Open-shell localized Hartree–Fock method based on the generalized adiabatic connection Kohn–Sham formalism for a self-consistent treatment of excited states

2005 ◽  
Vol 122 (24) ◽  
pp. 244102 ◽  
Author(s):  
Vincenzo Vitale ◽  
Fabio Della Sala ◽  
Andreas Görling
Keyword(s):  
Excited States ◽  
Open Shell ◽  
Hartree Fock ◽  
Self Consistent ◽  
Consistent Treatment

Self-Consistent Treatment of the Pauli Operator in the Brueckner-Hartree-Fock Approach

1973 ◽  
Vol 8 (1) ◽  
pp. 129-134 ◽  
Author(s):  
Ram K. Tripathi ◽  
Amand Faessler ◽  
Alan D. MacKellar
Keyword(s):  
Pauli Operator ◽  
Hartree Fock ◽  
Self Consistent ◽  
Consistent Treatment

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.

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