Correlation Energies from Hartree-Fock Electrostatic Potentials at Nuclei and Generation of Electrostatic Potentials from Asymptotic and Zero-Order Information

1981 ◽  
pp. 29-50 ◽  
Author(s):  
Mel Levy ◽  
Stephen C. Clement ◽  
Yoram Tal
Keyword(s):  
Zero Order ◽  
Electrostatic Potentials ◽  
Order Information ◽  
Hartree Fock

Some Approximate Atomic and Molecular Energy Formulas

2003 ◽  
Vol 68 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Peter Politzer ◽  
Abraham F. Jalbout ◽  
Ping Jin
Keyword(s):  
Density Functional ◽  
Electrostatic Potentials ◽  
Hartree Fock ◽  
Chemical Potentials ◽  
Approximate Formulas

We have tested several approximate formulas that relate atomic and molecular energies to the electrostatic potentials at the nuclei, V0 and V0,A, respectively. They are based upon the assumption that the chemical potentials can be neglected relative to V0 and V0,A. Exact, Hartree-Fock and density-functional values were used for the latter. The results are overall encouraging; the errors in the energies generally decrease markedly as the nuclear charges Z increase and the assumptions become more valid. Improvement is needed, however, in fitting the V0 and V0,A to Z.

Correlation in the Ground State of He Atom

1981 ◽  
Vol 36 (3) ◽  
pp. 272-275 ◽  
Author(s):  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Ground State ◽  
Zero Order ◽  
Consistent Variation ◽  
Hartree Fock ◽  
Perturbation Procedure ◽  
Self Consistent ◽  
He Atom ◽  
Atomic Parameters

It is possible to reproduce the entire results of Pekeris et al. of different atomic parameters for the He atom by introducing (ll) type correlation in a self consistent variation perturbation procedure using the Hartree-Fock (HF) wavefunction as the zero-order wavefunction

An expansion method for calculating atomic properties. IX. The dipole polarizabilities of the lithium sequence*

1966 ◽  
Vol 293 (1434) ◽  
pp. 365-377 ◽  
Keyword(s):  
Nuclear Charge ◽  
Expansion Method ◽  
Zero Order ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Atomic Properties ◽  
Dipole Polarizabilities

A theory is developed for expanding the dipole polarizabilities and shielding factors of an atom or ion in inverse powers of the nuclear charge Z in cases where the field links degenerate zero order configurations. Results for all members of the lithium isoelectronic sequence are presented both within the Hartree-Fock approximation and in a more accurate formulation, and are found to be in agreement with earlier work.

ON THE EVALUATION OF THE RIGOROUS ELECTROSTATIC POTENTIAL/ATOMIC ENERGY RELATIONSHIP

2007 ◽  
Vol 06 (04) ◽  
pp. 761-788
Author(s):  
ABRAHAM F. JALBOUT
Keyword(s):  
Electrostatic Potential ◽  
Ground State ◽  
Density Functional ◽  
Nuclear Charge ◽  
Electrostatic Potentials ◽  
Atomic Energy ◽  
Hartree Fock ◽  
Isoelectronic Series ◽  
Neutral Ground

A series of atomic energy formulas that relate atomic energies to the electrostatic potentials V0 at nuclei are obtained by a series of polynomial and series fits of V0 versus nuclear charge (Z). Density functional and Hartree–Fock V0 are used for a series of fits that involve an isoelectronic series of anions, cations, and neutral ground state atoms to approximate atomic energies. Comparisons to the exact energies were performed in order to demonstrate the efficacy of the rigorous expressions.

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

1974 ◽  
Vol 32 ◽  
pp. 366-367
Author(s):  
Wah Chi
Keyword(s):  
Scattering Amplitude ◽  
Present Report ◽  
Dark Field ◽  
Image Contrast ◽  
Single Atom ◽  
Optical Theorem ◽  
Hartree Fock ◽  
Heavy Atoms ◽  
Beam Stop ◽  
Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

Spatially Resolved Photoelectron Spectroscopy: Recent Progress and Future Plans

1990 ◽  
Vol 48 (2) ◽  
pp. 388-389
Author(s):  
A. M. Bradshaw
Keyword(s):  
Photoelectron Spectroscopy ◽  
Chemical Reactivity ◽  
Target Material ◽  
Orbital Energy ◽  
Light Sources ◽  
Analytical Technique ◽  
Hartree Fock ◽  
Spatially Resolved ◽  
Koopmans Theorem ◽  
Surface Analytical Technique

X-ray photoelectron spectroscopy (XPS or ESCA) was not developed by Siegbahn and co-workers as a surface analytical technique, but rather as a general probe of electronic structure and chemical reactivity. The method is based on the phenomenon of photoionisation: The absorption of monochromatic radiation in the target material (free atoms, molecules, solids or liquids) causes electrons to be injected into the vacuum continuum. Pseudo-monochromatic laboratory light sources (e.g. AlKα) have mostly been used hitherto for this excitation; in recent years synchrotron radiation has become increasingly important. A kinetic energy analysis of the so-called photoelectrons gives rise to a spectrum which consists of a series of lines corresponding to each discrete core and valence level of the system. The measured binding energy, EB, given by EB = hv−EK, where EK is the kineticenergy relative to the vacuum level, may be equated with the orbital energy derived from a Hartree-Fock SCF calculation of the system under consideration (Koopmans theorem).

Strain measurement in In0.2Ga0.8As/GaAs quantum wires by convergent beam electron diffraction

1995 ◽  
Vol 53 ◽  
pp. 444-445
Author(s):  
S. Hillyard ◽  
Y.-P. Chen ◽  
J.D. Reed ◽  
W.J. Schaff ◽  
L.F. Eastman ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Semiconductor Lasers ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Convergent Beam Electron Diffraction ◽  
Zero Order ◽  
Beam Electron ◽  
Local Lattice ◽  
Device Applications ◽  
Convergent Beam

The positions of high-order Laue zone (HOLZ) lines in the zero order disc of convergent beam electron diffraction (CBED) patterns are extremely sensitive to local lattice parameters. With proper care, these can be measured to a level of one part in 104 in nanometer sized areas. Recent upgrades to the Cornell UHV STEM have made energy filtered CBED possible with a slow scan CCD, and this technique has been applied to the measurement of strain in In0.2Ga0.8 As wires.Semiconductor quantum wire structures have attracted much interest for potential device applications. For example, semiconductor lasers with quantum wires should exhibit an improvement in performance over quantum well counterparts. Strained quantum wires are expected to have even better performance. However, not much is known about the true behavior of strain in actual structures, a parameter critical to their performance.

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