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Kohn

In a number of classic papers Hohenberg, Kohn and Sham established a theoretical framework for justifying the replacement of die many-body wavefiinction by one-electron orbitals [15, 20, 21]. In particular, they proposed that die charge density plays a central role in describing the electronic stnicture of matter. A key aspect of their work was the local density approximation (LDA). Within this approximation, one can express the exchange energy as... [Pg.95]

Kohn-Sham or Slater exchange was more accurate for realistic systems [H]. Slater suggested that a parameter be introduced that would allow one to vary the exchange between the Slater and Kolm-Sham values [19]. The parameter, a, was often... [Pg.96]

Once a solution of the Kohn-Sham equation is obtained, the total energy can be computed from... [Pg.96]

The wavevector is a good quantum number e.g., the orbitals of the Kohn-Sham equations [21] can be rigorously labelled by k and spin. In tln-ee dimensions, four quantum numbers are required to characterize an eigenstate. In spherically syimnetric atoms, the numbers correspond to n, /, m., s, the principal, angular momentum, azimuthal and spin quantum numbers, respectively. Bloch s theorem states that the equivalent... [Pg.101]

A completely difierent approach to scattering involves writing down an expression that can be used to obtain S directly from the wavefunction, and which is stationary with respect to small errors in die waveftmction. In this case one can obtain the scattering matrix element by variational theory. A recent review of this topic has been given by Miller [32]. There are many different expressions that give S as a ftmctional of the wavefunction and, therefore, there are many different variational theories. This section describes the Kohn variational theory, which has proven particularly useftil in many applications in chemical reaction dynamics. To keep the derivation as simple as possible, we restrict our consideration to potentials of die type plotted in figure A3.11.1(c) where the waveftmcfton vanishes in the limit of v -oo, and where the Smatrix is a scalar property so we can drop the matrix notation. [Pg.968]

Miller W H 1994 S-matrix version of the Kohn variational principle for quantum scattering theory of... [Pg.1003]

Parr B 2000 webpage http //net.chem.unc.edu/facultv/rap/cfrap01. html Professor Parr was among the first to push the density functional theory of Hohenberg and Kohn to bring it into the mainstream of electronic structure theory. For a good overview, see the book ... [Pg.2198]

Flohenberg P and Kohn W 1964 Inhomogeneous electron gas Phys. RevB 136 864-72... [Pg.2198]

The Flohenberg-Kohn theorem and the basis of much of density functional theory are treated ... [Pg.2198]

Kohn W and Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev A 140 1133-8... [Pg.2198]

In DFT, the electronic density rather than the wavefiinction is tire basic variable. Flohenberg and Kohn showed [24] that all the observable ground-state properties of a system of interacting electrons moving in an external potential are uniquely dependent on the charge density p(r) that minimizes the system s total... [Pg.2207]

Kleinman L 1997 Significance of the highest occupied Kohn-Sham eigenvalue Phys. Rev. B 56 12 042-5... [Pg.2230]

Kohn W and Rostoker N 1954 Soiution of the Sohrddinger equation in periodio iattioes with an appiioation to metaiiio iithium Phys. Rev. 94 1111-20... [Pg.2231]

Zhang J Z H and Miller W H 1989 Quantum reactive scattering via the S-matrix version of the Kohn variational principle—differential and integral cross sections for D + Hj —> HD + H J. Chem. Phys. 91 1528... [Pg.2324]

Kohn and Sham wrote the density p(r) of the system as the sum of the square moduli of a set of one-electron orthonormal orbitals ... [Pg.149]

By introducing this expression for the electron density and applying the appropriate variational condition the following one-electron Kohn-Sham equations result ... [Pg.149]

To. solve the Kohn-Sham equations a self-consistent approach is taken. An initial guess of the density is fed into Equation (3.47) from which a set of orbitals can be derived, leading to an improved value for the density, which is then used in the second iteration, and so on until convergence is achieved. [Pg.149]

The total electron density is just the sum of the densities for the two types of electron. The exchange-correlation functional is typically different for the two cases, leading to a set of spin-polarised Kohn-Sham equations ... [Pg.149]

