The polarized frozen core approximation: Energies and oscillator strengths of C(I) and N(II)

The frozen core and extended frozen core versions of the Hartree-Fock approximation have been improved significantly by means of l-dependent core polarization potentials. The resulting polarized frozen core procedure reproduces most of the observed 2pns, 2pnp and 2pnd terms of C(I) and N(II) with great accuracy; over 60 unobserved terms in N(II) have been calculated, which should prove sufficiently reliable for future identification purposes. Length and velocity forms of electric dipole oscillator strenghts, calculated with these polarized orbitals and the corresponding energies, are generally in excellent agreement, particularly for transitions between the more highly excited states.     

The absorption spectrum of beryllium

Energy terms, dipole oscillator strengths and photoionization cross-sections from the ground state are calculated. Autoionizing state transition energies and line widths for the ¹P⁰ resonances in the continuum are also obtained. The configuration interaction method for initial and final states is used, and atomic orbitals are generated through angular-momentum-dependent, scaled Thomas-Fermi-Dirac potentials.     

Application of the method of asymptotic projection to the calculation of vertical ionization potentials

An alternative method is proposed for the calculation of ionized states corresponding to the excitation of both valence and core electrons. Unlike the well-known approaches, in which such states are constructed by removing an electron from the corresponding spin orbital, the method proposed employs the requirement that all the spin orbitals of the ionized system are orthogonal to the spin orbitals of the neutral system. The proper spin symmetry and the orthogonality of the wave functions of these states to the wave function of the neutral molecule are ensured by a simple-to-use method of taking into account the orthogonality that was proposed by us earlier. The adequacy of the proposed scheme is demonstrated by the calculation of 15 ionization potentials of diatomic and triatomic molecules at different levels of the theory. The results of the calculations, performed in optimized basis sets including three to five Gaussian s functions per electron, are in good agreement with experimental data and state-of-the-art results obtained by other methods in extended basis sets.     

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.     

The absorption spectrum of B II,C III,N IV and O V beryllium-like ions

Energy terms, dipole oscillator strenghts and photoionization cross sections from the ground state are calculated for beryllium-like ions. Autoionizing state transition energies and line widths for the ¹P⁰ resonances in the continuum are also obtained. The configuration interaction method for initial and final states is used, and the atomic orbitals are generated through angular- momentum-dependent, scaled Thomas-Fermi-Dirac potentials.     

Electron shake-off in neon and the interaction of continuum states

Transition probabilities for shake-off of a 2p electron in a neon atom into the continuum following the creation of a vacancy in the 1s shell by an energetic electron or photon are calculated in the sudden approximation and include the electrostatic interaction between the shake-off electron and the residual ion core. The calculations is based on nonrelativistic Hartree-Fock-Slater wave functions, the residual interaction resulting from the electrostatic term being treated as a perturbation. In the first Born limit as well as in a complete calculation results for the ratio I(^3P)/I(1P = $\text{transition probability to continuum states with}{}^3\text{P}\text{core}\text{transition probability to continuum states with}{}^1\text{P}\text{core are lower than the value 3: 1 predicted by statistics in the independent particle limit}$.     

A theoretical investigation of the core ionized states of the simple carbenes,CH2, CHF and CF2

Non-empirical LCAO MO SCF computations have been carried out on the lowest energy singlet and triplet states and corresponding core hole states of the simple carbenes, CH₂, CHF and CF₂. An analysis is presented of changes in binding and relaxation energies for the core-ionized species and comparisons are drawn with the corresponding data for the dimers (viz. the appropriate substituted ethylenes). Changes in equilibrium geometries on core ionization have also been investigated and these suggest line broadening of the spectra arising from vibrational excitations accompanying core ionization.     

