scholarly journals Convergence Analysis of Direct Minimization and Self-Consistent Iterations

2021 ◽  
Vol 42 (1) ◽  
pp. 243-274 ◽  
Author(s):  
Éric Cancès ◽  
Gaspard Kemlin ◽  
Antoine Levitt
Keyword(s):  
Convergence Analysis ◽  
Direct Minimization ◽  
Self Consistent

GEOMETRIC DIRECT MINIMIZATION OF HARTREE–FOCK CALCULATIONS INVOLVING OPEN SHELL WAVEFUNCTIONS WITH SPIN RESTRICTED ORBITALS

2002 ◽  
Vol 01 (02) ◽  
pp. 255-261 ◽  
Author(s):  
BARRY D. DUNIETZ ◽  
TROY VAN VOORHIS ◽  
MARTIN HEAD-GORDON
Keyword(s):  
Closed Shell ◽  
Open Shell ◽  
Minimization Method ◽  
Hartree Fock ◽  
Direct Inversion ◽  
Consistent Field ◽  
Direct Minimization ◽  
Self Consistent ◽  
Self Consistent Field

Recently, we have introduced a method based on geometric considerations, termed geometric direct minimization (GDM), to achieve robust convergence of self consistent field calculations. GDM was limited to calculations involving either spin-unrestricted orbitals or closed shell systems. We report the extension of the GDM method to treat open shell systems involving spin-restricted orbitals. Open shell systems pose a challenge for achieving robust convergence of the calculation. We compare the convergence using the GDM method to the convergence achieved by the well known direct inversion in the iterative space (DIIS) technique. This comparison demonstrates the ability of the GDM method to achieve robust convergence. Additionally we assess the importance of geometric considerations by comparing against an alternative direct minimization method that is not geometrically correct.

The evolution of the Kuiper belt during the formation of the outer planets

1999 ◽  
Vol 173 ◽  
pp. 37-44
Author(s):  
M.D. Melita ◽  
A. Brunini
Keyword(s):  
Kuiper Belt ◽  
Outer Planets ◽  
Self Consistent ◽  
Planetary Bodies ◽  
Mass Depletion

AbstractA self-consistent study of the formation of planetary bodies beyond the orbit of Saturn and the evolution of Kuiper disks is carried out by means of an N-body code where accretion and gravitational encounters are considered. This investigation is focused on the aggregation of massive bodies in the outer planetary region and on the consequences of such process in the corresponding cometary belt. We study the link between the bombardment of massive bodies and mass depletion and eccentricity excitation.

THEORY AND SELF-CONSISTENT MODEL OF DUST-DRIVEN WINDS

2002 ◽  
Vol 5 ◽  
pp. 65-65
Author(s):  
S. Liberatore ◽  
J.-P.J. Lafon ◽  
N. Berruyer
Keyword(s):  
Consistent Model ◽  
Self Consistent

Étude de la molécule de méthane par la méthode du champ self-consistent

1959 ◽  
Vol 56 ◽  
pp. 250-256 ◽  
Author(s):  
Sylvette Besnainou ◽  
Monique Roux
Keyword(s):  
Self Consistent
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