Ionic soft sphere parameters from Hartree‐Fock charge densities

1973 ◽  
Vol 58 (5) ◽  
pp. 1905-1907 ◽  
Author(s):  
Edward H. Carlson
Keyword(s):  
Soft Sphere ◽  
Charge Densities ◽  
Hartree Fock

scholarly journals EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER–MULTIELECTRON INTEGRALS

2009 ◽  
Vol 08 (04) ◽  
pp. 597-602 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Charge Densities ◽  
Hartree Fock ◽  
Expansion Formulae ◽  
Multicenter Multielectron Integrals ◽  
Explicitly Correlated ◽  
Explicitly Correlated Methods ◽  
Exponential Type Orbitals ◽  
The One

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETO α = 1,0,-1,-2,…) introduced by the author. Three-center overlap integrals of Ψα appearing in these relations are expressed through the two-center overlap integrals between Ψα-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter–multielectron integrals occurring when the complete orthonormal sets of Ψα-ETO are used as basis functions in the Hartree–Fock–Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter–multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Ψα-orbitals.

scholarly journals Investigation of the nuclear structure of 84-108Mo isotopes using Skyrme-Hartree-Fock method

2019 ◽  
Vol 13 (26) ◽  
pp. 1-11
Author(s):  
Ali A. Alzubadi
Keyword(s):  
Density Functional ◽  
Good Description ◽  
Mean Field ◽  
Nucleon Nucleon ◽  
Effective Density ◽  
Skin Thickness ◽  
Neutron Skin ◽  
Energy Density Functional ◽  
Charge Densities ◽  
Hartree Fock

Over the last few decades the mean field approach using selfconsistentHaretree-Fock (HF) calculations with Skyrme effectiveinteractions have been found very satisfactory in reproducingnuclear properties for both stable and unstable nuclei. They arebased on effective energy-density functional, often formulated interms of effective density-dependent nucleon–nucleon interactions.In the present research, the SkM, SkM*, SI, SIII, SIV, T3, SLy4,Skxs15, Skxs20 and Skxs25 Skyrme parameterizations have beenused within HF method to investigate some static and dynamicnuclear ground state proprieties of 84-108Mo isotopes. In particular,the binding energy, proton, neutron, mass and charge densities andcorresponding root mean square radius, neutron skin thickness andcharge form factor are calculated by using this method with theSkyrme parameterizations mentioned above. The calculated resultsare compared with the available experimental data. Calculationsshow that the Skyrme–Hartree–Fock (SHF) theory with aboveforce parameters provides a good description on Mo isotopes.

Electron impact total and ionization cross sections for Sr, Y, Ru, Pd, and Ag atoms

2013 ◽  
Vol 91 (9) ◽  
pp. 744-750 ◽  
Author(s):  
Dhanoj Gupta ◽  
Rahla Naghma ◽  
Bobby Antony
Keyword(s):  
Electron Impact ◽  
Cross Sections ◽  
Optical Potential ◽  
Atomic Orbital ◽  
Atomic Charge ◽  
Ionization Cross ◽  
Charge Densities ◽  
Hartree Fock ◽  
Spherical Complex ◽  
Ionization Cross Sections

Calculation of electron impact total and ionization cross sections for Sr, Y, Ru, Pd, and Ag atoms were performed using spherical complex optical potential and complex scattering potential-ionization contribution methods. The complex optical potential model is formulated from the target parameters and the atomic charge density. The spherical charge densities are in turn derived from the Roothaan–Hartree–Fock wavefunctions defining the atomic orbital of the target. In the present study cross sections are computed in the energy range from ionization threshold to 2000 eV. The results obtained are compared with other theories and measurements wherever available and were found to be quite consistent and uniform. In general, present data show an overall reasonable agreement with other results. Dependence of total cross sections on the number of target electrons and peak of ionization cross section on target parameters were also found to be consistent with previous observations.

