactions and applied to the dehydrogenation of ethylbenzene. Periodic alternation of a reactant and a regenerating medium countercurrently over a fixed bed of catalyst in endothermic processes can be shown to result in higher conversions than traditional non-periodic systems. With this configuration several new process parameters are introduced such as total cycle time and the ratio of countercurrent flows. By judicious choice of operating conditions the hottest point of the reactor can be placed at the exit of the reactant stream allowing for much more favourable equilibriums and outlet conversions than if it were the coldest spot in the reactor as is common in steady-state processes. Two types of modeling are utilized. The first employs a technique which assumes that the switching is so rapid that the temperature distribution in the catalyst is in time independent steady-state. This high switching frequency model is compared against a more complicated time dependent dynamic model which traditionally is employed in reverse flow systems. Results for the first model are shown to be the limiting case of the dynamic model with fast switching. The models show significant conversion improvement with respect to existing steady state processes.

Basis set for the electronic states in solids.

We present a basis set for studying the electronic structure of large nonperiodic systems. This basis permits the solution of single-particle Hamiltonians with superpositions of atomic potential operators. The basis set is chosen so that it is sparse in the kinetic-energy and atomic-potential operators, to allow for the rapid solution of electronic-structure problems with the recursion method. Solutions are computed to machine precision or with minimal approximation. Only two-center integrals are required. We demonstrate the application of these basis sets to problems with over 1000 model atoms. The scaling and computational expenses are discussed for calculations in the free-particle and tight-binding limits with this basis.

First-principles linear muffin-tin orbital atomic-sphere approximation calculations in real space.

We have developed an approach, based on the linear muffin-tin orbital atomic-sphere approximation (LMTO-ASA) formalism and the recursion method, that allows us to perform first-principles density-functional calculations of electronic structure in real space. Using ${\mathrm{Zr}}_{2}$Fe as a test case, we compare our results with those obtained by using the standard reciprocal-space LMTO-ASA method. The scheme described here can be applied to nonperiodic systems and is also very useful in the study of complex metallic systems with a large number of atoms per unit cell. To illustrate the application of the first-principles real-space approach to a complex system, we calculate the electronic structure for a cluster of amorphous Zr. We use our results to evaluate the distribution of charge transfer among the sites of this randomly packed system. As a first guess we take the potential parameters to be the same for all atoms. The final self-consistent results show charge transfers that are almost an order of magnitude smaller than the ones obtained in the initial run. The major effect of the self-consistent process in this case is to rearrange the center of the bands in order to screen large charge fluctuations. This explains why the parametrized LMTO-ASA approach, where the relative position of the bands is fixed using approximate charge neutrality, works so well when applied to transition-metal alloys.