Relativistic calculations of atomic structure

A review of relativistic atomic structure calculations is given with a emphasis on the Multiconfigurational-Dirac-Fock method. Its problems and deficiencies are discussed together with the contributions which go beyond the Dirac-Fock procedure.

Calculations of the polycentric linear molecule H^2+_3 with the finite element method

A fully numerical two-dimensional solution of the Schrödinger equation is presented for the linear polyatomic molecule H^2+_3 using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the 1\sigma and 2\sigma orbitals is of the order of 10^-7 au.

Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method

We report on the self-consistent field solution of the Hartree-Fock-Slater equations using the finite-element method for the three small diatomic molecules N_2, BH and CO as examples. The quality of the results is not only better by two orders of magnitude than the fully numerical finite difference method of Laaksonen et al. but the method also requires a smaller number of grid points.

Relativistic atomic level calculations with nuclei carrying additional fractional charges

One-electron energy levels and wavelengths have been calculated for Na-like ions whose nuclei carry quarks with additional charges ±e/3, ±2e/3. The calculations are based on relativistic self-consistent field procedures. The deviations from experimental values exhibit regularities which allow an extrapolation for the wavelengths of 3s - 3p, 3s - 4p, 3p - 3d, and 3p - 4s transitions for the nuclear charge Z = 11± 1/3, ±2/3. A number of transitions are found in the region of visible light which could be used in an optical search for quark atoms.

Model calculations on the influence of quantum electrodynamical effects on the chemistry of superheavy elements.

Using a phenomenological model, the influence of quantum electrodynamical effects on the prediction of the chemical behavior of superheavy elements within a relativistic Dirac-Slater calculation was investigated. This influence will be small and nondetectable for elements up to Z = 114. For elements near Z = 164 some changes in the ground state configurations occur but the chemical behavior will not change. Using this heuristic model, it is also possible to calculate elements beyond Z = 175. As an example we have chosen element E184 and are now able to make more valid speculations about the chemical behavior of the element than Penneman and co-workers could.

Ionization potentials and radii of atoms and ions of element 104 (unnilquadium) and of hafnium (2+) derived from multiconfiguration Dirac-Fock calculations

Multiconfiguration relativistic Dirac-Fock (MCDF) values have been computed for the first four ionization potentials (IPs) of element 104 (unnilquadium) and of the other group 4 elements (Ti, Zr, and Hf). Factors were calculated that allowed correction of the systematic errors between the MCDF IPs and the experimental IPs. Single "experimental" IPs evaluated in eV (to ± 0.1 eV) for element 104 are: [104(0),6.5]; [104( 1 + ),14.8]; [104(2 + ),23.8]; [104(3 + ),31.9]. Multiple experimental IPs evaluated in eV for element 104 are: [(0-2+ ),21.2±0.2]; [(0-3+ ),45.1 ±0.2]; [(0-4+ ),76.8±0.3].Our MCDF results track 11 of the 12 experimental single IPs studied for group 4 atoms and ions. The exception is Hf( 2 + ). We submit our calculated IP of 22.4 ± 0.2 eV as much more accurate than the value of 23.3 eV derived from experiment.

Self-consistent relativistic molecular calculations of superheavy molecules: (_110 X)F_6

Using new relativistic molecular calculations within the Dirac-Slater scheme it is now feasible to study theoretically molecules containing superheavy elements. This opens a new era for the prediction of the physics and chemistry of superheavy elements. As an example we present the results for (_110 X) F_6, where it is shown that relativistic effects are nearly of the same order of magnitude as the crystal-field splitting.

Precise calculations of atomic electron binding energies in fermium

The comparison between the experimental binding energies for the K, L, and M electrons for fermium and the results of our Dirac-Fock calculation, taking into account all tractable corrections, leads to agreement within about 20 eV. This shows that the present method of calculation is an adequate description of this problem and that nonlinear electrodynamical effects will not be present in nature or will be smaller than 1% compared to the values recently proposed. It is found that the energies of electronic transitions can now be used to estimate the nuclear radius.

Test for basis-set errors in relativistic Dirac-Fock-Slater calculations with a numerical AO-DFS-basis

A fully relativistic four-component Dirac-Fock-Slater program for diatomics, with numerically given AO's as basis functions is presented. We discuss the problem of the errors due to the finite basis-set, and due to the influence of the negative energy solutions of the Dirac Hamiltonian. The negative continuum contributions are found to be very small.

