Narrow Results

We describe a heuristic algorithmic procedure by which a large number of points of minimal energy in configuration space of a polyatomic molecular system (isomers) can be determined. Making use of the intrinsic electronic structure energy scheme of the molecular system, the procedure is initiated from an arbitrary starting configuration and progresses via successive vertical spin, and/or charge state shifts with interposed optimization steps. In this systematic way, a great manifold of stable isomers not only on the ground state potential energy surface but also on excited spin and charge state surfaces can be located. The efficiency and computational practicability of the procedure has been tested on various examples. In these cases, the global minima have been found. Results for singlet and triplet states of the system P₄ are presented in detail.

We present a theoretical study of electronic states and magnetization of two interacting electrons confined in coupled quantum dots (CQDs) presented in a magnetic field. We obtain the eigenenergies of the CQD by solving the relative two-dimensional (2D) Hamiltonian using the combined variational–exact diagonalization method. The dependence of magnetization on temperature, magnetic field strength, confining frequency and barrier height has been investigated. We have shown the singlet–triplet transitions in the ground state of the CQD spectra and the corresponding jumps in the magnetization curves. The comparisons show that our results are in very good agreement with the reported works.

The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is $Ln=n\hslash$. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.

We have made the PL measurements on ruby at room temperature and 4.2 K. The characteristic R₁ and R₂ lines of chromium in ruby are found to be absent in the spectra recorded at 4.2 K. Instead of these characteristic lines a band centered on 1.6 eV is observed. A possible explanation has been discussed in terms of co-existence of the two electronic states due to presence of Cr³⁺ and Cr⁴⁺ ions in the ruby lattice.

In this paper, we present a novel method to study the electronic density-of-states of intercalation materials. We present evidence that electrochemical quasi-steady state potential curves of a number of materials exhibit fine structure in striking agreement with the density of electronic states, as obtained from ab initio calculations. The ability to probe the electronic structure by our electrochemical technique seems, in most cases, to be restricted to disordered materials. We suggest that localization of the band states is essential, in order for the technique to give a good picture of their density. The electrochemical density of states is often smaller than the computed one due to kinetic effects, i.e. very slow relaxations of the charge carriers. Our highly sensitive electrochemical method opens new vistas for studying the electronic structure of disordered materials, that can be intercalated with an ionic species.

Electronic States of Si and Ge QDs of 5 to 3127 atoms with saturated shapes in a size range of 0.57 to 4.92 nm for Si and 0.60 to 5.13 nm for Ge are calculated by using an empirical tight-binding model combined with the irreducible representations of the group theory. The results are compared with those of Si and Ge quantum dots with spherical shape. The effects of the shapes on electronic states in QDs are discussed.

A comprehensive ab-initio investigation of the stability, structural, electronic, optical and Raman-active properties has been performed for the small diameter armchair carbon nanotubes. A number of new features not discussed earlier are observed in the present study. The binding energies (BEs) for the ultrathin nanotubes with respect to the graphine sheet are negative and the magnitude of the negative BE decreases with the diameter of the tube approaching zero for the graphine sheet. The separation between the two van Hove singularities (vHs) around the Fermi level increases with the diameter of the tube. The main absorption arises from the transitions between the states at nonzero values of k_z lying in the range 0.38–0.50. There is a large variation in the magnitude of the optical matrix-element with the wave vector. The energy range of the strong optical absorption increases with the diameter of the tube. The presently predicted absorption and the RBM frequencies are in good agreement with the available experimental data. The variation of the radial breathing mode (RBM) frequency with diameter "d" of a tube obeys a relation which is very close to an experimentally determined relation obtained for a number of wide semiconducting nanotubes possessing a wide range of chiral angles.

Space-charge spectroscopy was employed to study electronic structure in a stack of four layers of Ge quantum dots coherently embedded in an n-type Si(001) matrix. Evidence for an electron confinement in the vicinity of Ge dots was found. From the frequency-dependent measurements the electron binding energy was determined to be ~50 meV, which is consistent with the results of numerical analysis. The data are explained by a modification of the conduction band alignment induced by inhomogeneous tensile strain in Si around the buried Ge dots.