Relativistic (e, 2e) collisions on atomic inner shells in symmetric geometry

We report here on an (e, 2e) experiment at relativistic electron energies (E ₀=300 keV and 500 keV) in coplanar symmetric geometry. Absolute triple differential cross section measurements forK-shell ionisation of gold, silver and copper are compared with a number of simple first order approximations. Appreciable discrepancies between theory and experiment are found, which reduce with decreasingZ and increasing primary energy. The theoretical calculations show that spin flip effects are important in symmetric geometry, in earlier works these had been neglected.     

Stieltjes imaging of atomic and molecular photoabsorption profiles

The effective transition frequencies and oscillator strenghts obtained from principal representations of spectral moments, or from variational procedures using appropriate square-integrable basis functions, are employed in the Stieltjes imaging of atomic and molecular photoabsorption profiles.     

Numerical investigations of different orders of relativistic effects in atomic shells

Summary Different orders in ² of the hydrogenic energy levels are discussed. The spurious contribution of – 0.2Z^{5 3} of the first order Douglas-Kroll-Hess (DKH) Hamiltonian is cancelled at the second order DKH level, which recovers the energy up to the order of Z^{6 4} at least to a large extent and includes also a significant part of the higher order terms. Concerning the valence shell energies of many electron atoms, their behavior is more similar to the one of the hydrogen-like 1 s than of the respective nlj levels. The convergence of the ² expansion becomes unsatisfactory for the very heavy elements.     

Effective atomic numbers for photoabsorption in alloys in the energy region of absorption edges

For photon interactions, the effective atomic numbers for 25 alloys containing different elements from carbon to bismuth at energies 10, 20, 30, 40 60, 80, 100 and 150 keV are derived. It is expected that the number should not vary with energy in this energy region, since photoabsorption is the dominant process. But, it is noticed that the number is not the same for alloys in the energy region of their respective constituent elemental photoabsorption edges. However, above the energy of the K absorption edge of the highest atomic number involved in each alloy, the number for photoabsorption more or less remains the same.     

Relativistic effects in chemistry

Relativistic effects become apparent when the velocity of the electron is arbitrarily close to the speed of light (137 au) without actually attaining it (in heavy atoms of elements at the end of Mendeleev's Periodic Table). At the orbital level, the relativistic effect is apparent in the radial contraction of penetrating s and p shells, expansion of nonpenetrating d and f shells, and the spin-orbit splitting of p-, d-, and f-shells. The appearance of a relativistic effect is indicated in the variation in the electronic configurations of the atoms in the Periodic Table, the appearance of new types of closed electron shells (6s_1/2 ², 6p_1/2 ², 7s_1/2 ², 5d_3/2 ⁴), the stabilization of unstable oxidation states of heavy elements, the characteristic variation in the ionization enthalpies of heavy atoms, their electron affinity, hydration energies, redox potentials, and optical electronegativities. In the spectra of coordination compounds, a relativistic effect is observed when comparing the position of the charge transfer bands in analogous compounds, the parameters characterizing the ligand field strength (10Dq), the interatomic distances and angles in compounds of heavy elements. A relativistic effect is also apparent in the ability of heavy metals to form clusters and superclusters. Relativistic corrections also affect other properties of heavy metal compounds (force constants, dipole moments, biological activity, etc.).Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 31, No. 3, pp. 181–199, May–June, 1995.     

Electric field effects in the photoionization and photoabsorption of methyl iodide

The effects of relatively high static electric fields (133–6533 V/cm) in the photoionization and photoabsorption of methyl iodide below the first and second ionization limits are reported. As opposed to the minor effect of the field in the photoabsorption, significant changes are observed in the photoionization below the thresholds. The changes induced by the field in the photoionization signal are explained in terms of a simple model based on the absorption spectra and on the photoionization spectrum recorded with the lowest applied field.     

Relativistic effects in kurchatovium chemistry

Using the relativistic multiconfigurational Dirac-Fock method, the first four ionization potentials of Ku, the promotion energies of the atom, and the atomic and ionic radii were calculated. The enthalpy of sublimation of metallic Ku was estimated. Relativistic SCF-X scattering wave Dirac-Slater computations of the tetrachlorides of group IV elements were performed. The lower halides of Ku are predicted to be more stable and less volatile than the respective Hf compounds, due to the ds² p ground state in the Ku atom.     

Relativistic effects in polarizational bremsstrahlung

We review the achievements of the theory of polarization bremsstrahlung of relativistic particles, including the case when both colliders have internal structure. The main features which the relativistic effects bring into the problem are discussed and illustrated by the results of numerical calculations.     

Relativistic effects in aromatic molecules

Evaluation of the relativistic correction due to the orbit-orbit operator of the Breit Hamiltonian has been considered in general, including the presence of a magnetic field. For conjugated molecules, the change in energy due to this relativistic effect is shown to be expressible in terms of two types of integrals and their derivatives. The interaction results in an intermolecular contribution to the diamagnetic susceptibility which, for two parallel benzene rings, is found to be smaller than the molecular terms by a factor of ². Several molecular integrals not previously evaluated were encountered, and their evaluation as asymptotic expansions is discussed.

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Zusammenfassung Die Berechnung eines relativistischen Termes, nÄmlich des Bahn-Bahn-Anteiles des Breit'schen Hamilton-Operators, ist bei vorhandenem Magnetfeld in allgemeiner Form durchgeführt worden. Bei konjugierten Molekülen erscheinen im Ausdruck für die zugehörige EnergieÄnderung zwei Arten von Integralen und ihren Ableitungen. Die Wechselwirkung liefert einen intermolekularen Beitrag zur diamagnetischen SuszeptibilitÄt, der allerdings im Fall zweier paralleler Benzolringe um den Faktor ² kleiner als die innermolekularen Terme ist. In diesem Zusammenhang traten einige bisher nicht benötigte Integrale auf, deren asymptotische Entwicklung durchgeführt wurde.

