Abstract: : This reprint shows self-consistent, spin-polarized calculations for free Fe13, Ni13, and Ni19 clusters with face-centered-cubic geometry and for a Fe14 C cluster with body-centered-cubic geometry. The calculations are made by expansion in a basis set of Gaussian orbitals. Results are discussed in relation to similiar calculations for bulk metals. Comparison of the present results with out previous calculations for Fe15 shows that the d-level distribution in the nickel cluster is narrower in comparison with the bulk that is found for iron, but that the spin distribution is closer to the bulk. The central atom in the Fe13 cluster is strongly spin polarized oppositely to the surrounding atoms. Effects due to replacement of the central iron atom in Fe15 by carbon are studied. The ionization potential of Fe14 was found to be 5.41 eV. Additional keywords: electronic states; excitation.

Abstract: The authors indicate a simple scheme for the evaluation of inclusive transition probabilities in atomic collision problems. Assuming that the time development of the orbitals can be represented in terms of an effective one-particle picture (as, for example, the time-dependent Hartree-Fock picture), inclusive probabilities are readily expressed in terms of one-particle density matrix elements.

Abstract: Andersen's atomic-sphere approximation has been utilized with approximations based upon linear-combination of atomic orbitals (LCAO) theory to obtain approximate energy-band parameters for solids. Simple analytic expressions for the bandwidth and position of the band center have been derived that require only free-atom wave functions evaluated at the Wigner-Seitz atomic-sphere radius. For convenience, the method has been named the atomic surface method (ASM). The following simple analytic expressions for the band parameters have been derived from the ASM: (i) The bandwidth is equal to the product of h/sup 2//m, the gradient of the electron density at the atomic-sphere radius, and the surface area of the sphere; (ii) the average band energy is shifted from the atomic-term-value energy by an amount given by the product of the bandwidth, electron density at the atomic-sphere radius, and atomic-sphere volume. The theory has been applied without adjustable parameters to the transition metals and f-shell metals with use of tabulated Hartree-Fock wave functions and is in reasonable agreement with full band-structure calculations. The same analysis is applied to atomic core states under compression and is also in reasonable agreement with complete band-structure calculations. The 2s and 2p states of Na and Al have been calculated tomore » the point where they merge with the conduction band as free-electron states. These bandwidths and shifts are also written in terms of the atomic term values by using the asymptotic form of the radial wave function. Finally, the LCAO energy bands of Ni are calculated with use of the ASM parameters.« less

Abstract: Within the framework of many‐body perturbation theory, the total correlation energy can be partitioned into: intraorbital pair energies, eii; interorbital pair energies, αβeij and ααeij; double‐excitation pair‐coupling terms eij,kl(D); and higher‐excitation pair‐coupling terms, eij,kl(S,T,Q,...). The asymptotic convergence of pair natural orbital expansions for each of these terms is determined for the model problem of n infinitely separated helium‐like ions with infinite nuclear charge. For example, the asymptotic form of the basis set truncation error in an αβ‐interorbital pair energy is LimitNij→∞Δαβeij =αβfij (Jμ=1Nij Cμij)2 ((−225/ 4608)) (Nij+δij)−1 , where Nij is the number of pair natural orbitals and Cμij is the coefficient of pair natural orbital configuration μij. Numerical studies of the neon atom verify that this model behavior applies to real many‐electron systems. The pair‐coupling terms beyond third‐order contribute less than 1% of the total correlation energy in a variety of atoms and mo...

Abstract: The utility of semiconductors in many device applications, such as high­ speed logic circuits ( 1-2), optoelectronic devices (3-4), microwave devices (5), and solar cells (6), rests on the characteristics of the intentionally introduced impurities (dopants) as much as on the properties of trace amounts of unintentional contaminations. Transition atom (T A) impurities in semiconductors form a special class of such contaminants. They were studied experimentally in great detail (e.g. review articles in References 7-10) using a broad range of techniques, including optical absorption, luminescence, photocapacitance, photoconductivity, electron para­ magnetic resonance (EPR), electron nuclear double resonance (ENDOR), deep level transient spectroscopy (DLTS), and Hall effect. This review article is concerned with the theoretical understanding of the electronic properties of T A impurities in Si, III-V, and II-VI semiconductors. First, we establish the nomenclature. When a transition atom takes up a substitutional site, say on a cation, its formal oxidation state when neutral (labeled A 0) becomes that of the site it replaces, e.g. T A 3 + if it replaces a column III element. When the impurity captures an electron its charge state becomes negative (denoted A ), and the oxidation state is TA2+. Conversely, when the impurity loses an electron its charge state becomes positive (labeled A +), and the oxidation state becomes TA4+. The tenfold degenerate atomic d orbitals can split in the cubic environment into a