Approximate SCF calculations on the [Mn(H2O)6]2+ complex with a minimal basis set

In the restricted Hartree-Fock scheme approximate SCF-LCAO calculations have been performed for the [Mn(H₂O)]₆ ²⁺ complex using a minimal basis set consisting of nine Slater-type orbitals of the manganese ion and four Slater-type orbitals of the water molecule. The 1s, 2s and 2p orbitals of the manganese ion and the 1s orbital of the oxygen atom are treated as frozen core orbitals. In evaluating the different parts of the Hartree-Fock operators we used a two-centre approximation for the multicentre integrals. A new aspect of the calculations is the use of the Hartree-Fock orbital energies of the free water molecule as a first approximation for the corresponding orbital energies of the complex. The calculations have been done for the ground states and six excited states of the complex with symmetry T _h and also for the ground states of two distorted complexes. From the resulting eigenvectors we calculated the hyperfine interaction of the valence electrons of the central ion with the protons of the water molecules for three different geometries. The excited states give two different ways of finding values of 10 Dq and the Racah parameters B and C. The results are encouraging.     

Excited states of a bound polaron

Expressions for the energies of the 3s, 3p and 3d states of a polaron, bound to a positively charged impurity ion in a polar crystal through a Coulomb potential, are obtained in analytic forms using perturbation theory. The values of these energies are calculated in several polar crystals.     

The Hartree-Fock method with orthogonality restrictions for doubly excited and ionized states

It is shown that the doubly excited and ionized states with vacancies in the K electronic shells can be considered within the framework of the same scheme on the basis of the asymptotic projection method proposed earlier. In contrast to the conventional methods, the electron detachment effect is achieved by imposing the requirement that the orbitals of the excited (hole) state be orthogonal to the orbitals of removed electrons. The solution of equations that determine the orbitals is implemented in terms of the conventional spin-unrestricted Hartree-Fock method with additional conditions that ensure the spin purity and provide a unique choice of the zero-order approximation in constructing the many-particle perturbation theory for taking into account the correlation effects. The performance of the method is demonstrated by calculating the excitation energies and ionization potentials corresponding to the removal of electrons from the inner K-shell.     

Theoretical study of processes of multiple excitation/ionization in K-photoabsorption of carbon and nitrogen in CO and N2 molecules

Spectra of multiple excitation/ionization in the region of photoabsorption K-edge of carbon and nitrogen of CO and N₂ molecules in the gas phase are studied theoretically. Processes of additional excitation/ionization from the 1π-and 5σ shells are taken into account. Single-electron wave functions in the excited state are calculated allowing for the effect of core wave functions in the field of a vacancy by the single-center method in the Hartree-Fock approximation. Cross sections for photoabsorption are calculated using the theory of nonorthogonal orbitals. The influence of many-electron correlations on the extension of the multiplet structure of certain configurations of multiple excitation is studied.     

Photoelectron spectroscopy of molecular systems and quantum-chemical calculations in terms of the density functional theory: Iron π complexes L-Fe(CO)3

The HeI and NeI photoelectron spectra of irontricarboniyl complexes with cyclic diene ligands—αmethylstyrene, orthoquinodimethane, and cyclooctatetraene—were obtained. The results of quantum-chemical calculations of the molecules of these compounds in the approximation of the density functional theory (B3LYP/6-31G*) are presented. It is shown that this approximation describes well the excited ionic states of the π complexes under study. The relative ionization cross sections σ_π and σ_3d , which characterize the probability of removal of electrons from the molecular π-ligand and 3d-metal orbitals, are estimated. The mechanism of the selective coordination of the Fe(CO)₃ groups to corresponding organic ligands is discussed. The energies of the L-Fe(CO)₃ chemical bond are calculated.     

Scattered-wave calculations of photoionization cross-sections and asymmetry parameters for CO,H2O and H2S

Partial photoionization cross-sections and asymmetry parameters are calculated for the valence orbitals of the molecules CO, H₂O, and H₂S and of the atoms O and S using a recently developed extension of the self-cosistent field— Xα—scattered-wave method to continuum states. The convergence of the partial-wave expansions for both initial and final states is studied for electron kinetic energies in the range 2–1000 eV. Since convergence is very slow at high kinetic energies, the interesting region between 2 and 50 eV is emphasized, and comparisons are made with experimental UV photoemission results where such data are available. Overall the method appears to be far more reliable than previous calculations for polyatomic molecules which have used plane-wave or orthogonalized plane-wave final states.     

