Abstract: The probability for either exciting or ionizing an electron from a given atomic orbital as the result of a sudden vacancy in one of the atomic shells, such as might occur with photoionization, has been calculated through the use of the sudden approximation. Calculations were made for each of the subshells of neon, argon, krypton, and xenon as a function of the location of the initial vacancy. The calculations were based on relativistic Hartree-Fock-Slater wave functions. The results were generalized in terms of the change in effective charge. For example, electron shake-off in the valence shell was found to be nearly independent of the location of the initial core vacancy, increasing slightly as one goes to the lower principal quantum numbers. The ionization potentials were also found to be nearly independent of the location of the core vacancy. The results of the electron-shake-off calculations were also used to obtain an evaluation of the relaxation energy arising from the promotion of a single vacancy, and compared with values obtained from binding-energy calculations. Results of the electron-shake-off calculations are applicable to any process that leads to a sudden creation of a vacancy in an atom. However, particular emphasis is given to photoelectron spectroscopy in discussing the results.

Abstract: The topics discussed are the beginnings of chemical physics and wave mechnnics, the development of quantum mechanics during 1924 to 1926, central fields in two vis-a-vis three dimensions, quantum theory of valence, the localization of electrons and the chemical bond, wave mechanical treatment of hydrogen bonded systems, hybrid bond orbitals, wave mechanics for the electronic structure of molecules through configuration interaction, spin and Pauli principle, time-dependent Hartree -- Fock theory for atomic properties, wave mechanics effects on inorganic chemistry, and ligand fields, also group theoretic view of weakly interacting sites, role of symmetry and spin restrictions in reactive and nonreactive collisions and molecular decompositions, the role of semi-empirical SCF MO methods, the influence of wave mechanics on organic chemistry, quantum biochemistry, wave mechanics for natural optical activity in organic molecules, photoelectron spectroscopy and the electronic structure of matter, electronic structures of complex molecules and solids determination, density matrix methods in x-ray scattering and momentum space calculations, and an approach to quantum theory are covered. (JFP)

Abstract: The approximation scheme suggested by Schneider, Taylor, and Yaris is applied to the scattering and the bound-state properties of the helium atom. Elastic scattering phase shifts for $s$, $p$, and $d$ partial waves, ionization potentials, one-electron ground-state properties (i.e., electron densities, the natural orbitals, and the ground-state energy), and excitation energies from the ground to the excited states of helium have been calculated simultaneously from the linear-response function and one-particle Green's function. This simultaneity is made possible by concentrating all computational effort on calculating the one- and two- particle amplitudes rather than on the ground- and excited-state wave functions. These amplitudes can be directly related to almost all the properties of physical interest in atomic and molecular systems. Our results for both the scattering- and stationary-state properties are in good agreement with experiment and other previous calculations.

Abstract: Expansion of atomic self‐consistent‐field orbitals in terms of Gaussian‐type primitive AO's calls for the most economic deployment and efficient use of all available basis functions to avoid computational waste. In even‐tempered representations maximal use of all primitives in representing all SCFAO's is ensured. Here, the optimal number of primitives per individual SCFAO, consistent with a given total number of primitives is investigated. Maximal effectiveness is found to occur when the following conditions prevail: (1) The number of primitives per SCFAO is approximately the same for all SCFAO's, say x; (2) the number of primitives needed to express the set of SCFAO's with angular‐momentum quantum number l in atom A is approximately given by Nl(A) = x[a + byl(A)] where a and b are constants and yl(A) is the number of different SCFAO's with quantum number l in atom A. Thus the efficiency rapidly increases with yl(A). Explicit results and optimal expansions based on 3–14 primitives are discussed for all at...

Abstract: When atoms are brought close together to form molecules the orbitals of individual atoms are perturbed and replaced by molecular orbitals. Inner orbitals, i.e. with higher binding energies, may still be regarded as atomic and belonging to specified atoms within the molecule, whereas the external orbitals combine to form the valence level system of the entire molecule. These orbitals take a more or less active part in the chemical bonds which are formed between the atoms in the molecule and which specify the chemical properties. The chemical bonds affect the charge distribution so that the original neutral atoms can be regarded as charged to various degrees and with different signs with a net charge of zero for a neutral molecule. We may describe the situation by regarding the individual atoms in the molecule as spheres with different potentials. Inside each charged sphere the atomic potential, set up by the removal of a certain small charge from its surface to the neighbouring atoms taking part in the chemical bond, is constant according to classical electrostatics. The result of this atomic potential is to shift the whole inner level system of any atom by a small amount, each level being shifted an equal amount. Levels belonging to different atoms in the molecule are generally shifted differently, however, and by measuring these “chemical shifts” for individual atoms in the molecule a mapping can in principle be made of the charge or the potential distribution in the molecule.