Abstract: The linear augmented-Slater-type-orbital method is applied to the electronic band structures of the 5d transition metals Lu through Au. Scalar relativistic, muffin-tin potential, and local density calculations are performed for each metal in both the fcc and bcc structures. Special sets of k points are used and the variation in crystal total energy as a function of mesh density (\ensuremath{\approxeq}10 to \ensuremath{\approxeq}110 points in 1/48th of the Brillouin zone) are studied, and it is found that the total energy usually converges to \ensuremath{\approxeq}1 millihartree when \ensuremath{\approxeq}30 k points are used. Cohesive energies are calculated (the hcp metals are taken to be fcc for this purpose). A cohesive energy is the difference in energy between the crystal and the free atom in its ground state; local density theory, as applied to the free atom, is usually appropriate to the average of a number of multiplet levels. For those cases where the promotion energy to this average can be estimated, the resulting cohesive energies are in accord with experiment. The fcc-bcc structural energy differences, taken as the difference in two total energies, are also calculated. These agree with experiment as to which structure is the more stable. There are no observed values for these differences but they are markedly greater in the middle of the 5d row than the generally accepted values, obtained in the course of constructing phase diagrams for alloys using regular solution theory. The present results suggest that these constructs should be reexamined. The s, p, and d orbital character of the occupied electron levels is also examined using a Mulliken population analysis, and the more standard analysis where the charge density, within a Wigner-Seitz sphere, is decomposed into l components. The Mulliken analysis indicates somewhat greater d occupancy. More notably it indicates much less s and more p character than the Wigner-Seitz cell analysis does for all the metals except for Au.

Abstract: CASSCF/CCI calculations are presented for the low‐lying states of Sc3 and Sc+3 and SCF/CI calculations are presented for the 1A’1 state of Ca3 arising from three ground state (4s2) Ca atoms, all for equilateral triangle geometries. The calculations use effective core potentials, developed by Hay and Wadt, which replace the Ne core but include the 3s and 3p core levels along with the valence electrons in the calculations. The bonding in Ca3 arises by 4s→4p promotion and leads to a well depth of about 0.5 eV for R(Ca–Ca)=7.5a0. For Sc3 the 4s bonding is similar to that in Ca3, but the 3d electrons are also strongly bonding leading to a 2A’2 ground state with a well depth of about 1.0 eV and R(Sc–Sc)=5.75a0. The good 3d bonding orbitals (bonding between all three atoms) are 3da″2 derived from atomic 3dπ″ and 3da1 derived from atomic 3dσ, while 3dπ’ atomic orbitals lead to 3de’ orbitals which are bonding between pairs of atoms, and the 3dδ’ and 3dδ″ derived levels are nonbonding. (Here the atomic symmetry is ...

Abstract: An ab initio treatment of the Breit–Pauli spin‐orbit interaction is presented for use with large (state‐averaged) MCSCF/CI wave functions and Cartesian Gaussian atomic orbitals. The first order perturbation theory equation which results from treating the Breit–Pauli interaction (Hso) as a perturbation to the nonrelativistic Born–Oppenheimer Hamiltonian (H0) is formulated in the configuration state function basis thereby permitting the coupling of all roots of H0 into the perturbed wave function. The basic atomic orbital integrals of Hso over Cartesian Gaussian functions are evaluated using a Rys quadrature approach. The method presented here is used to consider the spin forbidden transitions b 1Σ+→X 3Σ− and a 1Δ→X 3Σ− in NF. A comparison with a frequently used approach based on the few lowest eigenfunctions of H0 is presented.

Abstract: A theoretical and experimental study of electron transfer from an optically excited donor to randomly distributed acceptors in a glassy medium is presented. The influence on time dependent observables of an electron transfer rate which is dependent on the orientation of donor and acceptors in a system with random distance and angular distributions is examined. It is formally proven that an angular dependent electron transfer rate will affect the ensemble averaged functional form of the time dependence of donor emission. Calculations based on models of P orbital–P orbital and P orbital–S orbital angular overlap factors demonstrate that only at short time (less than a few hundred picoseconds) and high concentrations of acceptors does the time dependence deviate from that predicted by the angle independent Inokuti–Hirayama theory. At longer times (>1 ns) angle averaged electron transfer parameters can be extracted from time dependent data. Experimentally, the system pentacene (donor) and duroquinone (accepto...

