Publisher Summary This chapter provides a summary of the relativistic calculations on multielectron or multicenter problems. The Dirac–Fock Hamiltonian and the main quantum electrodynamical (QED) corrections are discussed and the atomic and bandstructure calculations are reviewed. Then the construction of relativistic molecular orbitals and the solvable one-electron molecular and solid-state models are described. The simplest possible system for studying relativistic effects in chemical bonding is H2+. Several variational linear combinations of atomic orbitals (LCAO)-type solutions of the Dirac equation for H2+ show that the relativistic effects decrease the electronic energy by about –7 ╳ 10–6 a.u. The Dirac-Fock and Dirac-Slater molecular calculations, the relativistic semiempirical methods, and the perturbation treatments of relativistic effects are also described. In relativistic treatments of several spectroscopic properties, the entire formulation must be changed if relativistic wavefunctions are used. Some of its examples are considered. The chapter also presents a preliminary account of the relativistic effects on the chemical properties of the periodic system of elements.

Relativistic Quantum Chemistry

The photoelectron spectrum of the chlorobenzene molecule has been studied using both monochromated synchrotron radiation with photon energies between 15 and 120 eV and HeI radiation at 21.22 eV. Photoelectron angular distributions and branching ratios have been determined over the entire energy range studied. Theoretical investigations have been performed using ab initio SCF and many-body Green’s function methods to evaluate wave functions, binding energies and relative intensities. The ADC(3) calculations of binding energies and pole strengths were particularly important for the interpretation of the inner valence spectrum where electron correlation effects are found to be important. The main part of the photoelectron spectrum is similar to that of benzene but some of the bands are characteristic of the chlorine atom. The Cooper minimum of the Cl 3p orbital is clearly reflected in some of the bands and is used to assess the mixing between ring orbitals and chlorine atomic orbitals. The HeI-excited spectra show extensive vibrational structure in the X 2 B 1 , A 2 A 2 , B 2 B 2 , C 2 B 1 and K 2 A 1 photoelectron bands. The vibrational structure is analysed in detail and compared to results obtained from multiphoton ionisation photoelectron spectroscopy.

An experimental and theoretical study of the valence shell photoelectron spectrum of the benzene molecule

: A revised and updated annotated bibliography on atomic transition probabilities covering the literature from 1914 through October 1977 is presented It contains approximately 2400 references and is divided into four main sections, with each article assigned a number The first section contains a listing, by number, of articles of general interest The second section lists by number all articles containing numerical data; it is arranged by element and stage of ionization and is further subdivided according to theoretical and experimental methods, comments, and compilations The third section contains a listing of all articles, including number, authors, title, and journal reference; it is arranged by year of publication and alphabetically by authors names within the year All foreign language papers are identified, and their titles are translated into English The final section contains a listing of all authors and the numbers of the papers they have authored or co-authored

Bibliography on Atomic Transition Probabilities: 1914 Through October 1977

This compilation is the third in a series of updates to a critical compilation published in 1969 by Wiese et al. [Atomic Transition Probabilities, Vol. II: Sodium through Calcium, NSRDS-NBS Vol. 22 (U.S. GPO, Washington, D.C., 1969)]. Atomic transition probabilities have been critically evaluated and compiled for about 5800 spectral lines of silicon (nuclear charge Z = 14 ). The cited values and their estimated uncertainties are based on our consideration of all available theoretical and experimental literature sources. All ionization stages (except for hydrogenic) are covered, and the data are presented in separate tables for each atom and ion. Separate listings are given for “allowed” (electric dipole) and “forbidden” (magnetic dipole plus electric and magnetic quadrupole) transitions. In each spectrum, lines are grouped into multiplets which are arranged in order of ascending lower and upper level energies, respectively. For each line, the emission transition probability A k i , the line strength S , and (for allowed lines) the absorption oscillator strength f i k are given, together with the spectroscopic designation, the wavelength, the statistical weights, and the energy levels of the lower and upper states. The estimated relative uncertainties of the line strength are also indicated, as are the source citations. We include only those lines whose transition rates are deemed sufficiently accurate to qualify as reference values. Short introductions precede the tables for each ion.

Atomic Transition Probabilities of Silicon. A Critical Compilation

Relativistic single-configuration Hartree-Fock oscillator strengths for the lowest ns2S 1 2 → np2P 1 2 , 3 2 transitions in the first few members of the rubidium (n = 5) and cesium (n = 6) isoelectronic sequences have been studied, both with and without allowance for core polarization. The effect of polarization of the core of the atom or ion by the valence electron is included by introducing a polarization potential in the one-electron Hamiltonian and by employing the corresponding correction for the dipole-moment operator in the transition matrix element. The results obtained compare well with available experimental data and indicate a significant influence of core-polarization effects on oscillator strengths. The behaviour of the oscillator strengths for the low Z part of the isoelectronic sequences is discussed.