Abstract: To ionize an electron in a molecule the ‘ionization energy’ of the electron must be supplied. As there are many electrons in each molecule there are many ionization energies, in a hydrocarbon from about 10 eV to about 300 eV.

Abstract: Generalized x‐ray scattering factors have been extended to include a 3d Slater‐type atomic orbital The new scattering functions include deformations that represent octapole and hexadecapole atomic charge distributions These terms are suitable for charge density analysis of atoms with high site symmetry For a reasonable exponential parameter, the 3d orbital does not introduce significantly different dipole and quadrupole radial scattering factors which have previously been constructed with 2s and 2p Slater‐type orbital products A new monopole term (M‐shell scattering factor) is significantly different from the L‐shell scattering factor, but it may be difficult to measure the corresponding population parameter from x‐ray diffraction data The valence scattering model is extended to second row atoms by restricting deformation terms to M‐shell Slater‐type orbitals Neglect of L‐shell deformation in the x‐ray scattering analysis of second row atoms may not be appropriate; the matter warrants further study

Abstract: From photoelectron spectroscopic studies at 584 A, the 2D5/2 : 2D3/2 intensity ratios of Zn, Cd, and Hg have been determined, and the latter two were found to be significantly larger than the statistical value (l+1)/l. Earlier experiments on Ar, Kr, and Xe have yielded 2P3/2 : 2P1/2 ratios smaller than statistical. We present Dirac-Slater calculations of the partial photoionization cross sections for the J=l±1/2 components of an atomic orbital which show that the ratio is larger or smaller than the statistical value depending on whether the partial cross sections are rising or falling.

Abstract: High resolution, inelastic electron scattering data can provide new spectroscopic information on the electronic structure of polyatomic molecules. Features in the acetone energy loss spectrum from 0 to 15 eV obtained for 100 eV incident electrons correspond to vibrational, electronic discrete, and electronic continuum excitations. These data are compared with optical measurements in a wide spectral region extending from the infrared to the vacuum ultraviolet. A comprehensive interpretation of the energy loss spectra is attempted with the use of photochemical and photoelectron data, as well as quantum‐chemical calculations in the literature. Three Rydberg series with quantum defects of 1.03, 0.81, and 0.315 join onto bands previously discussed in terms of transitions to valence orbitals. These series converge to an ionization limit of 9.705 eV in good agreement with previous optical determinations. Dissociative continua underlie the Rydberg region and give rise to a variety of neutral products observed in ...

Abstract: A tight-binding model is presented to study the density-of-states and some other electronic properties of a liquid metal and an amorphous solid composed of atoms with one-atomic orbital per site. A one-electron Green function is expanded in terms of atomic orbitals and described by a perturbation expansion series in powers of H'm.,.=Hm,.-WSmnHmn and Smn being a non-diagonal matrix element of Hamiltonian and an overlap integral, respectively, while w designates the energy. An extended chain approximation is introduced in order to express atomic correlation functions by means of a radial distribution function g(Rm,.). The ensemble-averaged Green function is evaluated based upon the single-site theory of Matsubara and Toyozawa, by which a short-range order of atomic configuration in a liquid metal and an amorphous solid is most properly taken into account. It . is mentioned that the present theory is applicable to liquid transition metals and to alkali metals under a supercritical con­ dition. The non-self-consistent treatment in our scheme is shown to be equivalent to the moment-expansion method of Cyrot-Lackmann. In actual implementation of numerical cal­ culation, both the non-self-consistent and self-consistent approximations in our theory are applied and the complete set of atomic orbitals is assumed to be quasi-orthogonal, i.e., Smn=lJmn· As a pair correlation g(Rm,.), we employ three models: (1) A random liquid, (2) a hard­ core-random liquid and (3) a hard-core-modified liquid; and one real liquid case; the experi­ mental value of Ni at T=1500'C. The effect of a short-range order in the atomic configura­ tion on the density-of-states, etc., is discussed.

Abstract: Natural orbitals are calculated by the application of perturbation theory without the use of many‐body techniques. They are obtained by diagonalization of a one‐electron density matrix, the elements of which are approximated by perturbation theory using the Bk method. Calculations on the H2O and O2 molecules demonstrate that these approximate NO's do not differ significantly from the exact NO's and that these NO's may be used to reduce the amount of effort in a configuration interaction calculation. Comparisons are also made with the iterative natural orbital approach.

Abstract: The expression for the three-body potential in ionic solids, derived quantum mechanically by Lundqvist, has been obtained classically by assuming a deformation in the charge-density distribution due to overlap of the nearest-neighbor electron cloud. A reexamination of the effect of this potential on the lattice dynamics of ionic solids has revealed an error in the original formulation of the so-called three-body-force shell model which has now been eliminated. The application of the corrected equations to MgO, with only the oxygen ion assumed polarizable, results in disperison curves which present a good agreement with the neutron spectroscopic data.