Hartree–Fock formalism for the calculation of total energies and charge densities of thin films

1979 ◽  
Vol 16 (5) ◽  
pp. 1318-1322 ◽  
Author(s):  
Frank E. Harris ◽  
Hendrik J. Monkhorst ◽  
William A. Schwalm
Keyword(s):  
Thin Films ◽  
Charge Densities ◽  
Hartree Fock ◽  
Total Energies

scholarly journals Study of the Static and Dynamic Nuclear Properties and Form Factors for Some Magnesium Isotopes 29-34 Mg

2021 ◽  
Vol 19 (49) ◽  
pp. 82-93
Author(s):  
Lubna Abduljabbar Mahmood ◽  
Gaith Naima Flaiyh
Keyword(s):  
Shell Model ◽  
Mean Field ◽  
Form Factors ◽  
Field Method ◽  
Inelastic Electron ◽  
Neutron Skin ◽  
Nuclear Excitation ◽  
Charge Densities ◽  
Hartree Fock ◽  
Transverse Form Factor

Nuclear structure of 29-34Mg isotopes toward neutron dripline have been investigated using shell model with Skyrme-Hartree–Fock calculations. In particular nuclear densities for proton, neutron, mass and charge densities with their corresponding rms radii, neutron skin thicknesses and inelastic electron scattering form factors are calculated for positive low-lying states. The deduced results are discussed for the transverse form factor and compared with the available experimental data. It has been confirmed that the combining shell model with Hartree-Fock mean field method with Skyrme interaction can accommodate very well the nuclear excitation properties and can reach a highly descriptive and predictive power when investigating different nuclear configurations of stable and unstable nuclei.

Stationary properties of approximate wave functions

1969 ◽  
Vol 47 (21) ◽  
pp. 2355-2361 ◽  
Author(s):  
A. R. Ruffa
Keyword(s):  
Wave Function ◽  
Total Energy ◽  
Helium Atom ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Expectation Value ◽  
Charge Densities ◽  
Hartree Fock ◽  
Approximate Wave

The accuracy of quantum mechanical wave functions is examined in terms of certain stationary properties. The most elementary of these, namely that displayed by the class of wave functions which yields a stationary value for the total energy of the system, is demonstrated to necessarily require few other stationary properties, and none of these appear to be particularly useful. However, the class of wave functions which yields both stationary energies and charge densities has very important stationary properties. A theorem is proven which states that any wave function in this class yields a stationary expectation value for any operator which can be expressed as a sum of one-particle operators. Since the Hartree–Fock wave function is known to possess these same stationary properties, this theorem demonstrates that the Hartree–Fock wave function is one of the infinitely many wave functions of the class. Methods for generating other wave functions in this class by modifying the Hartree–Fock wave function without changing its stationary properties are applied to the calculation of wave functions for the helium atom.

Comparison of Experimental and Theoretical Structure Amplitudes and Valence Charge Densities of GaAs

1998 ◽  
Vol 54 (3) ◽  
pp. 231-239 ◽  
Author(s):  
J. Stahn ◽  
M. Möhle ◽  
U. Pietsch
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Theoretical Data ◽  
Charge Densities ◽  
Hartree Fock ◽  
Structure Factors ◽  
Nearest Neighbours ◽  
Kinematic Limit ◽  
Order Of Magnitude ◽  
The One

The current best sets of X-ray structure amplitudes for GaAs, gallium arsenide, are completed by highly precise data recorded at 0.50 < sin θ/λ < 1.35 Å−1. For the strong reflections the required accuracy of ΔF/F ≤ 1% was realized by the use of Pendellösung measurements at λ = 0.30 Å, recording the integral intensities as a function of the effective thickness from ∼500 µm thick GaAs wafers. Additionally, several weak reflections were determined from their integral intensities within the kinematic limit at wavelengths λ = 0.3, 0.56 and 0.71 Å. From these data individual Debye–Waller factors for gallium and arsenic were determined using the model of independent spherical atoms [B Ga = 0.666 (4) and B As = 0.566 (4) Å2]. The extended set of experimental structure factors now available is compared with those obtained by ab initio solid-state Hartree–Fock (HF) and density functional (DF) calculations. Therefore, the theoretical data were adapted to room temperature using the experimentally evaluated Debye–Waller factors and the model mentioned above. The valence and difference charge densities obtained from experimental and theoretical data show the expected charge accumulation between nearest neighbours slightly shifted towards the arsenic site. The disagreement remaining between the experimental and theoretical data, on the one hand, and between those of both ab initio methods, on the other hand, are of the same order of magnitude.

Ionic Soft Sphere Parameters from Hartree‐Fock‐Slater Calculations

1972 ◽  
Vol 56 (10) ◽  
pp. 4907-4911 ◽  
Author(s):  
Charles Butterfield ◽  
Edward H. Carlson
Keyword(s):  
Soft Sphere ◽  
Hartree Fock
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