Relativistic Hartree-Fock oscillator strengths for the lowest s→p transitions in the first few members of the Rb(I) and Cs(I) isoelectronic sequences, with allowance for core polarization

Relativistic effects on transition probabilities in the Li and Be isoelectronic sequences

Photoionization cross sections and photoelectron angular distributions (asymmetry parameters) are obtained for $3p$-subshell ionization of the Cl ground state. A substantial amount of bound-state electron correlation is taken into account through use of a multiconfiguration description of the ground state and residual ionic core. Both independent-channel and coupled-channel final states are used in evaluating the length and velocity forms of the dipole transition amplitudes. In the coupled-channel case, channel interaction is included via the reaction-matrix ($K$-matrix) method which diagonalizes the total $N$-electron atomic Hamiltonian in the manifold of single-channel basis states of the model Hamiltonian. In all of the $^{2}D$ and $^{2}P$ final-state channels, the photoabsorption transition probabilities exhibit significant contributions from interchannel interaction. In determining the cross sections for any of the $^{2}S$ channels, it was necessary to include the low-lying $3s3{p}^{6}$; $^{2}S$ bound state because of its large Coulomb interaction with the continuum of the $3{p}^{4}^{1}D$, $\ensuremath{\epsilon}d$; $^{2}S$ channel. The addition of the channels which originate from a $3s\ensuremath{\rightarrow}\ensuremath{\epsilon}p$ transition into the set of interacting $^{2}S$ channels nearly cancels the effect of the $3s3{p}^{6}$; $^{2}S$ discrete state on the cross sections of both the $3{p}^{4}^{1}D$,$\ensuremath{\epsilon}d$; $^{2}S$ and $3{p}^{4}^{1}S$,$\ensuremath{\epsilon}s$; $^{2}S$ channels. The asymmetry parameters for the three ionic multiplets $^{3}P$, $^{1}D$, and $^{1}S$ all show strong channel-interaction effects. The effects of the $3s3{p}^{6}$; $^{2}S$ bound state and the $3s3{p}^{5}$; $^{3,1}P$,$\ensuremath{\epsilon}p$; $^{2}S$ channels on the $^{1}D$ and $^{1}S$ $\ensuremath{\beta}$ parameters are discussed.

Channel-interaction effects on the 3 p -subshell photoionization of chlorine

The relativistic electric dipole oscillator strengths in length and velocity forms are calculated for a number of elements in the argon sequence. The transitions studied are $3{p}^{6}\ensuremath{-}3{p}^{5}\mathrm{nd}$ $(n=3, 4)$ and $3{p}^{6}\ensuremath{-}3{p}^{5}4s$. The ground state includes correlation due to the configuration $3{p}^{4}3{d}^{2}$ in computing $p\ensuremath{-}d$ transitions. Relativistic effects on line strengths are found to be important in the $\ensuremath{\Delta}n\ensuremath{\ne}0$ transitions even at low $Z$. The origin of these large relativistic effects for low $Z$ in the $3{p}^{6}\ensuremath{-}3{p}^{5}4l$ transitions are discussed.

Relativistic oscillator strengths for E 1 transitions in the argon isoelectronic sequence

Using relativistic and nonrelativistic Hartree-Fock methods we have calculated some E1 and M2 transition probabilities for 2p/sup 5/3d ..-->.. 2p/sup 6/ + ..gamma.. and 2p/sup 5/3s ..-->.. 2p/sup 6/ + ..gamma.. in the Ne isoelectronic sequence. The heaviest ion considered is U. The relativistic effects on both the photon energies and the transition amplitudes are discussed. A comparison of our calculated M2 lifetimes with experimental results for the 2p/sup 5/3s-2p/sup 6/ transition in Ne-like Cu shows significant differences, while the calculated E1 lifetimes for Ne-like Cl indicates good agreement with experiment.

E1 and M2 transitions in the neon isoelectronic sequence

We discuss the use of the multiconfiguration Hartree-Fock (MCHF) to obtain initial state wave functions for photoionization calculations. An extension of the MCHF, a multiconfiguration V(N-1)LS, can be used to obtain final state wave functions such that most intrachannel corrections to these wave functions vanish. Application of these techniques to the rare gases and the Cl are discussed. In the case of Cl, the strong interchannel interactions are included through use of the K-matrix. Excellent agreement between theory and experiment is obtained for the rare gases.

Photoionization Cross Sections Using the Multiconfiguration Hartree-Fock and its Extensions

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