In addition to the energy terms for the exchange-correlation contribution (which enables the total energy to be determined) it is necessary to have corresponding terms for the potential, Vxc[p(i )]/ which are used to solve the Kohn-Sham equations. These are obtained as the appropriate first derivatives using Equation (3.52). [Pg.151]

To solve the Kohn-Sham equations a number of different approaches and strategies have been proposed. One important way in which these can differ is in the choice of basis set for expanding the Kohn-Sham orbitals. In most (but not all) DPT programs for calculating the properties of molecular systems (rather than for solid-state materials) the Kohn-Sham orbitals are expressed as a linear combination of atomic-centred basis functions ... [Pg.151]


See other pages where Kohn is mentioned: [Pg.289]    [Pg.749]    [Pg.135]    [Pg.2207]    [Pg.2208]    [Pg.2213]    [Pg.2229]    [Pg.2289]    [Pg.425]    [Pg.425]    [Pg.389]    [Pg.397]    [Pg.397]    [Pg.147]    [Pg.148]    [Pg.148]    [Pg.152]    [Pg.152]    [Pg.152]    [Pg.152]    [Pg.152]    [Pg.154]    [Pg.154]    [Pg.155]    [Pg.156]   


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Beyond Two-Body Interaction Fragment-Localized Kohn-Sham Orbitals via a Singles-CI Procedure

