Photoelectron spectroscopy of chemisorbed atoms

We outline a theory of UV and higher-energy photoemission spectroscopy of chemisorbed atoms, that aims at the accurate calculation of inner electron binding energies and photoabsorption cross sections by including solid state and localized relativistic and correlation effects. It is based on an “atom on (in) solids” approach where one first extracts a surface potential and then uses it in a coupled Hartree–Fock theory to obtain self-consistently the shifts and splittings of atomic levels. A first application of this theoretical program has been carried out on Na on the Al(100) system, by calculating from first principles the binding energies of the Na 1s and 2s electrons. For a coverage of 1.23 × 10¹⁴ adatoms/cm² we find BE (1s) = 1075.2 eV and BE (2s) = 66.2 eV. Also, the Na 2p orbitals are found to split in the cylindrical symmetry by about 0.2 eV.     

Quantum electrodynamic effects in atomic structure

Summary In high-Z atoms, quantum electrodynamic (QED) corrections are an important component in the theoretical prediction of atomic energy levels. The main QED effects in electronic atoms are the one-electron self-energy and vacuum-polarization corrections which are well known. At the next level of precision, estimates of the effect of electron interactions on the self energy and higher-order effects in two exchanged photon corrections are necessary. These corrections can be evaluated within the framework of QED in the bound interaction picture. For high-Z few-electron atoms, this approach provides a rapidly converging series in 1/Z for the corrections, which is the generalization of the well-known relativistic 1/Z expansion methods. This paper describes recent work on the effect of electron interactions on the self energy. The QED effects are particularly important for the theory for lithiumlike uranium where an accurate measurement of the Lamb shift has been made, as well as for numerous other cases where systematic differences appear between theory that does not include these QED effects and experiment.     

Relativistic effects in low-energy spin-dependent electron collisions with rare-gas atoms

The relativistic effects in low-energy spin-dependent electron scattering from rare-gas atoms Ar, Kr and Xe are analyzed by comparing the results obtained respectively with Dirac-Fock, Cowan's quasirelativistic Hartree-Fock and non-relativistic Hartree-Fock wave functions for target atoms. It is shown that the intra-target relativistic effects, in particular the explicit spin dependences of the one-electron orbitals of Dirac-Fock atomic wave function, create apparet quantitative changes in the spin polarization parameters at some collision energies and scattering angles.     

Study of electronic X-rays emitted from pionic and muonic atoms

The electronic X-ray energies of muonic atoms were precisely measured. The atomic number (Z) dependence of the energy difference between electronic X-rays of muonic atoms and Z-1 atoms (energy shift) was systematically investigated. The energy shifts in the low-Z region were compared with those of the high-Z region that had been obtained experimentally and theoretically in previous work. An obvious difference between these two regions was found in the atomic-number dependence of the energy shift. We also compared the energy shifts of muonic atoms with those of pionic atoms.     

Coulomb-Hole–Hartree–Fock functional

We have extended to molecules a density functional previously parametrized for atomic computations. The Coulomb-hole–Hartree–Fock functional, introduced by Clementi in 1963, estimates the dynamical correlation energy by the computations of a Hartree–Fock-type single-determinant wave function, where the Hartree–Fock potential was augmented with an effective potential term, related to a hard Coulomb hole enclosing each electron. The method was later revisited by S. Chakravorty and E. Clementi [Phys. Rev. A 39 , 2290 (1989)], where a Yukawa-type soft Coulomb hole replaced the previous hard hole; atomic correlation energies, computed for atoms with Z = 2 to Z = 54 as well as for a number of excited states, validated the method. In this article, we parametrized a function, which controls the width of the soft Coulomb hole, by fitting the first and second atomic ionization potentials of the atoms with 1 ? Z ? 18. The parametrization has been preliminarily validated by computing the dissociation energy for a number of molecules. A few-determinant version of the Coulomb-hole–Hartree–Fock method, necessary to account for the nondynamic correlation corrections, is briefly discussed. © 1994 John Wiley & Sons, Inc.     

Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

The concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

An iterative method for obtaining accurate atomic inner shell binding energies

A new method based on an iterative procedure for obtaining accurate atomic inner shell binding energies is described. The method makes use of the doubly modi-fied Moseley plot as the starting point. As an illustration accurate binding energies for the M ₁ shell in the atomic number range 57 ≤ Z ≤ 71 have been obtained. This has also resulted in the removal of the anomaly in the M ₁ binding energy of Z = 68. Our calculations point to a need for a fresh look at the theoretical calculations of inner shell binding energies for Z = 57 to 71 in which some unsuspected effects appear to occur when the 4f shell is opened, half filled and closed.     

