Electronic Eigenvalues Research Articles

Orbital polarization in narrow band systems: Application to the volume collapse in Ce

A novel technique for treating orbital polarization is presented. The single electron eigenvalue shifts that emanated from the orbital polarization are of the form − E 3 Lm l , where E 3 is the Racah parameter, L is the orbital moment and m l the azimuthal quantum number. Thereby the effect of Hund's second rule is included not only in the total energy, but also in the eigenvalue splittings which are required in the energy band calculation for the solid. The calculations also incorporate the exchange and correlation potential in the local spin density approximation as well as the spin-orbit coupling. The self-consistently calculated equation-of-state for the light lanthanide Ce is presented. The observed volume collapse is well described by the parameter free calculations and accordingly the volume collapse in Ce is described as a Mott transition of the 4f electron.

Theoretically-derived, energy-based criteria for aromaticity

Previous energy-based criteria for aromaticity developed from one electron eigenvalues (using methods ranging from Huckel to ab initio calculations) have not correlated well with experimentally derived criteria such as χ or chemical reactivity data, and are particularly poor for heteroaromatic compounds. Previous work has shown that criteria derived from the lowest π molecular orbitals of heteroaromatic compounds correlate well with χ and chemical reactivity, prompting us to modify Kollmar's procedure for determining aromatic stabilization energies by localizing the lowest π orbital rather than the entire π bonding manifold. This modified procedure was implemented with both the natural (NLMO) and Boys orbital localization methods, and was applied to a set of ten five-membered ring heteroaromatics and to pyridine and its diazine derivatives. The new criterion ΔπL correlated well with χ (R2 = 0.86 (NLMO); R2 = 0.92 (Boys)) for five-membered rings, and with theoretical measures of aromaticity for both sets of heteroaromatics. The Boys procedure gave better overall correlations and was markedly superior for pyrazole and pyridazine.

The atomic and electronic structure of metallic glasses: search for a structure-induced minimum in the density of states

The atomic and electronic structures of amorphous and crystalline Mg-Zn alloys are studied by computer simulation, electronic band-structure calculations and photoemission measurements. The spectra for the metallic glasses and for pure crystalline zinc show a narrow band of Zn 3d states centred at a binding energy EB of about -9.7 eV, overlapping the bottom of a broad sp band. There are indications of a minimum in the electronic density of states at the Fermi level for the glasses and for the pure metals. Molecular dynamics and potential-energy mapping calculations based on pseudopotential-derived interatomic forces are used to construct models for the atomic structure, with no other input than the composition and the atomic numbers and atomic weights of the components. The analysis of these models-which are in reasonable agreement with X-ray and neutron diffraction data-shows that the local topology of the glassy structure is very similar to that of the stable crystalline intermetallic compounds. The glassy structure is best described as a disordered tetrahedral close packing with a weak tendency to chemical short-range order whose precise degree remains to be detailed. The linearised muffin-tin orbital method in the atomic sphere approximation is used to perform self-consistent calculations of the electronic DOS of crystalline Mg and Zn, of the hexagonal Laves phase MgZn2 and of 'amorphous' supercells (each containing 60 atoms) representing glassy MgZn2 and Mg7Zn3 alloys. In each case the authors find a minimum in the DOS at EF, and d bands centred at EB approximately=-7.5 eV. A transition-state calculation shows that the d-band position in the photoemission spectra is shifted relative to the electronic eigenvalue due to self-energy corrections. Photoemission and X-ray emission intensities are calculated from the partial local DOS and the self-consistent potentials in a single-scatterer final-state approximation. The comparison with experimental confirms the validity of the electronic structure calculations. The work represents one of the first ab initio calculations of the atomic and the electronic structure of a metallic glass, and the first confirmation of the existence of a minimum in the electronic DOS at EF. The relevance of the DOS minimum to the structure-potential relationship and to the stability of the glassy phase is discussed.

Interplay between the geometry and the electronic shell model in small metal clusters

Electronic structures and geometries of clusters of simple metals are calculated using the local density approximation and model pseudopotentials. Systematic studies of clusters consisting of mixtures of monovalent and divalent pseudopotentials show that the total energies of the clusters and the single electron eigenvalues are well understood in terms of the simple spherical model. It is shown that the magic number 8 is determined by the filling of the single-electron levels and is not affected by actual ground state geometries of the clusters.

Optical Properties of Quasi‐1D n‐Merized Molecular Semiconductors

AbstractInteracting dimers and trimers in quasi‐one‐dimensional organic semiconductors are modelled by a linear supercluster of six molecules. The general expression for the complex frequency‐dependent conductivity of the compounds composed from such superclusters is derived and the electron coupling to the totally symmetric intrameolcular modes of vibration is taken into account. Electron eigenstates and eigenvalues of the supercluster are calculated in terms of Hubbard model in the limiting case of infinite Coulomb repulsion (U → ∞). Explicit calculations of the real part of the complex conductivity predict the shift of electronic excitation band to the lower energy as the interaction between dimers or trimers increase.