Realistic many electron coupled channel calculations in heavy ion scattering

The time dependent Dirac equation which describes a heavy ion-atom collision system is solved via a set of coupled channel equations with energy eigenvalues and matrix elements which are given by a selfconsistent field many electron calculation. After a brief discussion of the theoretical approximations and the connection of the many particle with the one particle interpretation we discuss first results for the systems F{^8+} - Ne and F{^6+} - Ne. The resulting P(b) curves for the creation of a Ne K-hole are in good agreement with the experimental results.

Many electron coupled channel calculations for the system F{^8+} - Ne

To describe the time dependence of an atomic collision system the Dirac equation usually is rewritten in a coupled channel equation. We first discuss part of the approximation used in this approach and the connection of the many particle with the one particle interpretation. The coupled channel equations are solved for the system F{^8+} - Ne using static selfconsistent many electron Dirac-Fock-Slater wavefunctions as basis. The resulting P(b) curves for the creation of a Ne K-hole are in reasonable agreement with the experimental results.

Ionization potentials and radii of atoms and ions of element 105 (unnilpentium) and ions of tantalum derived from multiconfiguration Dirac-Fock calculations

Multiconfiguration relativistic Dirac-Fock (MCDF) values were calculated for the first five ionization potentials of element 105 (unnilpentium) and of the other group 5b elements (V, Nb, and Ta). Some of these ionization potentials in electron volts (eV) with uncertainties are: 105(0), 7.4±0.4; 105(1 +), 16.3 ±0.2; 105(2 +), 24.3 ± 0.2; 105(3 + ), 34.9 ± 0.5; and 105(4 + ), 44.9 ± 0.1. Ionization potentials for Ta(1+), Ta(2 +), and Ta(3 + ) were also calculated. Accurate experimental values for these ionization potentials are not available. Ionic radii are presented for the 2+, 3+, 4 +, and 5+ ions of element 105 and for the + 2 ions of vanadium and niobium. These radii for vanadium and niobium are not available elsewhere. The ionization potentials and ionic radii obtained are used to determine some standard electrode potentials for element 105. Born-Haber cycles and a form of the Born equation for the Gibbs free energy of hydration of ions were used to calculate the standard electrode potentials.

Dye-sensitized solar cells based on perylene derivatives

The oil price rises more and more, and the world energy consumption is projected to expand by 50 percent from 2005 to 2030. Nowadays intensive research is focused on the development of alternative energies. Among them, there are dye-sensitized nanocrystalline solar cells (DSSCs) “the third generation solar cells”. The latter have gained attention during the last decade and are currently subject of intense research in the framework of renewable energies as a low-cost photovoltaic. At present DSSCs with ruthenium based dyes exhibit highest efficiencies (ca 11%). The objective of the present work is to fabricate, characterize and improve the performance of DSSCs based on metal free dyes as sensitizers, especially on perylene derivatives. The work begins by a general introduction to the photovoltaics and dye-sensitized solar cells, such as the operating principles and the characteristics of the DSSCs. Chapter 2 and 3 discuss the state of the art of sensitizers used in DSSCs, present the compounds used as sensitizer in the present work and illustrate practical issues of experimental techniques and device preparation. A comparative study of electrolyte-DSSCs based on P1, P4, P7, P8, P9, and P10 are presented in chapter 4. Experimental results show that the dye structure plays a crucial role in the performance of the devices. The dye based on the spiro-concept (bipolar spiro compound) exhibited a higher efficiency than the non-spiro compounds. The presence of tert-butylpyridine as additive in the electrolyte was found to increase the open circuit voltage and simultaneously decrease the efficiency. The presence of lithium ions in the electrolyte increases both output current and the efficiency. The sensitivity of the dye to cations contained in the electrolyte was investigated in the chapter 5. FT-IR and UV-Vis were used to investigate the in-situ coordination of the cation to the adsorbed dye in the working devices. The open-circuit voltage was found to depend on the number of coordination sites in the dye. P1 with most coordination sites has shown the lowest potential drop, opposite to P7, which is less sensitive to cations in the working cells. A strategy to improve the dye adsorption onto the TiO2 surface, and thus the light harvesting efficiency of the photoanode by UV treatment, is presented in chapter 6. The treatment of the TiO2 film with UV light generates hydroxyl groups and renders the TiO2 surface more and more hydrophilic. The treated TiO2 surface reacts readily with the acid anhydride group of the dye that acts as an anchoring group and improves the dye adsorption. The short-circuit current density and the efficiency of the electrolyte-based dye cells was considerably improved by the UV treatment of the TiO2 film. Solid-state dye-sensitized solar cells (SSDs) based on spiro-MeOTAD (used as hole transport material) are studied in chapter 7. The efficiency of SSDs was globally found to be lower than that of electrolyte-based solar cells. That was due to poor pore filling of the dye-loaded TiO2 film by the spin-coated spiro-MeOTAD and to the significantly slower charge transport in the spiro-MeOTAD compared to the electrolyte redox mediator. However, the presence of the donor moieties in P1 that are structurally similar to spiro-MeOTAD was found to improve the wettability of the P1-loaded TiO2 film. As a consequence the performance of the P1-based solid-state cells is better compared to the cells based on non-spiro compounds.

