Analytical method for calculating atomic structures based on the variational method for many-electron atomic structure in plasmas

2020 ◽  
Vol 98 (10) ◽  
pp. 959-969
Author(s):  
Kun Ma ◽  
Zhanbin Chen
Keyword(s):  
Variational Method ◽  
Atomic Structure ◽  
Quantum Plasma ◽  
Hartree Fock ◽  
Atomic Structures ◽  
Relativistic Mass ◽  
The One ◽  
Debye Plasma ◽  
Plasma Applications ◽  
Structure Properties

Within the framework of the Hartree–Fock method and the irreducible tensor theory, we have proposed an analytic formula for calculating the nonrelativistic energies of many-electron atoms. The relativistic mass, the one- and two-body Darwin, the spin–spin contact interaction, and the orbit–orbit interaction corrections to the energies are considered to make the results more precise. The angular interactions and spin sums involved in the formula are worked out explicitly using the irreducible theory. A program based on the variational method is developed to calculate the wave functions and atomic structure properties. The energies of the 1sns 1,3S (n = 1–4) and 1snp 1,3P (n = 2–4) states of the exemplary ions Ar16+, Fe24+, and Kr34+ in both Debye plasma and quantum plasma environments are given. Moreover, we analyzed the evolution of plasma screening parameters and provided some rules for practical and rapid evaluation in plasma applications.

Quasiperiodic interfaces: HREM observations of grain and phase boundaries

1990 ◽  
Vol 48 (4) ◽  
pp. 332-333
Author(s):  
K. L. Merkle
Keyword(s):  
Atomic Structure ◽  
Direct Determination ◽  
Lattice Parameter ◽  
Atomic Scale ◽  
Misfit Dislocations ◽  
Oxide Systems ◽  
Atomic Structures ◽  
Periodic Arrays ◽  
Parameter Ratio ◽  
Metal Metal

The atomic structures of internal interfaces have recently received considerable attention, not only because of their importance in determining many materials properties, but also because the atomic structure of many interfaces has become accessible to direct atomic-scale observation by modem HREM instruments. In this communication, several interface structures are examined by HREM in terms of their structural periodicities along the interface.It is well known that heterophase boundaries are generally formed by two low-index planes. Often, as is the case in many fcc metal/metal and metal/metal-oxide systems, low energy boundaries form in the cube-on-cube orientation on (111). Since the lattice parameter ratio between the two materials generally is not a rational number, such boundaries are incommensurate. Therefore, even though periodic arrays of misfit dislocations have been observed by TEM techniques for numerous heterophase systems, such interfaces are quasiperiodic on an atomic scale. Interfaces with misfit dislocations are semicoherent, where atomically well-matched regions alternate with regions of misfit. When the misfit is large, misfit localization is often difficult to detect, and direct determination of the atomic structure of the interface from HREM alone, may not be possible.

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 Evaluation of the one electron expectation values for different wave function of Be atom

2007 ◽  
Vol 4 (3) ◽  
pp. 393-396
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Slater Determinant ◽  
Open Shell ◽  
Expectation Values ◽  
Electronic Density ◽  
Expectation Value ◽  
Hartree Fock ◽  
Shell System ◽  
Electronic Wave Function ◽  
The One

The aim of this work is to evaluate the one- electron expectation value from the radial electronic density function D(r1) for different wave function for the 2S state of Be atom . The wave function used were published in 1960,1974and 1993, respectavily. Using Hartree-Fock wave function as a Slater determinant has used the partitioning technique for the analysis open shell system of Be (1s22s2) state, the analyze Be atom for six-pairs electronic wave function , tow of these are for intra-shells (K,L) and the rest for inter-shells(KL) . The results are obtained numerically by using computer programs (Mathcad).