Abstract: The possibility of interpreting doubly excited states of the two-electron atom as vibro-rotational states is discussed in the current literature. In particular the model problem of two particles moving on the sphere was studied by Ezra and Berry (1982). The object of the present series of papers is to perform ab initio analysis of the problem. It begins by the proper choice of variables: Euler angles describing the rotation of both electrons collectively and the dynamical variables-the electron distances from the nucleus and the distance between the electrons. The transition between the Euler angles representation and the conventional one-electron orbitals is generated by the functions describing the free electrons moving on concentric spheres. These functions are calculated with the help of recurrence relations or as a solution of the system of differential equations. The latter approach gives explicit expressions but the solutions are obtained only for some particular cases (Se, Pe, Po and Do states). The motion of two particles of the sphere (Se and Pe states) is studied for some model interaction between them ('the hyperspherical hydrogen-atom model'). The analysis of the wavefunctions shows that the particles are situated primarily on the opposite ends of the sphere diameter. This observation can be used in the development of the ab initio approximate analysis.

Abstract: Publisher Summary This chapter focuses on atomic charges within molecules The geometrical structure of a molecule is determined by its energy E(R) This is the energy, in the Born–Oppenheimer sense, when the nuclei are given a fixed conformation R and the electrons take up the minimum energy distribution around them The energy E can be defined as the mean value of the Born–Oppenheimer Hamiltonian H , if the wave function is known On the other hand, the electron density is an observable quantity, which can be deduced from X-ray diffraction and electron scattering Furthermore, the atomic charge must presuppose some definition of a localized electron density around a particular nucleus In the population approach, this is defined using atomic orbitals because these do concentrate in the appropriate neighborhood and are natural to the form of the wave function The partitioning approach provides a definite volume around each nucleus to constitute the atomic region so the localization is strictly non-overlapping and precise The point charge approach carries localization to its ultimate form by using distributions such as delta functions and their derivatives

Abstract: Charge-transfer (sublevel) cross sections for He/sup 2 +/ + H collisions have been calculated in the 20-eV--to--10-keV center-of-mass energy region. Both a time-independent quantum-mechanical close-coupling method (20--500 eV) and a semiclassical impact-parameter method (0.1--10 keV) were used. The close-coupling formalism is developed in terms of a molecular-state description of the HeH/sup 2 +/ system and is extended to include both radial and rotational couplings. The potentials and radial and rotational couplings for the 2ssigma, 2psigma, 3dsigma, and 2p..pi.. molecular states were computed by expressing the molecular orbitals as variationally determined linear combinations of Slater-type orbitals centered at the atoms. Common molecular-electron translation factors were introduced to ensure proper asymptotic behavior of the wave functions and were found to be crucial for agreement between calculated and experimental cross sections. The usual practice of compensating for the neglect of these factors by using couplings evaluated at an atomic origin rather than at the center of mass of the nuclei is analyzed. Quantum-mechanical and semiclassical results are compatible only if Coulomb trajectories instead of straight-line trajectories are used. In particular the sublevel cross section for He/sup +/(2p/sub plus-or-minus1/) production is found to be extremely sensitive to the trajectory. At all energies above 50more » eV radial and rotational couplings are about equally important. Below 100 eV cross sections fall off rapidly, and radiative charge transfer becomes the dominant process below 25 eV.« less

Abstract: The electronic structure of alpha -Al2O3 has been studied by means of cluster calculations in order to investigate the influence of chemical bonding on the quadrupole coupling of 27Al and 17O. Charge transfer from oxygen into Al(3s, 3p, 3d) orbitals was found to account for the major part of the quadrupole coupling constant of 27Al. The contribution of these orbitals to the valence states is in agreement with X-ray emission spectra and with previous band calculations in which, however, Al(3d) participation was neglected. The calculated charge density maps are comparable with those from refinements of X-ray diffraction data.

Abstract: A unified treatment of slow ion-atom and atom-atom collisions for many-electron systems is proposed. The time-dependent electronic wave function is expanded in terms of traveling atomic orbitals of the two collision centers at large internuclear separations and is matched to the solution in the inner region where it is expanded in terms of molecular orbitals without translational factors. It is shown that this method avoids the difficulties associated with the conventional perturbed-stationary-state approximation. Application to charge transfer in the ${\mathrm{H}}^{+}$+${\mathrm{He}}^{+}$ collision is illustrated.

Abstract: The INDO method is used with single and double-zeta Slater atomic orbital basis to calculate the wave functions and binding energies of ethylene iodine and benzene iodine which are treated as “super” molecules. The relative stability of the resting and axial structures of these complexes is investigated. It is found that the axial structure forms a stable bound state while the resting structure is rather unstable. Both, the polarization and charge transfer forces seem to play a more important role in the formation of the axial structure than in the resting one. A detailed description of the complex molecular orbitals is presented.