Calculations Dirac-Kohn-Sham

Canonical Kohn-Sham orbitals

Charge density Kohn-Sham

Coherent potential approximation Korringa-Kohn-Rostoker

Complex Kohn variational method

Constrained Search Method for Constructing Kohn-Sham Potentials

Correlation energy Kohn-Sham theory, physical

Coupled perturbed Kohn-Sham theory

Coupled perturbed-Kohn Sham

Coupled perturbed-Kohn Sham method

Coupled-perturbed Kohn-Sham equations

Current DFT Methods The Kohn-Sham Approach

DFT as an effective single-body theory The Kohn-Sham equations

Definitions Within Kohn-Sham Theory

Degenerate ground states Hohenberg-Kohn theorems

Density Functional Theory and the Kohn-Sham Equation

Density Hohenberg-Kohn theorems

Density Kohn-Sham formulation

Density function method Kohn-Sham orbital

Density function theory Kohn-Sham orbitals

Density functional Kohn-Sham equations

Density functional Kohn-Sham orbitals

Density functional theory Hohenberg-Kohn theorem

Density functional theory Kohn-Sham approach

Density functional theory Kohn-Sham approximation

Density functional theory Kohn-Sham construction

Density functional theory Kohn-Sham equations

Density functional theory Kohn-Sham method

Density functionals Hohenberg-Kohn theorem

Density functionals Slater-Kohn-Sham-type methods

Density matrices Kohn-Sham

Density-functional theory and Kohn-Sham orbitals

Derivation Kohn-Sham model

Derivation of the Kohn-Sham equations

Dirac-Kohn-Sham method

Dirac-Kohn-Sham relativistic wave functions

Effective Kohn-Sham potential

Electron correlation Hohenberg-Kohn theorem

Electron density Hohenberg-Kohn theorems

Electron density Hohenberg-Kohn-Sham equations

Electron density Kohn-Sham theory

Electronic Kohn-Sham energy

Electronic structure Korringa-Kohn-Rostoker method

Electronic structure methods Kohn-Sham equations

Electronic structure, Kohn-Sham

Energy Kohn-Sham theory, physical

Exact Kohn-Sham potentials

Exchange energy Kohn-Sham theory, physical

Exchange potential Kohn-Sham

Exchange potential from Kohn-Sham equations

Excited Kohn-Sham determinants

Extended Kohn-Sham

Extended Kohn-Sham hardness

Extended Kohn-Sham method

Fragment Localized Kohn-Sham orbitals

Fukui function Kohn-Sham potential

Full Solution of the Kohn-Sham Equations

Generalized Kohn-Sham method

Giant Kohn anomaly

Hamiltonian operator Kohn-Sham

Hardness Hohenberg-Kohn theorem

Hermitian Kohn-Sham

Highest occupied orbital Kohn-Sham theory

Hohenberg and Kohn

Hohenberg and Kohn theorem

Hohenberg-Kohn

Hohenberg-Kohn and Two Other Density Theorems

Hohenberg-Kohn functional

Hohenberg-Kohn principle

Hohenberg-Kohn properties

Hohenberg-Kohn relations

Hohenberg-Kohn theorem

Hohenberg-Kohn theorem energy surfaces

Hohenberg-Kohn theorem ground-state electron density

Hohenberg-Kohn theorem, electronic

Hohenberg-Kohn theorem, electronic kinetic energy

Hohenberg-Kohn theorem, wave function

Hohenberg-Kohn theorem, wave function calculations

Hohenberg-Kohn theorems exchange correlation functional energy

Hohenberg-Kohn theorems local density approximation

Hohenberg-Kohn theorems orbital functional theory

Hohenberg-Kohn theorems relationship

Hohenberg-Kohn theorems theory

Hohenberg-Kohn theorems uniqueness

Hohenberg-Kohn theory

Hohenberg-Kohn theory definition

Hohenberg-Kohn theory energy density functionals

Hohenberg-Kohn variational theorem

Hohenberg-Kohn “existence theorems

Hohenberg-Kohn-Sham

Hohenberg-Kohn-Sham density functional

Hohenberg-Kohn-Sham density functional theory

Hohenberg-Kohn-Sham equations

Hohenberg-Kohn-Sham equations electronic energy

Hohenberg-Kohn-Sham formalism

Hohenberg-Kohn-Sham theorem

Hohenberg-Kohn-Sham theory

INDEX Kohn-Sham functional

Implementation of Kohn-Sham LCAO Method in Crystals Calculations

Is the Kohn-Sham Approach a Single Determinant Method

KS-LCAO (Kohn-Sham Linear Model

Kohn Formulation

Kohn Sham exchange-correlation

Kohn Sham theorem

Kohn and Sham

Kohn anomalies

Kohn approach

Kohn equations

Kohn expression

Kohn functional

Kohn linear scaling techniques

Kohn matrix

Kohn operator

Kohn orbital energies

Kohn orbitals

Kohn potential

Kohn unrestricted formalism

Kohn variation principle

Kohn variational method

Kohn variational method formation

Kohn variational method scattering

Kohn variational principle

Kohn variational theory

Kohn, David

Kohn, Walter

Kohn-Rostoker variational principle

Kohn-Sham

Kohn-Sham DFT

Kohn-Sham Density Functional Theory Predicting and Understanding Chemistry

Kohn-Sham Energy Functional and Equations

Kohn-Sham Equations with Constrained Electron Density

Kohn-Sham Fukui functions

Kohn-Sham Hamiltonian

Kohn-Sham Hamiltonian, matrix element

Kohn-Sham Hamiltonian, matrix element calculations

Kohn-Sham LCAO Method for Periodic Systems

Kohn-Sham MO theory

Kohn-Sham Non-interacting System

Kohn-Sham Self-consistent Field Methodology

Kohn-Sham Theory by Legendre Transforms

Kohn-Sham approach

Kohn-Sham approximation

Kohn-Sham assumption

Kohn-Sham atomic orbitals

Kohn-Sham chemical potential

Kohn-Sham computational methodologies

Kohn-Sham construction

Kohn-Sham density

Kohn-Sham density functional theory

Kohn-Sham density functional theory KS-DFT)