A QTAIM-based energy partitioning for understanding the physical origin of conformational preferences: Application to the Z effect in O=C-X-R and related units

A quantum theory of atoms in molecules-based energy partitioning was carried out for Z and E conformers of a series of O=C-X-R containing compounds. The results obtained for the simplest compound (formic acid) indicate that the attraction of the electron density within carbonyl oxygen by the nucleus of the acid hydrogen is the most important energy term for Z preference. This conclusion can be extended (mutatis mutandis) to larger carboxylic acids, esters, sulfur derivatives, secondary amides, and carbonyl isocyanates, and even explains the sequence of relative conformational energies in the HCXOH series (X = O, S, Se). In contrast, although the hyperconjugative model has been traditionally employed to explain this preference, we observe it is incompatible with: (i) relative values of diverse QTAIM atomic populations for the Z / E conformational equilibrium; (ii) conformational energies in the HCXOH series. © 2012 Wiley Periodicals, Inc.     

Relativistic effects in transitions of highly ionized heavy atoms

Wavelenghts, oscillator strengths, and lifetimes of KL shell heavy ions such as Fe²⁰⁺, Br³⁰⁺, etc. are predicted, including both relativistic and correlation effects. In such ions the distinction between “normal” electric dipole (El) and spin—orbit allowed electric dipole transitions (SOAEl) disappears and the Z-dependence of oscillator strengths is very different from the predictions of non-relativistic orbital theories. The feasibility of observing these ions in heavy ion accelerators is indicated. The results have implications for relativistic many-electron theory, ESCA, X-ray spectra, and molecular total energies.     

Near-Dirac–Hartree–Fock results for first-row atoms calculated with GTO basis sets

Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree–Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac–Hartree–Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been presented. The smallest Gaussian expansions (13s8 p expansions) yield Dirac–Hartree–Fock total energies accurate through six significant digits, while the largest expansions (18s13p expansions) give these energies accurate through seven significant digits. These results are more accurate than some of the results reported earlier, particularly for the open-shell atoms, indicating that the basis employed is reasonably economical for relativistic calculations. © 1995 John Wiley & Sons, Inc.     

Transition probability of lithium atom and lithiumlike ions with weakest bound electron wave functions and coupled equations

One of us has presented a new theory called the Weakest Bound Electron Potential Model theory (WBEPM theory) to determine the exact potential field in atoms. A concise analytic form of the potential of the weakest‐bound electron is proposed. In the new potential and the wave function derived afterward, the integral atomic number Z and quantum numbers n and l are replaced by nonintegral Z*, n*, and l*, respectively. In this article, we employed the WBEPM theory to calculate the transition probability for the lithium atom and lithiumlike ions and obtained very good results compared with the accepted values and other results. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 51–61, 2000     

General variation method for the relativistic calculations of atoms and molecules

Use of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as 1p_½ or 2d_3/2 appearing in atomic systems. Problems in extending the method to many-electron atoms and molecules are discussed.     

Experimental and ab initio calculational studies on nitrato[2,4-dichloro-6-((pyridin-2-ylmethylimino)methyl)phenolato]copper(II)

The mononuclear Schiff-base copper(II) compound, [Cu(C₁₃H₉C_l2N₂O)(NO₃)], has been synthesized and characterized by elemental analysis and X-ray single crystal determination. The compound crystallizes in the orthorhombic, space group Cmc2₁ with unit cell dimensions a?=?6.713(1), b?=?22.147(3), c?=?9.976(1)?Å?, M _r?=?405.67, V?=?1483.2(3)?ų, Z?=?4, R ₁?=?0.0568 and wR ₂?=?0.1331. X-ray structure determination revealed that the compound possesses crystallographic mirror symmetry. The Cu^II ion in the compound is five-coordinate in a distorted trigonal bipyramid with one O and two N atoms of the Schiff-base and by two O atoms of the nitrate anion. In the crystal structure, the molecules are linked via intermoleclular C?H?···?O non-classical hydrogen bonds, forming a two-dimensional network. Density functional theory (DFT) and Hartree-Fock (HF) calculations of the structure, atomic charge distribution and natural bond orbital analyses have been performed. The calculated results show that the Cu^II ion mainly adopts spd² hybridization and forms five bonds with the NNO donor set of the Schiff-base ligand and with two O atoms of nitrate from four orientations. The coordinate stabilization energies show that the Schiff-base copper(II) compound is very stable.     

