scholarly journals Microscopic derivation of density functional theory for superfluid systems based on effective action formalism

2020 ◽  
Author(s):  
Takeru Yokota ◽  
Haruki Kasuya ◽  
Kenichi Yoshida ◽  
Teiji Kunihiro
Keyword(s):  
Density Functional Theory ◽  
Effective Action ◽  
Density Functional ◽  
Variational Equation ◽  
Exact Expression ◽  
Flow Equation ◽  
Equilibrium Density ◽  
Functional Theory ◽  
Hartree Fock ◽  
Bogoliubov Theory

Abstract Density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and nonlocal pairing densities and demonstrate that the Hohenberg–Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from 0 to 1, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn–Sham potential generalized to including the pairing potentials. The resultant Kohn–Sham potential has a nice feature that it expresses the microscopic formulae of the external, Hartree, pairing, and exchange-correlation terms, separately. It is shown that our Kohn–Sham potential gives the ground-state energy of the Hartree–Fock–Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to systematically improve the correlation part.

scholarly journals An investigation of the performance of a hybrid of Hartree-Fock and density functional theory

1992 ◽  
Vol 44 (S26) ◽  
pp. 319-331 ◽  
Author(s):  
Peter M. W. Gill ◽  
Benny G. Johnson ◽  
John A. Pople ◽  
Michael J. Frisch
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Hartree Fock

scholarly journals Effect of Hartree–Fock pseudopotentials on local density functional theory calculations

2018 ◽  
Vol 20 (27) ◽  
pp. 18844-18849 ◽  
Author(s):  
Hengxin Tan ◽  
Yuanchang Li ◽  
S. B. Zhang ◽  
Wenhui Duan
Keyword(s):  
Density Functional Theory ◽  
Band Gap ◽  
Density Functional ◽  
Local Density ◽  
Density Functional Theory Calculations ◽  
Optimal Choice ◽  
Functional Theory ◽  
Hartree Fock ◽  
Local Density Functional Theory ◽  
Local Density Functional

Optimal choice of the element-specific pseudopotential improves the band gap.

Theoretical Methods

1992 ◽  
Author(s):  
John A. Tossell ◽  
David J. Vaughan
Keyword(s):  
Density Functional Theory ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Point Group ◽  
Theoretical Background ◽  
Wave Functions ◽  
General Reference ◽  
Functional Theory ◽  
Hartree Fock ◽  
Self Consistent Field

In this chapter, the most important quantum-mechanical methods that can be applied to geological materials are described briefly. The approach used follows that of modern quantum-chemistry textbooks rather than being a historical account of the development of quantum theory and the derivation of the Schrödinger equation from the classical wave equation. The latter approach may serve as a better introduction to the field for those readers with a more limited theoretical background and has recently been well presented in a chapter by McMillan and Hess (1988), which such readers are advised to study initially. Computational aspects of quantum chemistry are also well treated by Hinchliffe (1988). In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first; that is, the “localized” side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (CI) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. The focus then shifts to the “delocalized” side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field Xα method (MS-SCF-Xα) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is followed by discussion of empirical simulation, and we conclude by mentioning a recent approach incorporating density-functional theory and molecular dynamics (Car and Parrinello, 1985).

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