Abstract: The bonding in inorganic molecules of the main group and transition metals is discussed in terms of a model which accounts simultaneously for their stereochemistries and their adoption of the inert gas counting rules. A molecular compound can be viewed initially as a central atom surrounded by a spherical shell of electron density, which is representative of the ligand co-ordination sphere. Since the wave functions for this spherical shell are derived from the particle on a sphere problem it is an easy matter to define the conditions for the inert gas rule in this hypothetical situation, because the wave functions for the sphere and the central atom are both expressed in terms of spherical harmonics with identical quantum numbers. The linear combinations of ligand orbitals in a real complex can be expressed as spherical harmonic expansions and their nodal characteristics defined by the same quantum numbers. Only co-ordination polyhedra where the atoms provide effective coverage or packing on the sphere generate linear combinations in the sequential fashion S, P, D, etc. These orbitals interact in a complementary fashion with the valence orbitals of the central atom to give a complete set of molecular orbitals, which emulate those of an inert gas in number and nodal characteristics. This Complementary Spherical Electron Density Model thereby provides an effective way of accounting for the stereochemistries of main group and transition metal compounds.

Abstract: Bond lengths and vibrational frequencies for Xe2 + and Au2 were computed using non-relativistic valence-electron wavefunctions with relativistic effective potentials and also using relativistic valence-electron wavefunctions with non-relativistic effective potentials For both molecules the former gives the relativistic bond length and the latter and non-relativistic bond length This appears to support the points of view that the relativistic bond length contraction is largely independent of atomic orbital contractions

Abstract: Bromomethane (CH 3 Br) and iodomethane (CH 3 I) have been studied by binary (e,2e) coincidence spectroscopy at 1200 eV using non-coplanar symmetric kinematics. Separation energy spectra have been determined in the energy range up to 47 eV at azimuthal angles of 0° and 8° for CH 3 Br and 0° and 6° for CH 3 I. The separation energy spectra and the electron momentum distributions measured for each of the valence orbitals are compared with theoretical predictions employing SCF wavefunctions and outer valence type and extended 2 ph-TDA Green function calculations. Electron density and momentum density maps have been calculated for all the valence orbitals using the SCF wavefunctions, and they are used to explain trends and contrasts in the electronic structure and bonding properties of these halomethanes in both position and momentum space.

Abstract: A nonempirical two‐electron propagator is employed in the characterization of molecular Auger spectra. Based on the Mulliken approximation for many‐center Coulomb integrals, the model Hamiltonian requires three parameters for each valence atomic orbital: an exponent for a Slater function, an orbital energy, and an electron–electron repulsion integral. All of these quantities are taken from results of atomic calculations. Certain adjustments of resonance integrals are made to improve agreement with ab initio calculations of orbital energies. Forms of approximate two‐electron propagators are discussed, with an emphasis on qualitative factors that assist in interpreting the results. Important orbital energy differences and electron repulsion integrals that govern final state configuration mixing are identified. Intensities for various final states are separated according to the atoms on which the Auger process is initiated for CH3CN, CH3NC, and CH3CCH. Information about local bonding environments is gathered...

Abstract: We have constructed an extended Hartree–Fock computational method and program which is very similar to standard quantum chemical program packages for molecular electronic structure calculations but allows exchange and/or correlation to be treated by a local approximation as an option The local spin density functionals accounting for exchange and/or correlation can be included in the self‐consistent field (SCF) iterations to examine their effect or added in the final estimation of the total energy to gain efficiency at an often marginal loss in accuracy We report calculations for H2, HF, N2, F2, and OH− in modest basis sets to examine the effect of local approximations for exchange and/or correlation on the bond strength, bond length, and vibrational frequencies of small covalently bonded molecules The results show a systematic pattern which can be understood in terms of the dependence of the Hartree–Fock exchange effect on the spatial extent of the canonical orbitals

Abstract: The potential energy curves as a function of the out‐of‐plane displacement of the iron atom in Fe‐porphine were calculated for various spin states and oxidation states of the iron atom by the ab initio SCF MO method. It was found that porphine attracts the iron atom to the center of the porphine plane for all the electronic states. The force constant for the out‐of‐plane motion of the iron atom is decreased by the occupation of the dx2−y2 orbital and increased by oxidation of the iron atom. It was also found that the force constant is strongly correlated with the overlap population between the dx2−y2 orbital and the pyrrole–nitrogen orbitals.