One-electron Orbitals Research Articles

Simultaneous photoionization and excitation of Li, Na and K atoms in the ground and excited states

Photoionization cross sections of the main line and shake-up satellites of the outermost inner shell electrons for lithium, sodium and potassium atoms in the ground state and the first excited state are calculated. A relaxed Hartree-Fock approach within the dipole approximation is applied. Large deviations of cross sections of some terms calculated with the term dependent one-electron radial orbitals from those of the average of configuration are found. A strong enhancement of relative intensity of the shake-up satellites to the main line of photoionization from the outermost closed shell for the atoms in the excited state as compared to the similar process for the atoms in the ground state is also found.

Intra-atomic relativistic effects on the spin polarization in low-energy electron scattering from Ca, Sr, Ba, and Yb atoms.

The influence of intratarget relativistic effects on electron spin polarization is studied for low-energy electron scattering from Ca, Sr, Ba, and Yb atoms, for which a low-lying d-wave shape resonance is predicted. The motion of the scattering electron is described by solving the continuous-state Dirac-Fock equations plus a parameter-free correlation-polarization potential. The targets are represented using Dirac-Fock, Cowan's quasirelativistic Hartree-Fock, and nonrelativistic Hartree-Fock wave functions, in which the intra-atomic (also called the indirect) relativistic effects are incorporated in varying degrees. It is shown that the intra-atomic relativistic effects, in particular the spin dependence of the Dirac-Fock one-electron orbitals, create apparent quantitative changes in the spin polarization parameters around the d-wave shape resonances.

Molecular orbital coefficients and transition dipoles of real polyenes

A simple four configuration model that quantitatively reproduces all of the 11Bu and 21Ag state 0-0 energies that have been measured in high resolution spectroscopic experiments has been described previously. This model has been useful for explaining trends in the electronic properties of series of unsubstituted and substituted linear polyenes. While this model led to analytical expressions for the excitation energies, there were no closed form expressions for other quantities, such as the transition dipoles, that depend explicitly on the coefficients of the one-electron molecular orbitals. This paper derives exact expressions for the one-electron molecular orbital coefficients for an alternating chain as well as exact expressions for the transition dipole moments. This facilitates a detailed examination of the dependence of the transition dipole moments on the polyene length and alternation parameter which leads to an expression that accurately describes the dependence of the transition dipole moments on these chain parameters. The application of these expressions to an analytical analysis of nonlinear response in linear polyenes will be the subject of a subsequent paper.

Relativistic effects in low-energy spin-dependent electron collisions with rare-gas atoms

The relativistic effects in low-energy spin-dependent electron scattering from rare-gas atoms Ar, Kr and Xe are analyzed by comparing the results obtained respectively with Dirac-Fock, Cowan's quasirelativistic Hartree-Fock and non-relativistic Hartree-Fock wave functions for target atoms. It is shown that the intra-target relativistic effects, in particular the explicit spin dependences of the one-electron orbitals of Dirac-Fock atomic wave function, create apparet quantitative changes in the spin polarization parameters at some collision energies and scattering angles.

Vibronic pairwise charge transfer in copper-oxide sheets: A possible approach to high temperature superconductivity theory

To accommodate the number of holes and fractional number of atoms in doped highTc superconductors, and to produce a periodic structure with given symmetry, we postulate a quadruple cell with four copper atoms on the CuO2 layer. The quadruple cell structure hasD2h symmetry which can be distorted toC2h geometry underB1g vibration. Such a structure allows the interconversion of different spin angular momenta into paired spins similar to Cooper pairs. It also provides vibronic interactions that lower the energy of the ground state. For electron (hole) pairing, we construct the running wave Bloch sums consisting of linear combination of bonding/antibonding geminals (instead of one-electron atomic orbitals) in these quadruple cells. For “bond” movement we construct the Bloch sums consisting of linear combination of “Covalon” waves in quadruple cells related to the movement of conjugate (alternating) bonds. In both cases the pair-wise charge (hole/electron) transfer is coupled with antisymmetric vibrations under a double-well potential related to Peierls distortion. The vibronic mixing of different running bonds with different antisymmetric vibrations at various distances, accounts for the different long-range order of charge transfer. Our formulations represent an alternative view of BCS theory, Bisoliton theory and Resonanting Valence Bond theory by using a quantum chemical, position-space approach to a more tight binding situation.

