RELATION BETWEEN ELECTRONS AND HOLES, AND THE VECTOR-COUPLING COEFFICIENTS FOR pmfq AND dnfq CONFIGURATIONS

1966 ◽  
Vol 44 (12) ◽  
pp. 1451-1454 ◽  
Author(s):  
Gulzari L. Malli
Keyword(s):  
Atomic State ◽  
Electrostatic Energy ◽  
Coupling Coefficients ◽  
Vector Coupling ◽  
Energy Expression ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Scf Calculations

The electrostatic energy of an atomic state arising from a configuration involving holes differs by ΔW from the energy expression of the same state arising from the configuration involving electrons where ΔW can be expressed in terms of Slater's integrals.General formulas for ΔW are given for the pmfq and dnfq configurations. In addition, the vector-coupling (VC) coefficients useful for atomic self-consistent field (SCF) calculations are presented for all the states arising from the pmfq and dnfq configurations.

OPTICAL TRANSITIONS IN A PARABOLIC GaAs/Ga1-xAlxAs SUPERLATTICES

2001 ◽  
Vol 08 (03n04) ◽  
pp. 321-325
Author(s):  
ŞAKIR ERKOÇ ◽  
HATICE KÖKTEN
Keyword(s):  
Transition Matrix ◽  
Optical Transition ◽  
Matrix Elements ◽  
Electron States ◽  
Parabolic Potential ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Transition Matrix Elements ◽  
Scf Calculations

We have performed self-consistent field (SCF) calculations of the electronic structure of GaAs/Ga 1-x Al x As superlattices with parabolic potential profile within the effective mass theory. We have calculated the optical transition matrix elements involving transitions from the hole states to the electron states, and we have also computed the oscillator strength matrix elements for the transitions among the electron states.

Faster Self-Consistent Field (SCF) Calculations on GPU Clusters

2021 ◽  
Author(s):  
Giuseppe M. J. Barca ◽  
Melisa Alkan ◽  
Jorge L. Galvez-Vallejo ◽  
David L. Poole ◽  
Alistair P. Rendell ◽  
...  
Keyword(s):  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Gpu Clusters ◽  
Scf Calculations

scholarly journals Optimizing Single Slater Determinant for Electronic Hamiltonian with Lagrange Multipliers and Newton-Raphson Methods as an Alternative to Ground State Calculations via Hartree-Fock Self Consistent Field

2018 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Slater Determinant ◽  
Basis Set ◽  
Variation Principle ◽  
Single Individual ◽  
Hartree Fock ◽  
Energy Expression ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Newton Raphson

Considering the emblematic Hartree-Fock (HF) energy expression with single Slater determinant and the ortho-normal molecular orbits (MO) in it, expressed as a linear combination (LC) of atomic orbits (LCAO) basis set functions, the HF energy expression is in fact a 4th order polynomial of the LCAO coefficients, which is relatively easy to handle. The energy optimization via the Variation Principle can be made with a Lagrange multiplier method to keep the ortho-normal property and the Newton-Raphson (NR) method to find the function minimum. It is an alternative to the widely applied HF self consistent field (HF-SCF) method which is based on unitary transformations and eigensolver during the SCF, and seems to have more convenient convergence property. This method is demonstrated for closed shell (even number of electrons and all MO are occupied with both, alpha and beta spin electrons) and restricted (all MOs have single individual spatial orbital), but the extension of the method to open shell and/or unrestricted cases is straightforward.

Die Reaktivitäten des Porphins, Chlorins, Bacteriochlorins und Phlorins. Ladungsdichten, Freie Valenzen und Außenelektronendichten / The Reactivities of Porphin, Chlorin, Bacteriochlorin, and Phlorin. Electron Densities, Free Valences and Frontier Orbital Densities

1970 ◽  
Vol 25 (7) ◽  
pp. 729-734 ◽  
Author(s):  
J. V. Knop ◽  
J.-H. Fuhrhop
Keyword(s):  
Bond Orders ◽  
Frontier Orbital ◽  
Electron Densities ◽  
Reactivity Indices ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Frontier Orbital Model ◽  
Scf Calculations

The π-electron densities, bond orders, free valences, and reactivity indices according to Fukui's “frontier orbital”-model were calculated for all reactive centers of porphin, chlorin, bacteriochlorin and phlorin by means of Self Consistent Field (SCF) calculations using the approxima tiaons of Pariser, Parr, and Pople. The results were compared with known experimental facts. The relative reactivities of different reactivity centers (e. g. methine-bridges and β-pyrrolic carbon atoms) are well predicted by calculated π-electron densities, whereas the characteristics of similar reactivity centers (e. g. the different methine-bridges in chlorin) are better reflected in the reactivity indices of the “frontier orbital’ model. Reasons for the partial inadequacies of the models used are shortly discussed.

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