scholarly journals Variational Calculation of Lithium-Like Ions from B+2 to N+4 Using β-Type Roothaan–Hartree–Fock Wavefunction

2021 ◽  
Vol 66 (8) ◽  
pp. 684
Author(s):  
Hamid Al-Jibbouri
Keyword(s):  
Diamagnetic Susceptibility ◽  
Variational Calculation ◽  
Basis Set ◽  
Magnetic Shielding ◽  
Electron Systems ◽  
Position Space ◽  
X Ray ◽  
Hartree Fock ◽  
Electronic Densities ◽  
The One

Within the KaKB, KaLa, and KBLa shells in the position space, the properties of a series of three-electron systems, for instance, B+2, C+3, and N+4 ions, have been studied. This required the partitioning of the two-particle space-spin density and was explicit for the Hartree–Fock description which have been proposed by considering a basis set based on single-zeta B-type orbitals (BTOs). The one- and two-body radial electronic densities R(r1), R(r1, r2), moments ⟨rn1⟩, X-ray form factor F(s), nucleus density R(0), nuclear magnetic shielding constant qd, and the diamagnetic susceptibility бs in the position space are reported. Our results are realized via the Mathematica program and compared with previous theoretical values in the literature.

scholarly journals Studying the x- ray atomic Scattering form Factor and Nuclear Magnetic Shielding Constant for Be atom in its Excited state (1s2 2s 3s) and the Be - like ions

2015 ◽  
Vol 12 (1) ◽  
pp. 204-209
Author(s):  
Baghdad Science Journal
Keyword(s):  
Form Factor ◽  
Excited State ◽  
Computer Software ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Electron Systems ◽  
X Ray ◽  
Hartree Fock ◽  
Atomic Scattering ◽  
Nuclear Magnetic

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

Basis set dependence of magnetic shielding constant calculated by the Hartree-Fock/finite perturbation method

1996 ◽  
Vol 203 (2) ◽  
pp. 159-175 ◽  
Author(s):  
Takuji Higashioji ◽  
Masahiko Hada ◽  
Manabu Sugimoto ◽  
Hiroshi Nakatsuji
Keyword(s):  
Perturbation Method ◽  
Basis Set ◽  
Magnetic Shielding ◽  
Hartree Fock ◽  
Finite Perturbation

The time-dependent coupled Hartree-Fock approximation

1966 ◽  
Vol 291 (1425) ◽  
pp. 291-295 ◽  
Keyword(s):  
Refractive Index ◽  
Variational Calculation ◽  
Time Dependent ◽  
Electron Systems ◽  
Frequency Dependent ◽  
Hartree Fock ◽  
Helium Gas

A coupled Hartree-Fock approximation for describing the effects of time-dependent perturbations on many-electron systems is presented. It is applied to the calculation of the frequency-dependent refractive index of helium gas with results that differ by between 4 and 8% from the accurate values obtained by a refined variational calculation.

scholarly journals A study of some atomic properties for He-like selected ions

2007 ◽  
Vol 4 (2) ◽  
pp. 301-304
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Configuration Interaction ◽  
Diamagnetic Susceptibility ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Hartree Fock ◽  
Atomic Properties ◽  
Atomic Form Factor ◽  
He Atom

The atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained.

Computation of the Hartree-Fock Exchange by the Tensor-Structured Methods

2010 ◽  
Vol 10 (2) ◽  
pp. 204-218 ◽  
Author(s):  
V. Khoromskaia
Keyword(s):  
Building Blocks ◽  
Basis Set ◽  
Low Rank ◽  
Convolution Product ◽  
Large Molecules ◽  
Hartree Fock ◽  
Rank Tensor ◽  
Coulomb Matrix ◽  
The One ◽  
Algebraic Optimization

AbstractWe propose a novel numerical method for fast and accurate evaluation of the exchange part of the Fock operator in the Hartree-Fock equation which is a (nonlocal) integral operator. Usually, this challenging computational problem is solved by analytical evaluation of two-electron integrals using the “analytically separable” Galerkin basis functions, like Gaussians. Instead, we employ the agglomerated “grey-box” numerical computation of the corresponding six-dimensional integrals in the tensor-structured format which does not require analytical separability of the basis set. The point of our method is a low-rank tensor representation of arising functions and operators on an n×n×n Cartesian grid and the implementation of the corresponding multi-linear algebraic operations in the tensor product format. Linear scaling of the tensor operations, including the 3D convolution product, with respect to the one-dimension grid size n enables computations on huge 3D Cartesian grids thus providing the required high accuracy. The presented algorithm for evaluation of the exchange operator and a recent tensor method for the computation of the Coulomb matrix are the main building blocks in the numerical solution of the Hartree-Fock equation by the tensor-structured methods. These methods provide a new tool for algebraic optimization of the Galerkin basis in the case of large molecules.

The Z−1 Expansion of the Nuclear Magnetic Shielding Constant and X-Ray Form Factor for 2-, 3-, and 4-Electron Ions

1972 ◽  
Vol 50 (9) ◽  
pp. 947-952 ◽  
Author(s):  
Robert Benesch ◽  
S. R. Singh ◽  
Vedene H. Smith Jr.
Keyword(s):  
Form Factor ◽  
Ground States ◽  
Magnetic Shielding ◽  
X Ray ◽  
First Order ◽  
Hartree Fock ◽  
Nuclear Magnetic

The convergence of the Z−1 expansion of the nuclear magnetic shielding constant σ and the X-ray form factor F(μ) is studied within the Hartree–Fock (HF) approximation for the ground states of 2-, 3-, and 4-electron atoms and ions. The agreement of σ through first order with the total HF σ is excellent, whereas the agreement between first-order and total HF F(μ)'s is unsatisfactory.

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