scholarly journals A Hartree - Fock Program for Atomic Structure Calculations

1999 ◽  
Vol 52 (6) ◽  
pp. 973 ◽  
Author(s):  
J. Mitroy
Keyword(s):  
Open Shell ◽  
Fortran Program ◽  
Basis Functions ◽  
Slater Type Orbitals ◽  
Matrix Equations ◽  
Slater Type ◽  
Hartree Fock ◽  
The Matrix ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The Hartree–Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals.

scholarly journals UNSYMMETRICAL AND SYMMETRICAL ONE-RANGE ADDITION THEOREMS FOR SLATER TYPE ORBITALS AND COULOMB–YUKAWA-LIKE CORRELATED INTERACTION POTENTIALS OF INTEGER AND NONINTEGER INDICES

2008 ◽  
Vol 07 (02) ◽  
pp. 257-262 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Basis Functions ◽  
Slater Type Orbitals ◽  
Addition Theorems ◽  
Slater Type ◽  
Interaction Potentials ◽  
Hartree Fock ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Multicenter Multielectron Integrals ◽  
Exponential Type Orbitals

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer nSTOs derived in this study with the help of ψa-exponential type orbitals (ψa-ETOs, a = 1, 0, -1, -2,…), the general formulas through the integer nSTOs are established for the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb–Yukawa-like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for the computations of arbitrary multicenter multielectron integrals that arise in the Hartree–Fock–Roothaan (HFR) approximation and also in the correlated methods based upon the use of STOs as basis functions.

scholarly journals Nonlinear approximations for electronic structure calculations

2013 ◽  
Vol 469 (2158) ◽  
pp. 20130231 ◽  
Author(s):  
G. Beylkin ◽  
T. S. Haut
Keyword(s):  
Electronic Structure ◽  
Functional Form ◽  
Integral Form ◽  
Electronic Structure Calculations ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Hartree Fock ◽  
Nonlinear Approximations ◽  
Novel Algorithms ◽  
Structure Calculations

We present a new method for electronic structure calculations based on novel algorithms for nonlinear approximations. We maintain a functional form for the spatial orbitals as a linear combination of products of decaying exponentials and spherical harmonics centred at the nuclear cusps. Although such representations bare some resemblance to the classical Slater-type orbitals, the complex-valued exponents in the representations are dynamically optimized via recently developed algorithms, yielding highly accurate solutions with guaranteed error bounds. These new algorithms make dynamic optimization an effective way to combine the efficiency of Slater-type orbitals with the adaptivity of modern multi-resolution methods. We develop numerical calculus suitable for electronic structure calculations. For any spatial orbital in this functional form, we represent its product with the Coulomb potential, its convolution with the Poisson kernel, etc., in the same functional form with optimized parameters. Algorithms for this purpose scale linearly in the number of nuclei. We compute electronic structure by casting the relevant equations in an integral form and solving for the spatial orbitals via iteration. As an example, for several diatomic molecules we solve the Hartree–Fock equations with speeds competitive to those of multi-resolution methods and achieve high accuracy using a small number of parameters.

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 Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

Atoms ◽  
2018 ◽  
Vol 6 (2) ◽  
pp. 22 ◽  
Author(s):  
Thomas Gomez ◽  
Taisuke Nagayama ◽  
Chris Fontes ◽  
Dave Kilcrease ◽  
Stephanie Hansen ◽  
...  
Keyword(s):  
Atomic Structure ◽  
Line Broadening ◽  
Matrix Methods ◽  
Hartree Fock ◽  
Atomic Structure Calculations ◽  
Structure Calculations

scholarly journals Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

2018 ◽  
Author(s):  
Thomas Gomez ◽  
Taisuke Nagayama ◽  
Dave Kilcrease ◽  
Stephanie Hansen ◽  
Mike Montgomery ◽  
...  
Keyword(s):  
Differential Equation ◽  
Atomic Structure ◽  
Shooting Method ◽  
Local Density ◽  
Line Broadening ◽  
Matrix Methods ◽  
Hartree Fock ◽  
Spectral Line Broadening ◽  
Atomic Structure Calculations ◽  
Structure Calculations

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

scholarly journals Atomic structure calculations and beam-foil observations of La IV

2009 ◽  
Vol 87 (12) ◽  
pp. 1275-1282 ◽  
Author(s):  
Émile Biémont ◽  
Mathieu Clar ◽  
Saturnin Yoca Enzonga ◽  
Vanessa Fivet ◽  
Pascal Quinet ◽  
...  
Keyword(s):  
Atomic Structure ◽  
Extreme Ultraviolet ◽  
Complex Situation ◽  
Time Resolved ◽  
Hartree Fock ◽  
Spark Discharges ◽  
Ion Energies ◽  
Atomic Structure Calculations ◽  
Structure Calculations ◽  
Beam Foil

Relativistic Hartree–Fock and multiconfigurational Dirac–Fock calculations of atomic structure and transition rates have been carried out in trebly ionized lanthanum (La3+, Z = 57). The calculations have to cope with configuration interaction effects but also with the very complex situation of the collapse of the 4f wave function. The calculations are compared to experimental data obtained with beam-foil spectroscopy in the extreme ultraviolet, at ion energies that favour the production of the spectrum La IV. Besides lines known from sliding spark discharges, many more lines are observed that have not yet been identified. Time-resolved measurements yield three level lifetimes in La IV that agree roughly with the results of our own calculations.

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