Symmetry of electronic states in garnets

The paper presents the classification of the electronic empty lattice eigenvalues and the classification of the Bloch sums for the garnet structureIa3d (Oh10) at the symmetry pointsΓ, H, P, andN of the Brillouin zone. This provides a starting point for the energy band studies of these technologically important materials.

Selfconsistent Discrete Equations for Nonlinear Defects in Peierls Systems with Broken Electron–Hole Symmetry

AbstractThe SSH‐Hamiltonian extended by long‐range hopping parameters and long‐range interatomic elastic forces is investigated. A discrete system of electron eigenvalue equations together with self‐consistency conditions for atomic displacements is derived and numerically solved for soliton states in polyacetylene. As a novel feature it is found that (1) the soliton level is slightly shifted from the exact midgap position and (2) a weak internal charge structure appears for neutral solitons and antisolitons and gives rise to a long‐range repulsive interaction between them.

A Higher Order Approximation for the Electronic Structure of Hydrogen in Metals

A functional energy difference method based on first principles is used to calculate the electronic contribution to the storage energy of hydrogen impurities in metals. That electronic problem is treated in a higher order approximation which means considering the coupling between one-electron wavefunctions and three-particle amplitudes. A formalism is presented to eliminate all higher order correlations and to reduce the whole system to a one-particle Schrödinger equation with the help of a suitable G reen’s function. The resulting one-electron eigenvalue problem contains some logarithmic singularities due to the fact that there is no gap between occupied and unoccupied electron states in the band structure of a metal. In an electron gas model a convergent theory is reached by an improvement of the Green’s function leading to a screening of the long-range Coulomb potentials. The result is a complicated non-linear algebraic eigenvalue equation which is solved numerically for the special case of a single hydrogen perturbation in a magnesium crystal. The solution shows the influence of higher order electron correlations on the electronic energy eigenvalue of an interstitial hydrogen centre plot as a function of host lattice distortions.

Yukawa potentials for atomic negative ions

For the purpose of calculating bound-state properties (e.g., energy levels) and scattering properties (e.g., cross sections) of atomic systems, we seek a precise independent-particle model (IPM) for electrons in atomic negative ions from Z=3 up to Z=85. The IPM potential is a combination of two Yukawa potentials whose strengths and ranges are functions of two adjustable parameters. The parameters are varied until the inner energy levels are close to the experimental energy levels of neutral atoms, and the last electron eigenvalue is precisely equal to the electron affinity of negative ions. Systematic trends in the parameters are determined.

On the optimization of gaussian basis sets for hartree-fock-dirac calculations

Gaussian basis sets for atomic one-electron systems have been optimized by straight minimization of the electronic ground-state eigenvalue of the finite basis set representation of the Dirac operator, using the “kinetic energy balance” procedure in conjunction with appropriate additional variational freedom. The results, which are apparently upper bounds, are presented and compared with previous data.

Electronic Structure of a Single Hydrogen Centre in Magnesium Crystals

In the present work, the problem “hydrogen storage in metals” is treated with the aid of the so-called New Tamm-Dancoff (NTD) procedure. We employ this method in lowest approximation for the evaluation of the electronic energy difference eigenvalue between a metal crystal with and without hydrogen centre. As an example we use Magnesium with hexagonal structure. For this system we calculate the difference eigenvalue with dependence on the displacement of the nearest neighbours and next nearest neighbours of the hydrogen centre, respectively. Finally we calculate the radial electron density distribution in the environment of the proton.

Calculation and spectroscopic assignment of charge-transfer states in solid anthracene, tetracene and pentacene

The Fourier-transform method of calculating polarization energies is used to evaluate the energies of electron-hole pairs in anthracene, tetracene and pentacene crystals as a function of separation, r. Charge-quadrupole interactions are included which refine and extend previous calculations on anthracene. Detailed analysis of the long-range behaviour shows that the total electrostatic energy has the coulombic 1/r dependence, mediated by an apparent dielectric constant which depends on direction, varying more weakly than the dielectric tensor itself and in the opposite sense. The calculated charge-transfer (CT) energies determine the potential for the CT eigenstates of the crystal hamiltonian. Several methods to approximate these states are discussed and a generalization of the Merrifield-Choi model is adopted for their description. It is shown that the lowest CT state is split by electron-transfer interaction between translationally equivalent molecules in the unit cell. By combining the calculated electronic eigenvalues with the expected vibrational structure of the CT states, a satisfactory assignment is obtained for all CT bands observed by Sebastian, Weiser, Peter and Bassler in the electro-absorption spectra of anthracene, tetracene and pentacene. This assignment is shown to be in qualitative agreement with the observed intensity distributions. The results of this spectroscopic analysis are compared with observed yields of optically generated charge carriers produced by isothermal dissociation of CT states. The available experimental results are shown to be consistent with the assumption that this process involves direct optical population of both electronic and vibronic CT levels, the latter relaxing vibrationally before (or independent of) their diffusive dissociation.

