scholarly journals Reparametrization of the Colle–Salvetti formula

2022 ◽  
Vol 9 (1) ◽  
Author(s):  
Adam L. Baskerville ◽  
Msugh Targema ◽  
Hazel Cox
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Electron System ◽  
High Accuracy ◽  
Electron Detachment ◽  
Original Formulation ◽  
Functional Theory ◽  
Hartree Fock ◽  
Hydride Ion

We investigate the Colle–Salvetti (CS) formula, the basis of the Lee, Yang and Parr (LYP) correlation functional used in approximate density functional theory. The CS formula is reparametrized using high-accuracy Hartree–Fock (HF) wavefunctions to determine the accuracy of the formula to calculate anions. Fitting to the hydride ion or the two-electron system just prior to electron detachment at the HF level of theory does not, in general, improve the calculated correlation energies using the parameters derived from the CS/LYP method. An analysis of the CS parameters used in the popular LYP functional demonstrates the ingenuity and perhaps fortuitousness of the original formulation by CS.

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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