Negative Eigenvalue Theorem Research Articles

Theoretical Designing of Novel Donor Acceptor Type Copolymer Comprising of Thiophene

Using ab initio band structure results of three novel donor acceptor polymers (A)x PCDT, (B)x PMCT and (C)x PFTh as the input, the electronic structures and conduction properties of their periodic and aperiodic copolymer (AmBnCk)x have been investigated. The method involves using negative factor counting method based on Dean’s negative eigenvalue theorem. In this article, the quasi-one-dimensional Type II staggered copolymers comprising of thiophene units on the basis of the band alignments of the constituent homopolymers were studied. The trends in their electronic structures and conduction properties as a function of (i) block sizes (m, n, k) and (ii) arrangement of the blocks (periodic or aperiodic) in the various copolymer chains are discussed. These trends are important guidelines to the experimentalists for designing novel electrically conducting polymers with tailor made conduction properties.

Dimensionality-induced effects on transport properties of poly(G)–poly(C)

We consider a ladder model of DNA for addressing the relation between the transport properties and electronic structure and the interbase coupling in poly(G)–poly(C). Based on the negative eigenvalue theorem and transfer matrix method, the density of states and current–voltage characteristics are evaluated, and an expression for the dependence of the band gap on intra- and inter-strand nucleobase couplings is proposed. There exists a semiconducting-metallic transition in poly(G)–poly(C) by modulating the interbase coupling, and the physical nature is traced back to dimensionality-induced effects. Our results provide possibility for interpreting a variety of transport behaviors observed in DNA molecules.

Molecular designing of copolymers of donor–acceptor polymers based on polythiophene

Using the ab-initio band structure results of polycyclopentadithiophene-4-one (PCDT) and polydicyanomethylenecyclopentadithiophene (PCNTh) (the two known conjugated polymers consisting of successive bithiophene units bridged by an electron-accepting carbonyl group in PCDT and a dicyanomethylene group in PCNTh), the electronic density of states (DOS) of the various copolymers of PCDT and PCNTh (AmBn)x, (A=PCDT; B=PCNTh) has been determined using the simple NFC method on the basis of Dean's negative eigenvalue theorem. The trends in their electronic structures and conduction properties as a function of (1) composition (m/n); (2) block sizes m and n and (3) arrangement of the blocks in the copolymer chain are discussed for both periodic and aperiodic distributions.

Two-dimensional kinetics of binary nucleation in sulfuric acid–water mixtures

Homogeneous nucleation theory for binary mixtures is developed as a two-component extension of the classical multistate kinetics rate theory. A matrix formulation, based on the stochastic model of Shugard and Reiss [J. Chem. Phys. 65, 2827 (1976)], provides the framework for solving the strongly coupled two-dimensional flux network associated with tracking the evaporation and growth kinetics of each component for several thousand binary clusters, of varying composition, throughout the region of critical size. This approach avoids the assumption of a single nucleation path, e.g., through the saddle point of the binary free-energy surface, and considers, instead, all possible paths whose current density contributes to the nucleation rate. Calculations are presented for the steady-state nucleation rate and, by a new method based on the negative eigenvalue theorem, for the distribution of relaxation times in sulfuric acid–water mixtures. At water relative humidities typical of the atmosphere, quantitative agreement with the predictions of a closed-form rate expression due to Shugard et al. is found. At high supersaturations, typical of diffusion cloud chamber operation, the nucleation current is found to bypass the saddle point, due to kinetic forcing, resulting in a higher-than-expected nucleation rate.

Electronic properties of the generalized Fibonacci lattices: energy spectrum and wavefunction

The authors study the electronic properties of a one-dimensional diagonal tight-binding model with potentials (Vn) arranged in generalized Fibonacci (GF) sequences. Using the negative-eigenvalue theorem, they calculate the density of states (DOS). The DOS and the V dependence of energy spectra for silver-mean (SM) and copper-mean (CM) series clearly show distinctive features. The relation of the energy spectral feature to the geometry of the underlying lattices is emphasized. Various states of the CM lattice are examined in detail by means of wavefunctions, resistances and a multifractal analysis. Critical states are characterized both by scaling transformations and by multifractal behaviours. They find that states with a strongly localized wavefunction under a given system size exhibit additional wavepackets with increasing system size. This shows that the localized behaviour of allowed states is a feature of the finite size of the system, and implies the absence of strongly localized states in a system of infinite size.

Electronic and Vibrational Properties of One‐Dimensional Quasi‐Crystals

AbstractThe electronic structure of a one‐dimensional quasi‐crystal in the form of a Fibonacci sequence in tight‐binding model is extended to include next nearest neighbor couplings in addition to the nearest neighbor couplings previously included. The vibrational properties are also studied using negative eigenvalue theorem. The results of density of electronic states and square phonon frequencies are presented.

Self‐Consistent Field Approximation for the Vibrational Spectra of Quaternary Alloys

AbstractA mean‐field approach is applied to the lattice dynamics of quaternary alloys. Specific results are obtained for the quaternaries AlxGa1−xAs1−yPy and GaxIn1−xP1−yAsy. Calculations are restricted to a mass‐disordered linear chain model. For the end‐member components the approach reproduces the results of the coherent‐potential approximation (CPA). The cluster density of states of eight atoms embedded in the mean‐field effective medium is compared with the numerical spectrum obtained for a 20000‐atom random chain by using the negative eigenvalue theorem. The predictions of the calculated mean‐field dielectric susceptibility agree at least qualitatively with experimental results. With some qualifications the approach can explain the change of mode behaviour within the composition range, as it is expected to occur in some III–V quaternary alloys.