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Résumé Nous avons étudié, en forme générale, la correction relativiste due a l'opérateur orbite-orbite de Breit en présence d'un champ magnétique. Pour les molécules conjuguées, l'effet énergétique de ce terme peut Être exprimé par deux types d'intégrales et leurs dérivées. La contribution intermoléculaire a la susceptibilité diamagnetique est trouvée, pour deux noyaux parallèles de benzène, d'Être d'un facteur ² plus petit que les termes moléculaires. Quelques intégrales moléculaires, incalculées jusque la, ont été évaluées par expansion asymptotique.

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This investigation was supported in part by Public Health Service Fellowship No. 1F2 GM-18, 898-01 from the Division of General Medical Sciences, National Institutes of Health, U.S.A.     

Relativistic many-body and QED calculations on atomic systems

A review is given of many-body perturbation methods, particularly in the all-order and coupled-cluster forms. Relativistic many-body schemes are analyzed in terms of one- and two-photon potentials, derived by means of QED. A complete second-order (nonradiative) calculation for He-like ions is presented, including repeated Breit interactions as well as the effects of retardation and of negative-energy states, but omitting the Lamb shift. Numerical results of some Lamb-shift calculations are also given. From the analysis, conclusions can be drawn concerning the accuracy of certain relativistic many-body approaches. © 1996 John Wiley & Sons, Inc.     

Relativistic effects on the Fukui function

The extent of relativistic effects on the Fukui function, which describes local reactivity trends within conceptual density functional theory (DFT), and frontier orbital densities has been analysed on the basis of three benchmark molecules containing the heavy elements: Au, Pb, and Bi. Various approximate relativistic approaches have been tested and compared with the four-component fully relativistic reference. Scalar relativistic effects, as described by the scalar zeroth-order regular approximation methodology and effective core potential calculations, already provide a large part of the relativistic corrections. Inclusion of spin–orbit coupling effects improves the results, especially for the heavy p-block compounds. We thus expect that future conceptual DFT-based reactivity studies on heavy-element molecules can rely on one of the approximate relativistic methodologies.     

Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

We present the first relativistic study of the electric-field-gradient induced birefringence (Buckingham birefringence), with application to the series of molecules CX₂ (X?=?O, S, Se, Te). A recently developed atomic-orbital-driven scheme for the calculation of time-dependent molecular properties using one-, two- and four-component relativistic wave functions (Bast et?al. in Chem Phys 356:177, 2009) is extended to first-order frequency-dependent magnetic-field perturbations, using London atomic orbitals to ensure gauge-origin independent results and to improve basis-set convergence. Calculations are presented at the Hartree?CFock and Kohn?CSham levels of theory and results for CO₂ and CS₂ are compared with previous high-level coupled-cluster calculations. Except for the heaviest member of the series, relativistic effects are small??in particular for the temperature-independent contribution to the birefringence. By contrast, the effects of electron correlation are significant. However, the reliability of standard exchange-correlation functionals in describing Buckingham birefringence remains unclear based on the comparison with high-level coupled-cluster singles-and-doubles calculations.     

Allowance for polarization of atomic electron shells in MO LCAO calculations

The application of MO LCAO methods to molecules containing elements in the higher periods is discussed, especially compounds containing two phenyl rings linked via an oxygen atom. The calculated -electron density is found to agree with the observed electronic absorption spectra, dipole moment, effects of polarity on reactivity, and so on, provided that the wave function used for the heteroatom with n>2 is =c₁ npz+ +c_{2 nd}+...; the terms c_{2 nd}... provide correction for the change in the atomic function _npz produced by the surrounding atoms. This effect is not important for O, N, and C (first period). The effects of surrounding atoms on _npz for the halogen atom have evidently to be considered in computations on the -electron density for any molecule containing such an atom.     

Relativistic two-component infinite order method for atomic core ionization potentials

In this paper the authors have applied the infinite-order two-component method (IOTC) to compute the valence and inner shell ionization potentials for the Ne, Ar, Kr, and Xe elements. The obtained results show the very good performance of the recently defined relativistic IOTC method. They also confirm the importance of the relativistic effects in the determination of the inner shell ionization potentials.     

Relativistic total energy of heavy atomic ions: Dimensionality dependent scaling

The scaling property of the relativistic total energy E (Z, N) established by Marconi and the writer for heavy positive ions with N electrons and atomic number Z is demonstrated, by setting up the self-consistent relativistic Thomas–Fermi equation in d dimensions, to be a special case of the scaling property α being the fine structure constant.     

Relativistic effects in low-lying electronic states of iron

Excited electronic states of Fe I have been calculated using the MRCI Douglas?CKroll?CHess method. Average spin-free excitation energies of the eight lowest even electronic terms ( $\hbox{a}^5\hbox{D}, \hbox{a}^5\hbox{F}, \hbox{a}^3\hbox{F}, \hbox{a}^5\hbox{P}, \hbox{a}^3\hbox{P2}, \hbox{a}^3\hbox{H}, \hbox{b}^3\hbox{F2}, \hbox{and a}^3\hbox{G}$ ) are reported. The RASSI method was employed for calculation of individual J levels of the four lowest terms. All reported values are in good agreement with experiment. Our study pointed out significant relativistic effects even in relatively light element like iron.