Oscillator strengths for some systems with the ns2np ground-state configuration. III. Indium isoelectronic sequence

For pt. II see ibid., vol. 26, p.1403 (1993). Configuration interaction gf values for transitions between the 2P0 and 2S, 2D states of some low-lying configurations are reported for the indium isoelectronic sequence up to Ba VIII. As in previously investigated aluminium and gallium sequences, we employ a self-consistent-field method to generate one-electron orbitals. The method includes relativistic effects albeit in an approximate way and the configuration interaction scheme accounts for correlation effects. Comparison with other theoretical or experimental data is difficult due to a severe shortage of such data; nevertheless in most cases fair agreement is found for those that are available.

Variational spaces of electronic calculations in quantum chemistry

The exterior algebra formalism is presented, then used to obtain, in a very simple way, Brillouin's theorem, and to derive the general algebraic equations of the various variational spaces explored by RHF, ROHF, UHF, CASSCF, UCASSCF, CI methods. When a given basis set of one-electron orbitals (not necessarily orthogonal) is fixed, these equations lead to analytical equations for the CI coefficients only. The important algebraic concepts (i.e. concepts that do not refer to any particular basis set) of internal space, length and factorization of a multi-configuration are also introduced.

Symmetry adaptation of configuration basis in MCSCF method

A novel approach of space symmetry adaptation is developed for multiconfigurational (MC) functions in fully optimized reaction space and complete active space SCF calculations. The bonded tableau and two box symmetric tableau are basic representations (rep) of configuration functions; the group symmetric localized orbitals are used as one-electron orbitals. The method is proposed for generating a complete and orthonormal set of MC single excited functions. The redundant variable in MCSCF can be eliminated by symmetry adaptation.

The resonating-valence-bond state; the singlet ground state

The resonating-valence-bond (RVB) State with one localized state per site is a state in which correlations are important and therefore for its determination it is necessary to go beyond the one-determinant approximation. Although the number of one-electron space orbitals is equal to the number of electrons, N, the number of necessary determinants increases factorially with N, thus making a rigorous treatment of the correlation effects impracticable even for systems containing relatively small number of electrons. On the other hand, by introducing a many-electron spin function a coupled system of equations for one-electron localized non-orthogonal space orbitals and N-electron spin function can be obtained which can be solved in practice. In this procedure the main difficulty resides in the equation for the N-electron spin function. In this paper it is shown that a perturbation theory based on the decomposition of the spin system into clusters, when taken beyond the first order can, in general, offer a suitable method of mapping the results of numerical calculations of spin clusters onto the total system.

On the partial wave method for self energy calculations for non-hydrogenic electrons

Abstract A method for computing the self-energy correction for highly-ionized and high-Z many electron atoms is proposed and developed. The method is based on a partical wave analysis, and is immediately applicable to general potentials and many-electron wavefunctions. In this work we discuss the general approach, develop a formalism amenable to practical anal- ysis, provide the angular momentum reduction for arbitrary one-electron orbitals, and describe the computation of the twdimensional integrals and their kernels required for the partial wave analysis. Analytical results allowing for a practical renormalization scheme are discussed. This work is exploratory and developmental, and the present document provides a status report of our eforts. To date we have obtained numerical evidence that the method successfully handles the renormalization, and we report on significant progress in numerical methods for evaluating and approximating the two-dimensional integrals which occur in the method. We believe that this method can ultimately achieve an accuracy which is competitive with that of modern Brown's method calculations. The methods discussed within this work for approximating the two-dimensional radial matrix eIements including the full retarded couIomb interaction can be applied to other relativistic atomic physics calculations as a practical way to obtain improvements over the coulomb and Breit approximations.

Optimal group symmetric localized molecular orbitals

The concept and generating method of optimum group symmetric localized molecular orbitals (OSLMOs) are proposed. The OSLMOs have strong points of orthogonality, equivalence and symmetry, and they are simultaneously as close to the classical VB structure as possible. By using the OSLMOs as one-electron orbitals the multiconfigurational correlation calculations are reduced. The scheme is also a valuable popularization and development to hybridization theory.