Cluster model calculations for Cl chemisorbed Si and Ge (111) surfaces by iterative extended Hückel theory

Local densities of states are calculated by use of a cluster model. Resonant states due to Cl 3p orbitals appears in the valence band. The calculated energy-splittings between non-bonding p_x(p_y) and bonding p_z orbitals agree well with the observed ones.     

Magneto-optical absorption spectrum of D- Ion in GaAs-Ga0.75Al0.25As quantum well

The magneto-optical absorption spectrum of a D^- ion in a GaAs-Ga_0.75Al_0.25As quantum well is calculated. We used the variational method based on a two orbital picture of a D^- ion, in which each single electron orbital is represented by a linear combination of anisotropic Gaussian orbitals. The calculated magnetic field dependence of the binding energy of a D^- ion agrees semi-quantitatively with the experimental result. In a magnetic field perpendicular to the well interface, the energies of the one-electron excited states of a D^- ion are completely quantized, and broadening is essential for the calculation of the line shape of the magneto-optical absorption spectrum. We considered two types of broadening effect, lifetime broadening and inhomogeneous broadening. Only the lifetime broadening effect reproduces fairly well the observed line shape of the magneto photo-conductivity spectrum. The assumed value of the lifetime is consistent with the measured Hall mobility. The effects of correlation on the one electron excited states of a D^- ion are also discussed.     

清洁Si(111)表面电子结构的理论研究

本文报道在原子集团模型下用CNDO-SCF方法对清洁Si(111)表面电子结构的系统研究结果:(1)计算了表面上的净电荷分布、电荷转移以及局域在各原子轨道上的电荷;发现T₃⁰,T₃⁺和T₃^-式的表面悬挂键结构较难存在;表面原子趋于形成带有分数电荷的悬挂键,而实际上这些悬挂键彼此结合成弯键;表面原子及其悬挂键上有净电荷积累,且有很强的定域性和取向性。(2)计算了原子集团模型的静 关键词：     

The calculation of valence shell ionization potentials by the ΔSCF method

Valence shell ionization potentials for several small molecules (HF, H₂O, CH₄, CO, H₂S, PH₃, SiH₄, SO₂ and F₂CO) are calculated by means of ab initio ΔSCF calculations on all the valence hole states of each molecule. The results are compared with the experimental low energy photoelectron spectra. In the case of the higher energy ion states, particular attention is paid to finding practical means for obtaining convergence of the ΔSCF iterations, and numerical evidence is presented, indicating that the ΔSCF procedure provides upper bounds to the energy of such states, at least for the cases studied herein. A new procedure, the ‘ combined ΔSCF ’ method, for the determination of a common set of molecular orbitals for use in the construction of wavefunctions for a number of ion states is described.     

Ab initio studies on the electronic structure of CeSi5

We investigated the electronic properties of CeSi₅ by band structure calculation based on the density functional theory within LDA, LDA+U, and fully relativistic schemes. The calculated band structure scheme shows that the spin-orbit coupling splits the Ce 4f states into three manifolds. When the on-site Coulomb potential is added to the Ce-derived 4f orbitals, the degeneracy between the f orbitals would be lifted and they are split into lower Hubbard bands and upper Hubbard bands. It was found that quasiparticle mass enhancement inferred by comparing γ to the density of states (DOS) at the Fermi level indicates the effective mass of CeSi₅ is enhanced with the fully relativistic results.     

On the interpretation of the photoelectron spectrum of CO chemisorbed on Ni

A LCAO-SCF calculation on the NiCO molecule is reported. In addition to the ionization potentials the vibrational structure due to ionization is calculated. The computed ionization potentials are compared with those of recent semiempirical calculations on the CO — Ni system and with the photoelectron spectra of CO chemisorbed on nickel surfaces. We produce further evidence that the first peak in the photoelectron spectrum relates to the 5σ and 1π orbitals of CO and that the peak at higher ionization energy represents the 4σ orbital.