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

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Lagrange Multipliers ◽  
Ground State ◽  
Slater Determinant ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Newton Raphson

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.

Self-consistent Field Orbital Methods

2020 ◽  
pp. 128-149
Author(s):  
Jochen Autschbach
Keyword(s):  
Density Functional ◽  
Slater Determinant ◽  
Closed Shell ◽  
Open Shell ◽  
Initial Guess ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Definition Of

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.

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.

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