Breaking of symmetry of one-electron orbitals at oxygen vacancies in perovskite-type oxides

Some general relationships have been derived in terms of the unrestricted Hartree-Fock method that define the conditions leading to the breaking of symmetry of one-electron orbitals at oxygen vacancies in oxides of the perovskite family. Numerical calculations of the critical values of relevant parameters have been carried out. Experimental data are discussed in the light of the results obtained.

The advantages of the general Hartree–Fock method for future computer simulation of materials

The general Hartree–Fock (GHF) method is a quantum mechanical method for electronic structure calculations that uses a single determinantal wave function with no restrictions on the one-electron orbitals other than orthonormality and the use of a specific basis set. The more familiar restricted Hartree–Fock (RHF) and unrestricted Hartree–Fock (UHF) methods can be regarded as special cases of the GHF method in which additional restrictions are imposed on the occupied orbitals. We propose that the GHF method is very suitable as an electronic structure method to be incorporated into computer simulations that combine the calculation of the Born–Oppenheimer ground state surface with the simulation of the motion of the nuclei on that surface. In particular, for many problems of interest there is only a single GHF minimum of the energy, and the GHF wave function is a continuous function of nuclear positions. The RHF and UHF methods, in comparison, typically have a multiplicity of local minima with curve crossings that generate a discontinuous behavior of the ground electronic state wave function as a function of nuclear positions. In this paper, we use energy minimization techniques to identify and characterize the UHF and GHF electronic minima at fixed nuclear positions for three model systems. The results verify the above assertions and suggest that the GHF method would be more suitable than the RHF or UHF methods for computer simulations.

Oscillator strengths for some systems with the ns2np ground-state configuration. II. Gallium isoelectronic sequence

For pt.I see ibid., vol.26, no.8, p.1391-402 (1993). Trends in the behaviour of gf values among the gallium isoelectronic sequence up to Sr VIII have been studied for transitions between ground 4s24p 2P0 and some low-lying excited 2P0, 2S, 2D states. The configuration interaction approach has been used to account for electron correlations. The one-electron orbitals has been generated using two self-consistent-field methods which differ in their treatment of relativistic effects. Fair agreement was found with available experimental and theoretical data.

Oscillator strengths for some systems with the ns2np ground-state configuration. I. Aluminium isoelectronic sequence

The gf values for transitions between the 2P0 and 2S, 2D states of some low-lying configurations have been investigated for the aluminium isoelectronic sequence up to Ca VIII. Both intra- and inter-complex electron correlations have been included within the configuration interaction approach. Two self-consistent-field methods which differ in accounting for relativistic effects are used to generate one-electron orbitals. Comparison with other available theoretical and experimental data is presented showing fair agreement.

Regional virial theorem in density-functional theory.

Regional virial theorems for the Kohn-Sham one-electron orbitals are derived. The regional virial theorem of the density-functional theory is obtained.Received 14 April 1992DOI:https://doi.org/10.1103/PhysRevA.46.5417©1992 American Physical Society

Electronic structure, bonding, geometry, and some spectroscopic properties of the scandium-nickel molecule

A set of LDF-LCAO computations that take into account electron-electron exchange and correlation are used to investigate the structure, bonding and spectroscopic properties of the five lowest states (X{sup 2}{Sigma}{sup +}, A{sup 2}{Sigma}{sup +}, A{sup {prime}2}II, B{sup {prime}2}II, A{sup {prime}{prime}2} {Delta}) of ScNi. Both compact and extended one-particle Gaussian basis sets are employed in the calculations. The {sup 2}{Sigma}{sup +} ground state arises from the 13{delta}{sup {dagger}}5{pi}{sub x}{sup 2}5{pi}{sub y}{sup 2}1{delta}{sub x}{sup 2}-y{sup 2}1{delta}{sub xy}{sup 2} electronic configuration and is the same as that predicted by EPR spectroscopy. In both studies, the unpaired electron is suggested to reside mainly on the scandium atom, and the computed Sc s-character is in agreement with that determined from the experimental hyperfine splittings. A detailed description of the bonding and the valence one-electron molecular orbitals is presented. The {omega}{sub e}, {omega}{sub 3}x{sub e}, B{sub e}, {Phi}{sub e}, {alpha}{sub e}, B{sub e} spectroscopic constants, {mu}(R){vert_bar}{sub Re} and its derivatives are also computed for the five states. Vertical excitation energy computations predict that the experimental B{sup {prime}2}II state observed recently has the 12{sigma}{sup 2}5{pi}{sub x}{sup 2}5{pi}{sub y}{sup 2}7{pi}{sub x}{sup 1}1{delta}{sub x}{sup 2}-y{sup 2}{sup 2}1{delta}{sub xy}{sup 2} electronic configuration. 51 refs., 8 figs., 3 tabs.

