scholarly journals The Theory and Computational Implementation of Quadratically Convergent Hartree-Fock Orbital Optimization Methods and Their Relationship to the Time-dependent Hartree-Fock and RPA Methods

1982 ◽  
Vol 35 (5) ◽  
pp. 639 ◽  
Author(s):  
George B Bacskay
Keyword(s):  
Optimization Methods ◽  
Second Quantization ◽  
Hartree Fock ◽  
Orbital Optimization ◽  
Consistent Field ◽  
Computational Implementation ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Newton Raphson ◽  
Raphson Method

The theory of quadratically convergent Hartree-Fock or self-consistent field (QC-SCF) orbital optimization is presented using the language of second quantization. Two methods that are appropriate for the computational implementation of QC-SCF are described: the Newton-Raphson method and an approximate super configuration interaction (CI) approach, both of which can be implemented such that no four-index transformation is necessary.

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.

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.

scholarly journals HARTREE--FOCK SELF-CONSISTENT FIELD CALCULATIONS FOR IRIDIUM.

1969 ◽  
Author(s):  
L. Panek ◽  
G. Perlow
Keyword(s):  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Hartree Fock Slater self consistent field calculations

1970 ◽  
Vol 1 (3) ◽  
pp. 216-222 ◽  
Author(s):  
J.P. Desclaux
Keyword(s):  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

A General Theory of Self-Consistent Field Beyond Hartree-Fock

1993 ◽  
Vol 20 (2) ◽  
pp. 239-242
Author(s):  
Huan-wu Peng
Keyword(s):  
General Theory ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field
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