Abstract: Orbital energy spectra of CO and Hg adsorbed individually and co-adsorbed on Ni (100) have been determined by ion-neutralization spectroscopy (INS) and ultraviolet photoelectron spectroscopy (UPS) at 45 ° incidence. In the case of CO, two orbitals derived from the 5σ and 1π orbitals of free CO are observed 7.8 and 11.1 eV below the Fermi level, respectively, by UPS, with INS revealing only the 7.8-eV orbital since 11.1 eV is outside its accessible range. In the case of Hg, UPS and INS both reveal orbital peaks 7.8 and 9.7 eV below EF, identified, respectively, with the 5d5/2 and 5d3/2 states of Hg. The Hg(6s) orbital is not in evidence in the energy spectra obtained by either method. We have determined energy shifts of the observed orbitals with respect to their positions in the free molecule or atom and have discussed these shifts in terms of the effects of bonding and electric charge shifts in the metal-adsorbate complexes. This work permits a fairly detailed intercomparison of INS and UPS. It also bear...

Abstract: Even‐tempered atomic orbital bases are formulated which have the property that atomic orbital scaling can be closely simulated through variation of linear expansion coefficients. This ``adaptation to pseudoscaling'' involves two types of adjustments: (1) Optimal orbital exponents and basis sizes are determined for the even‐tempered exponential or Gaussian primitives and (2) optimal linear combinations of even‐tempered Gaussian primitives are found to serve as a ``reduced basis of contracted functions.'' The efficiency of the method is discussed.

Abstract: The metal-to-insulator transition in V2O3 is described by a model that is based on the electronic band structure of this material. The vanadium 3d-t 2g band decomposes in the trigonal symmetry into two bands, a 1g and e π. The a 1g band consists of orbitals connecting pairs of c-axis neighbouring atoms, while the e π band consists of orbitals in the plane perpendicular to the c-axis. The change in distance between c-axis neighbours changes the nature of the a 1g band from molecular (delocalized) to atomic (localized). The localization of the a 1g electrons causes through the atomic exchange interaction also the localization of the e π electrons, and this localization creates a gap in the e π band which causes the material to become insulating. This model is treated in the Hartree-Fock approximation (the ‘Excitonic’ model) at zero and finite temperatures, and various aspects of the transition, such as changes in the c/a ratio, the creation of magnetic moments, changes in covalency, the effect of p...

Abstract: The relative bonding energies of nitrogen chemisorbed at three symmetric sites on a W(100) surface, represented by finite arrays of tungsten atoms [L. W. Anders. R. S. Hansen, and L. S. Bartell, J. Chem. Phys. 59, 5277 (1973)] were obtained by means of the extended Huckel molecular orbital theory (EHMO). The preferred site for nitrogen chemisorption was found to be the five coordination number (5 CN) site or the fourfold site with a tungsten atom below four tungsten atoms surrounding the nitrogen atom. The 5p orbital repulsive energy, in the case of hydrogen chemisorption, could be adequately approximated by the sum over pairs of empirical exponential repulsive terms; in the case of nitrogen chemisorption, this same method was approximately 10% in error at the equilibrium bond distance, and repulsive energies were therefore obtained from calculations including tungsten 5p orbitals but with smaller arrays.

Abstract: To obtain further information concerning the interaction between Walsh-orbitols of ‘conjugated’ cyclopropane rings, the photoelectron spectra of the following compounds have been recorded: bicyclo[4.1.0]heptane 1, cis- and trans-tricyclo[5.1.03, 5]octane 2, 3, diademane 4, trans-pentacyclo[3.3.2.02, 9.04, 10, 06, 8]decan 5 and bicyclo[4.1.0]heptene-2 6. The first bands in the PE.-spectra of these compounds have been assigned on the basis of a ZDO HMO-approximation. For 2 and 4 the value for resonance integral between linked 2p atomic orbitals of two adjacent eclipsed cyclopropane rings is found to be −1.73 eV.

Abstract: The structure of the mineral kernite has been reinvestigated, using a new set of accurate X-ray diffractometer data. The conventional least-squares refinement leads to a final value of R.(F) of 3.6 percent (R(F) = 3.4Vo). Determination of the net atomic charges with the Extended L-shell (ELS) method gives partial positive charges for the sodium (0.4-0.5 units) and boron (0.4-0,7 units) and negative charges (0.4-0.5 units) for the oxygen atoms. No difference in charge was detected between trigonal and tetrahedral boron and between bridging and hydroxylic oxygen atoms, The value of the least-squares scale factor is quite sensitive to the nature of the atomic scattering factors used. The result of an experimental measurement of the scale factor shows that the atomic densities in kernite are described better by contracted Slater-type orbitals than by isolated atom Hartree-Fock orbitals. Difference density maps based on high-order refinements (sin a/x > 0.6 A-') show more density in the B-O than Na-O bonds, supporting the covalent nature of the bonds between boron and oxygen atoms.