scholarly journals Extended theoretical transition data in C i–iv

2021 ◽  
Vol 502 (3) ◽  
pp. 3780-3799
Author(s):  
W Li ◽  
A M Amarsi ◽  
A Papoulia ◽  
J Ekman ◽  
P Jönsson
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Internal Validation ◽  
Hartree Fock ◽  
Relativistic Configuration ◽  
The Difference ◽  
The One ◽  
Relative Differences

ABSTRACT Accurate atomic data are essential for opacity calculations and for abundance analyses of the Sun and other stars. The aim of this work is to provide accurate and extensive results of energy levels and transition data for C i–iv. The Multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods were used in this work. To improve the quality of the wavefunctions and reduce the relative differences between length and velocity forms for transition data involving high Rydberg states, alternative computational strategies were employed by imposing restrictions on the electron substitutions when constructing the orbital basis for each atom and ion. Transition data, for example, weighted oscillator strengths and transition probabilities, are given for radiative electric dipole (E1) transitions involving levels up to 1s22s22p6s for C i, up to 1s22s27f for C ii, up to 1s22s7f for C iii, and up to 1s28g for C iv. Using the difference between the transition rates in length and velocity gauges as an internal validation, the average uncertainties of all presented E1 transitions are estimated to be 8.05 per cent, 7.20 per cent, 1.77 per cent, and 0.28 per cent, respectively, for C i–iv. Extensive comparisons with available experimental and theoretical results are performed and good agreement is observed for most of the transitions. In addition, the C i data were employed in a re-analysis of the solar carbon abundance. The new transition data give a line-by-line dispersion similar to the one obtained when using transition data that are typically used in stellar spectroscopic applications today.

scholarly journals Numerical Procedures for Relativistic Atomic Structure Calculations

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 85
Author(s):  
Charlotte Froese Fischer ◽  
Andrew Senchuk
Keyword(s):  
Variational Methods ◽  
Atomic Structure ◽  
Finite Differences ◽  
Heavy Elements ◽  
Transition Rates ◽  
Numerical Accuracy ◽  
Hartree Fock ◽  
Atomic Structure Calculations ◽  
Structure Calculations

Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences for integration and differentiation. The numerical accuracy and efficiency of existing procedures are evaluated and some modifications proposed with heavy elements in mind.

scholarly journals Atomic structure of the human herpesvirus 6B capsid and capsid-associated tegument complexes

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Yibo Zhang ◽  
Wei Liu ◽  
Zihang Li ◽  
Vinay Kumar ◽  
Ana L. Alvarez-Cabrera ◽  
...  
Keyword(s):  
Human Cytomegalovirus ◽  
Atomic Structure ◽  
Human Herpesvirus ◽  
Murine Cytomegalovirus ◽  
Capsid Assembly ◽  
High Similarity ◽  
Tegument Proteins ◽  
Atomic Structures ◽  
Organizational Differences ◽  
Particle Reconstruction

AbstractHuman herpesvirus 6B (HHV-6B) belongs to the β-herpesvirus subfamily of the Herpesviridae. To understand capsid assembly and capsid-tegument interactions, here we report atomic structures of HHV-6B capsid and capsid-associated tegument complex (CATC) obtained by cryoEM and sub-particle reconstruction. Compared to other β-herpesviruses, HHV-6B exhibits high similarity in capsid structure but organizational differences in its CATC (pU11 tetramer). 180 “VΛ”-shaped CATCs are observed in HHV-6B, distinguishing from the 255 “Λ”-shaped dimeric CATCs observed in murine cytomegalovirus and the 310 “Δ”-shaped CATCs in human cytomegalovirus. This trend in CATC quantity correlates with the increasing genomes sizes of these β-herpesviruses. Incompatible distances revealed by the atomic structures rationalize the lack of CATC’s binding to triplexes Ta, Tc, and Tf in HHV-6B. Our results offer insights into HHV-6B capsid assembly and the roles of its tegument proteins, including not only the β-herpesvirus-specific pU11 and pU14, but also those conserved across all subfamilies of Herpesviridae.

Sign in / Sign up

Export Citation Format

Share Document