Numerical computation of the density of states for disordered magnetic chains

Using the negative eigenvalue theorem we compute the density of magnon states for a disordered magnetic chain of 5 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ spins. Good agreement is obtained with the asymptotic expansion of the coherent potential approximation for a half-Gaussian distribution of nearest-neighbor interactions.

Bipolaronic states in doped polyacetylene from electronic and vibrational densities of states by negative eigenvalue theorem

It is shown that the negative eigenvalue theorem is a useful numerical tool for the calculation of the electronic density of states for disordered one-dimensional systems in the Hueckel approximation. Application is made to the case of doped polyacetylene when a random distribution of centro-symmetrical defects is considered.

Densities of electronic states for tight-binding two-dimensional square-lattice ternary alloys AxB1− xC

The densities of electronic states for model two-dimensional A x B 1− x C tight-binding alloys are calculated for 10 4-atom crystals, using the negative eigenvalue theorem.

Density of states for the two-dimensional, simple-square Anderson model

By means of the negative eigenvalue theorem, the density of states is evaluated for the two-dimensional, simple-square Anderson model with diagonal disorder.

Electronic density of states of a stereo-irregular polyethylene

The electronic density of states for a stereo-irregular model of polyethylene is calculated by the generalised negative eigenvalue theorem within the framework of the extended Huckel molecular orbital theory. The results are in good agreement with photo-electron spectra. Assignment of bands is possible by comparison with results on periodic chains.

Vibrational spectra of one-dimensional mass-disordered quaternary alloys

The spectral density of vibrational states for one-dimensional mass-disordered quaternary alloys A y B 1− y C 1− x D x is evaluated using the negative eigenvalue theorem. Spectra for masses corresponding to Al yGa 1−yAs 1−xP x are presented.

Analytic conditions for the existence of localized electron states in a linear chain with an arbitrary number of impurities

The effective Hamiltonian and the negative eigenvalue theorem are used to obtain an analytic formula for the integrated density of electron states in a linear chain with an arbitrary number of impurities within the tight binding approximation. From this formula, the analytic conditions for the existence of localized electron states lying above or below the band of states of host atoms are obtained. The way of obtaining the energies of localized states and the form of eigenvectors are also discussed.

Density of States for a Three-dimensional Disordered Alloy

Abstract Densities of states for three-dimensional models of binary alloys are calculated with a method based on the negative eigenvalue theorem. Comparison is made with the densities of states obtained by diagonalizations of the Hamiltonian for a certain number of physically different clusters of impurities.

Analytic conditions for the existence of localized electron states in linear chains with two impurities

The negative eigenvalue theorem is used to obtain an analytic result for the integrated density of electron states in several types of low-dimensional lattices with two impurities in the tight binding approximation. From this expression, analytic conditions for the existence of localized electronic states are obtained. The result is directly applicable to the problem of surface states and that of chemisorption on a linear chain.

Lattice dynamics of mixed crystals: HCl–DCl

The method of ``negative eigenvalue theorem'' has been applied for the determination of the vibrational density of states of mixed crystals of HCl and DCl. The corresponding atomic motions have been derived, thus making it possible to understand the dynamics of these systems. The fitting with the infrared spectrum has been obtained by weighting the density of states with a transition moment based on a rigid ion assumption.

The vibrational spectrum of the disordered hydrogen bonded chain

The vibrational spectra of disordered hydrogen bonded chains are calculated for various degrees of disorder using the negative eigenvalue theorem. The disorder is involved in the distribution of the protons between left and right minima in the double minimum potential. The spectra are compared with the most simple configurations of ordered structure in the chain. Some sample eigenvectors corresponding to the frequencies of maximal density of states are also presented.

Vibrations of Glasslike Disordered Systems. II. The A2B3 Network in Two Dimensions—Application to Vitreous As2Se3 and As2S3

A computer-generated two-dimensional A2B3 glasslike disordered network having a Gaussian distribution of A–B–A bond angles has been formulated as an approximate model of the vitreous layer-type chalcogenides As2Se3 and As2S3. A two-parameter potential function involving nearest-neighbor central and noncentral interactions has been used to generate the equations of motion which have been solved by application of the negative eigenvalue theorem. Under the appropriate choice of boundary conditions, the bands in the computed densities of states adequately reproduce those in the experimental spectra in number and position. Eigenvectors have been computed for selected frequencies throughout the spectra, and assignments of observed spectral bands to specific normal modes have been formulated.

Vibrations of Glasslike Disordered Systems. I. Diatomic Chains in Two Dimensions

A computer program has been written to generate disordered, two-dimensional chains of randomly oriented B–A–B V-shaped units with a Gaussian distribution of bond angles between successive units. The radial distribution function of the system shows it to be essentially vitreous in that it exhibits only short-range order. The equations of motion are derived using a simplified valence force potential function, and the distribution of squared normal mode frequencies is obtained using the negative eigenvalue theorem. The frequency spectra are discussed in terms of the ordered chain in two dimensions and the glasslike disordered chain in one dimension. The existence of a band gap is confirmed, but the size and position are complicated by the disorder of the system, as is the over-all shape of the spectrum. A feature in the spectra, near the LO zone-edge frequency of the ordered chain, is found to be the result of wavelength-dependent coupling between “transverse” and “longitudinal” vibrations. The more general results of the present calculations appear applicable to three-dimensional models.