Combination of pseudopotentials and density functionals

Semilocal pseudopotentials have been determined for first–row (Li to Ne), second row (Na to Ar), and third-row atoms (K, Ca). Core–valence correlation is included by adjusting the pseudopotentials to experimental energies of ions with a single valence electron. Correlation within the valence shell is taken into account by using the spin–density functional formalism. The approximations involved in this approach are tested for atomic ionization energies as well as binding energies of monohydrides and alkali diatomics, agreement with experiment is usually satisfactory, but in certain applications density functionals should be already included in the fitting of the local part of the pseudopotential. In addition, 3s/3p and 3s/2p basis sets (for first and second row, respectively), designed for use in connection with our pseudopotentials, are given; it is shown that they yield reasonable results for both SCF and correlation energies.     

Theoretical studies of structural and electronic properties of AlnAsn clusters

We present theoretical results of size dependent structural, electronic, and optical properties of ligand‐free stoichiometric Al_nAs_n clusters of zinc‐blende modification. The investigation is done using a simplified parametrized linear combination of atomic orbital–density functional theory‐local density approximation–tight‐binding (LCAO–DFT–LDA–TB) method and consider clusters with n up to around 100. Initial structures have assumed as spherical parts of infinite zinc‐blende structure and then allowed to relax to the closest local‐energy‐minimum structure. We analyze the radial distributions of atoms, Mulliken populations, electronic energy levels (in particular, HOMO and LUMO), bandgap, and stability as a function of size and composition. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Relativistic study of tautomerism and core electron binding energies of thio- and selenocytosine

We applied the spin-free relativistic infinite-order two-component method to calculate the core-electron binding energies of different tautomeric structures of thio- and selenocytosine. The importance of relativistic effects in the ionization of 1s electrons was studied for selenocytosine. The present method provides a reasonably simple and reliable computational tool for calculating the core electron binding energies of molecules containing heavy atoms. The method can also be used for characterization of different tautomeric structures of nucleic acid basis.     

Synthesis,crystal structure and silver complexation of a novel saddle-shaped stilbenophane: NMR and theoretical study on the complex

A new Z,Z-stilbenophane was synthesised and characterised. According to an X-ray structure analysis, the structure has a saddle shape, with the π-electrons of the double bonds and the oxygen atoms pointing towards the centre of a cavity. The ligand forms a 1:1 complex with Ag⁺. Both NMR spectra and theoretical analysis (Gauge-independent atomic orbitals (GIAO) and Quantum theory of atoms in molecules (QTAIM)) suggest that the silver cation is bound within the molecular cavity. The metal is coordinated by the two olefinic double bonds and the four oxygen atoms in an approximately octahedral environment. The coordination motif is unusual because the soft silver cation prefers the interaction with the four hard oxygen atoms over the bonding to the arene units, which is frequently observed in Ag⁺ arene complexes.     

Perturbation energy expansions based on two-component relativistic Hamiltonians

The approximate elimination of the small-component approach provides ansätze for the relativistic wave function. The assumed form of the small component of the wave function in combination with the Dirac equation define transformed but exact Dirac equations. The present derivation yields a family of two-component relativistic Hamiltonians which can be used as zeroth-order approximation to the Dirac equation. The operator difference between the Dirac and the two-component relativistic Hamiltonians can be used as a perturbation operator. The first-order perturbation energy corrections have been obtained from a direct perturbation theory scheme based on these two-component relativistic Hamiltonians. At the two-component relativistic level, the errors of the relativistic correction to the energies are proportional to ⁴ Z ⁴, whereas for the relativistic energy corrections including the first-order perturbation theory contributions, the errors are of the order of ⁶ Z ⁶–⁸ Z ⁸ depending on the zeroth-order Hamiltonian.Contribution to the Björn Roos Honorary Issue     

Generalized spherical functions in the theory of many-electron atoms

A new method for finding non-relativistic and relativistic wave-functions of an electron moving in the field of a nuclear charge in the jj coupling scheme is proposed. It is based on the usage of generalized spherical functions. The mathematical apparatus necessary to find the expressions for matrix elements of the non-relativistic and relativistic energy or electron transition operators is developed. The formulas obtained for these matrix elements are more convenient than those usually used in jj coupling scheme; only their radial integrals and some phase multipliers depend on orbital quantum numbers.     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001