Relaxation effects on the 3d photoionisation of atomic krypton and the bromine negative ion

A calculation for the photoionization parameters for the 3d shell of Kr and Br- is performed within the framework of the relativistic random-phase approximation including excitations from the 3d, 4s and 4p shells. The relaxation of the 3d subshell is included by using a set of relaxed one-electron orbitals in solving the random-phase approximation equations for both atomic systems and is found to be quite significant for the reproduction of the experiment. The total cross sections for Kr and Br- are found to display similar behaviour over a wide energy range starting from their thresholds. The results for Kr are compared with experimental data.

State-specific theory and method for the computation of diatomic molecules: Application to He22+ 1 Sigma g+

We present a state-specific approach to the calculation of correlated wave-functions and potential-energy surfaces (PES's) of ground and excited states of diatomic molecules. Its emphasis is on the optimal choice of zeroth-order and of correlation-function spaces, which are computed separately. The zeroth-order Fermi-sea multiconfigurational wave function is obtained numerically, using McCullough's partial-wave multiconfiguration self-consistent field (Comput. Phys. Rep. 4, 265 (1986)) program PWMCSCF and numerical one-electron two-center orbitals as input. The correlation functions are obtained from partial and total configuration interaction (CI), using two-center virtual molecular orbitals, optimized by minimizing the energy. The method is demonstrated on the prototype He{sub 2}{sup 2+} {sup 1}{Sigma}{sub {ital g}}{sup +}. A number of wave functions of acsending accuracy have been calculated. The most accurate one is composed of 116 configurations (multiconfiguration Hartree-Fock plus higher-order correlations), arising from 43 orbitals. It yields results which are lower over the entire PES than those obtained from the conventional linear combination of atomic orbitals including full CI with 158 basis functions and 2282 configurations. Compared with a published large CI calculation with {ital r}{sub {ital i}{ital j}}-dependent basis sets, only at the equilibrium position, where the influence of the Coulomb cusp increases, does the present approach yieldmore » a slightly (4{times}10{sup {minus}4} a.u.) higher energy. For the rest of the PES, our calculation yields the lowest energies yet.« less

Structural optimization andd-band holes in Cu monolayers

The equilibrium lattice parameter and bandstructure of copper monolayers, both in the square (100) and hexagonal (111) symmetry, have been determined using self-consistent full-potential local density approximation (LDA) calculations. Two quite different procedures have been employed: FILMS, a linear-combination-of-gaussian-type-orbitals method, and a full-potential linearized augmented plane-wave (F-LAPW) method. The copper monolayer is bound with respect to the atomic LSDA ground state in the configurationd10s1. Nearest-neighbor distancesann are determined as 4.25 a.u. in the square geometry and 4.42 a.u. in hexagonal geometry, the latter being favored in energy by 0.33 eV/atom. Both monolayers thus exhibit a nearest-neighbor distance substantially shorter than that found in bulk copper,ann=4.8238 a.u. Excellent agreement between the two methods is obtained for the bandstructure, with no indication of ad-band hole at theM point (corner) of the Brillouin zone, in contrast to some other recent self-consistent calculations. Combined use of the von Barth-Hedin LDA and scalar-relativistic corrections produces the smallest gap at theM point, 0.15 eV, at the Hedin-Lundqvist equilibrium geometry. This may be suggestive evidence for the origin ofd-band holes when combined with further approximations in the representation of the one-electron orbitals and the charge density.