Abstract: 'Shake-up' satellite peaks have been observed for 2s and 2p lines in the X-ray photoemission spectra of solid compounds of the d0 ions Sc3+ and Ti4+. For this configuration (and presumably for the other 3d ions) these satellites cannot arise from simultaneous transitions of electrons from 3d orbitals; the data suggest that they originate from the excitation of electrons in ligand orbitals to the metal 3d states.

Abstract: X-Band e.p.r. spectra of magnetically dilute glasses containing (π-C5H5)2VX2 and (π-C5H5)2NbX2(X = Cl, SCN, OCN, and CN) have been recorded at 77 and 290 K and are analysed in detail. The metal-ion spin–orbit coupling constants, ξv and ξNb, for these molecules are estimated to be +133 and +490 cm–1 respectively. Spin Hamiltonian parameters are listed for each substance and are equated to the atomic orbital coefficients in some of the molecular orbitals involved in bonding in these molecules. Except for the cyanides, in each case the unpaired electron lies essentially in a non-bonding ndz2 metal-ion orbital mixed with a small amount of the corresponding metal ion ndx2–y2 orbital, the z-axis coinciding with the C2 axis of the compound; in the cyanides this unpaired electron is delocalised into px orbitals on the ligands. π-Electrons of the cyclopentadienide rings and σ-bonding electrons derived from the other ligands X are almost completely delocalised, π-bonding to the cyclopentadienide residues being stronger than σ-bonding to the ligands X. Several redistribution complexes (π-C5H5)2NbXY have been detected. E.p.r. techniques can be used to distinguish compounds of the type (π-C5H5)2MX2 from other compounds which contain vanadium(IV) or niobium(IV). Huckel LCAO molecular orbital calculations carried out on these molecules appear to give reasonable descriptions of their ground states.

Abstract: A systemmatic set of analytic atomic orbitals (AO's) is presented, which spans the atoms and principal ions of the second transition series elements in ground states of the configurations (Kr)4dn,0≤ n ≤ 10. The s and p AO's are expanded in a minimum set of Slater type orbitals (STO's); the chemically and spectrally more significant d orbitals are represented by four STO's. All coefficients and STO exponents have been chosen to minimize the nonrelativistic self‐consistent‐field total energy. Various computed energies are compared with experiment and with similar quantities obtained from earlier Hartree‐Fock results for the corresponding first‐row elements. The results indicate that the 4d AO's have sufficient accuracy to make them reliable in studies of spectra and bonding in compounds of these elements.

Abstract: The first data, obtained by the (e,2e) reaction, are presented on the binding energies and momentum distributions for electrons in valence orbitals of a polyatomic molecule, methane. The vertical ionization potentials obtained for the 1t2 and 2a1 electrons are 13.8±0.15 eV and 23.1±0.1 eV respectively. The angular correlations observed for these groups of electrons are compared with that predicted by the impulse approximation using various calculated wave functions. None of the wave functions used adequately describes the observed momentum distributions.

Abstract: Generalized oscillator strengths f(K) for one‐electron atomic transitions involving atoms in the first through third rows of the Periodic Table are studied within the first Born approximation. A one‐electron model employing hydrogenlike orbitals is used with appropriate effective nuclear charges. For single electron excitations, the Born matrix element f(K) = 2Δ E|∫ φb*e iK· rφadV|2/K2 can be scaled to yield a reduced generalized oscillator strength f (κ) which depends on the ratio of effective nuclear charges ζ(final)/ζ(initial), and a reduced momentum transfer κ = K /ζ(initial). Transitions to a Rydberg series exhibit extrema in f(K) which are nearly the same for all members of the series, whereas excitations to different series exhibit a different number and positioning of the extrema. This behavior suggests that trends in generalized oscillator strengths can be used as an experimental tool to probe various types of transitions and to unravel Rydberg series. Comparison of theoretical calculations with available experimental results yields good agreement and new experimental goals are suggested.

Abstract: The techniques of many‐body Green's function theory have been applied to the calculation of properties of the lithium atom. Using basis set expansion techniques and a second‐order expansion of the self‐energy, Dyson's equation was solved, and the first‐order reduced density matrix and the first ionization potential for the lithium ground state were computed. The natural spin orbitals of s symmetry were in excellent argeement with those computed from wavefunctions. The ionization potential was within 0.01 eV of the exact experimental result.