Model Calculations and Implementation of Filters and Hybrid Green VCSELs based on Optical Thin Film Stacks

This work introduced the novel conception of complex coupled hybrid VCSELs for the first time. Alternating organic and inorganic layers in the lasers provide periodic variation of refractive index and optical gain, which enable single mode operation and low threshold of the VCSELs. Model calculations revealed great reduction of the lasing threshold with factors over 30, in comparison with the existing micro-cavity lasers. Tunable green VCSEL has been also designed, implemented and analyzed taking advantage of the broad photoluminescence spectra of the organics. Free standing optical thin films without compressive stress are technologically implemented. Multiple membrane stacks with air gap in between have been fabricated for the implementation of complex coupled VCSEL structures. Complex coupled hybrid VCSEL is a very promising approach to fill the gaps in the green spectral range of the semiconductor lasers.

Magnetic interactions between transition metal impurities and clusters mediated by low-dimensional metallic hosts: A first principles theoretical investigation

The magnetic properties and interactions between transition metal (TM) impurities and clusters in low-dimensional metallic hosts are studied using a first principles theoretical method. In the first part of this work, the effect of magnetic order in 3d-5d systems is addressed from the perspective of its influence on the enhancement of the magnetic anisotropy energy (MAE). In the second part, the possibility of using external electric fields (EFs) to control the magnetic properties and interactions between nanoparticles deposited at noble metal surfaces is investigated. The influence of 3d composition and magnetic order on the spin polarization of the substrate and its consequences on the MAE are analyzed for the case of 3d impurities in one- and two-dimensional polarizable hosts. It is shown that the MAE and easy- axis of monoatomic free standing 3d-Pt wires is mainly determined by the atomic spin-orbit (SO) coupling contributions. The competition between ferromagnetic (FM) and antiferromagnetic (AF) order in FePtn wires is studied in detail for n=1-4 as a function of the relative position between Fe atoms. Our results show an oscillatory behavior of the magnetic polarization of Pt atoms as a function of their distance from the magnetic impurities, which can be correlated to a long-ranged magnetic coupling of the Fe atoms. Exceptionally large variations of the induced spin and orbital moments at the Pt atoms are found as a function of concentration and magnetic order. Along with a violation of the third Hund’s rule at the Fe sites, these variations result in a non trivial behavior of the MAE. In the case of TM impurities and dimers at the Cu(111), the effects of surface charging and applied EFs on the magnetic properties and substrate-mediated magnetic interactions have been investigated. The modifications of the surface electronic structure, impurity local moments and magnetic exchange coupling as a result of the EF-induced metallic screening and charge rearrangements are analysed. In a first study, the properties of surface substitutional Co and Fe impurities are investigated as a function of the external charge per surface atom q. At large inter-impurity distances the effective magnetic exchange coupling ∆E between impurities shows RKKY-like oscillations as a function of the distance which are not significantly affected by the considered values of q. For distances r < 10 Å, important modifications in the magnitude of ∆E, involving changes from FM to AF coupling, are found depending non-monotonously on the value and polarity of q. The interaction energies are analysed from a local perspective. In a second study, the interplay between external EF effects, internal magnetic order and substrate-mediated magnetic coupling has been investigated for Mn dimers on Cu(111). Our calculations show that EF (∼ 1eV/Å) can induce a switching from AF to FM ground-state magnetic order within single Mn dimers. The relative coupling between a pair of dimers also shows RKKY-like oscillations as a function of the inter-dimer distance. Their effective magnetic exchange interaction is found to depend significantly on the magnetic order within the Mn dimers and on their relative orientation on the surface. The dependence of the substrate-mediated interaction on the magnetic state of the dimers is qualitatively explained in terms of the differences in the scattering of surface electrons. At short inter-dimer distances, the ground-state configuration is determined by an interplay between exchange interactions and EF effects. These results demonstrate that external surface charging and applied EFs offer remarkable possibilities of manipulating the sign and strength of the magnetic coupling of surface supported nanoparticles.