Hot-electron magnetophonon spectroscopy on micron- and sub-micron-size n+nn+GaAs structures

Magnetophonon resonance is used to study electronic conduction processes in a series of short n+nn+GaAs sandwich structures with active (n) layer thickness between 0.25 and 9 mu m for E up to 20 kV cm-1and B up to 18 T. The high electric fields induce a new contribution to sigmaxx, quasi-elastic inter-Landau-level scattering. The onset condition for this process can be derived from the properties of the electron eigenfunctions and eigenvalues in crossed E and B fields. A possible relation between this process and the destruction of the non-dissipative current in the quantum Hall effect is discussed. Electric-field-induced damping of the amplitudes of the magnetophonon extrema is reported and discussed in terms of the intracollisional field effect and the theory of Barker.

Potentials for atomic negative ions

For the purpose of astrophysical, aeronomical, and laboratory applications, we seek a precise independent-particle model for electrons in atomic negative ions from $Z=3$ up to $Z=85$. We obtain analytic potentials whose inner energy levels are close to the experimental levels of neutral atoms but whose last electron eigenvalue is adjusted so as to be in precise agreement with the electron affinity of negative ions. Systematic trends in the potential parameters are discussed.

Electronic aspects of enzymatic catalysis

AbstractEnzymes are large aperiodic structures and this hinders both ab initio molecular orbital and Bloch‐type band theory of calculations. A frontier orbital perturbation theory of catalysis is applied to enzymes. Reasons are given for proposing that the induced‐fit conformational changes, essential to enzymatic catalysis, leads to an increase in the electronic eigenvalue density at the active site, enhancing the necessary catalytic orbital perturbation.

Electronic energy-levels in dense plasmas

Modern inertial-confinement fusion experiments subject matter to extreme physical conditions previously studied only in theoretical astrophysics. At very high plasma density, atomic energy states are significantly altered by electric fields of neighboring ions and by free electrons; the resulting phenomena of pressure ionization and continuum lowering may be analyzed with a sequence of models, each adding new subtleties to a complex picture. In this paper, we develop a simple parameterization of pressure ionization, discuss limitations of the Debye-Huckel model for plasma perturbations, and survey an approximate description of X-ray spectra based on the WKB approximation. WKB theory leads to a simple derivation of the screened hydrogenic model for plasma ionization and radiative properties. Electron eigenvalues are obtained from the total ion energy in agreement with Koopman's theorem, and the representation of spectral terms is improved by a new set of screening coefficients.

Pressure effects on bonding in CaO: Comparison with MgO

The electronic charge distribution and eigenvalues of B1 and B2 CaO were obtained through a set of self‐consistent band structure calculations. The zero pressure electron density is in good agreement with the available X ray determination. The results of the calculations demonstrate that bonding in essentially ionic oxides involves considerable delocalization of the valence electrons. This conclusion is supported by the X ray data and by molecular orbital calculations. A comparison of the electronic structures of MgO and CaO shows that they are consistent with expected trends in ionicity. However, large compressions tend to invert the relationship, with predicted compressions at metallization being lowest for BaO and highest for MgO. Pressure induced changes in the bonding of MgO differ significantly from the corresponding changes in the heavier alkali‐earth oxides because of the presence in the latter of low‐energy d bands. It is suggested that under compression, d bands move down relative to other conduction bands and the valence band. The mechanism that causes this may be quite general and is expected to play a significant role in the optical properties of high pressure transition metal‐bearing minerals. In particular, it is possible that this mechanism is responsible for the pressure‐induced opacity to thermal radiation.

Independent-particle models for light negative atomic ions

For the purposes of astrophysical, aeronomical, and laboratory application, we seek a precise independent-particle model for electrons in negative atomic ions of the second and third period. The optimum-potential model (OPM) of Talman et al. is first used to generate numerical potentials for eight of these ions. Results for total energies and electron affinities are found to be very close to Hartree-Fock solutions. However, the OPM and HF electron affinities both depart significantly from experimental affinities. For this reason we develop two analytic potentials whose inner energy levels are very close to the OPM and HF levels but whose last electron eigenvalues are adjusted precisely with the magnitudes of experimental affinities. These models are (1) a four-parameter analytic characterization of the OPM potential and (2) a two-parameter potential model of the Green, Sellin, Zachor type. The system ${\mathrm{O}}^{\ensuremath{-}}$ or $e$-O, which is important in upper atmospheric physics is examined in some detail.

The effective interaction arising from the irregular surface of a small metallic particle

The calculation of the eigenvalues of free electrons, confined by an irregular surface, is transformed into that of electrons confined by a spherical surface, but subject to an effective interaction. A perturbation series is developed to investigate the spacing distribution of electrons in small, irregular metallic particles at low temperatures.

On the Electronic Molecular Structure of the Organic Semiconductor Copper Phthalocyanine

AbstractThe electronic eigenvalue problem of the molecule of copper phthalocyanine is approximated using the molecular orbital formalism. The symmetry of the molecule allows a group theoretical reduction of the secular equations and a classification of the eigenvalues and eigenfunction coefficients. The model statements are compared with the experimental molecular spectra in the vapour phase and in solution from the near UV to the near IR.