Kohn-Sham density functional theory procedures

Kohn-Sham density functional theory, orbital

Kohn-Sham density functional theory, orbital occupation numbers

Kohn-Sham derivation

Kohn-Sham determinant

Kohn-Sham effective

Kohn-Sham eigenfunctions

Kohn-Sham eigenvalues

Kohn-Sham electron density

Kohn-Sham energy

Kohn-Sham energy expression

Kohn-Sham energy functional

Kohn-Sham equation

Kohn-Sham equation, density

Kohn-Sham equations Jellium model

Kohn-Sham equations LCAO method

Kohn-Sham equations conclusions

Kohn-Sham equations defined

Kohn-Sham equations exchange energy

Kohn-Sham equations introduction

Kohn-Sham equations local density approximation

Kohn-Sham equations method determination

Kohn-Sham equations methodology

Kohn-Sham equations numerical basis sets

Kohn-Sham equations relativistic

Kohn-Sham equations self-consistent solution

Kohn-Sham equations solution

Kohn-Sham equations solving

Kohn-Sham equations total energy

Kohn-Sham exchange

Kohn-Sham formalism

Kohn-Sham formalism, description

Kohn-Sham formulation

Kohn-Sham formulation of DFT

Kohn-Sham framework

Kohn-Sham functional

Kohn-Sham functionals

Kohn-Sham gap

Kohn-Sham kinetic energy

Kohn-Sham local potential

Kohn-Sham matrices

Kohn-Sham matrix elements

Kohn-Sham method

Kohn-Sham method linear-scaling methods

Kohn-Sham modifications

Kohn-Sham molecular orbital method

Kohn-Sham one-electron equations

Kohn-Sham orbital

Kohn-Sham orbital eigenvalues

Kohn-Sham orbital energies

Kohn-Sham orbital expansion

Kohn-Sham orbitals

Kohn-Sham orbitals Density functional theory

Kohn-Sham orbitals and potentials for beryllium by means of local scaling transformations

Kohn-Sham orbitals requirements

Kohn-Sham orbitals theory

Kohn-Sham orbitals, comparison

Kohn-Sham perturbation theory

Kohn-Sham perturbed

Kohn-Sham positive-energy

Kohn-Sham potential Subject

Kohn-Sham potential linear-scaling methods

Kohn-Sham potentials

Kohn-Sham potentials comparison

Kohn-Sham potentials definition

Kohn-Sham procedure

Kohn-Sham radial wave function

Kohn-Sham relation

Kohn-Sham representation

Kohn-Sham response function

Kohn-Sham scheme

Kohn-Sham scheme/orbitals

Kohn-Sham self-consistent-field

Kohn-Sham self-consistent-field methods

Kohn-Sham single-particle energies

Kohn-Sham system

Kohn-Sham theorem, wave function calculations

Kohn-Sham theory

Kohn-Sham theory Koopmans theorem

Kohn-Sham theory Subject

Kohn-Sham theory adiabatic connection methods

Kohn-Sham theory derivative

Kohn-Sham theory electronegativity

Kohn-Sham theory exchange-correlation energy functional

Kohn-Sham theory field)

Kohn-Sham wavefunction, definition

Kohn-Sham-Dirac equation

Kohn-Sham-Fock operator

Kohn-Sham-like equations

Kohn-Sham/Hartree-Fock

Kohn-Sham/Hartree-Fock model

Korringa, Kohn, Rostoker

Korringa, Kohn, and Rostoker

Korringa-Kohn-Rostocker

Korringa-Kohn-Rostoker Green-function method

Korringa-Kohn-Rostoker method

Lang and Kohn

Lang-Kohn theory

Luttinger-Kohn Hamiltonian

Molecular orbitals Kohn-Sham

Operator Kohn-Sham,

Orbitals self-consistent, Kohn-Sham, structure

Pores of Kohn

Reference state Kohn-Sham

Relativistic Dirac-Kohn-Sham method

Relativistic Hohenberg-Kohn Theorem

Restricted Open-Shell Kohn-Sham Theory (ROKS)

Restricted ensemble Kohn-Sham

Restricted open-shell Kohn-Sham

Restricted open-shell Kohn-Sham ROKS)

S-Matrix Kohn method

S-matrix version of the Hulthen-Kohn-variational principle

Slater-Kohn-Sham potential

Solution of the Kohn-Sham-Dirac Equations

Solving the Kohn-Sham Equations

Spin-restricted open-shell Kohn-Sham

Spin-restricted open-shell Kohn-Sham method

Spin-unrestricted Kohn—Sham equations

Strategies for Solving the Kohn-Sham Equations

Summary of Kohn-Sham Spin-Density Functional Theory

The Dirac-Kohn-Sham scheme

The First Hohenberg-Kohn Theorem Proof of Existence

The Four-Component Kohn-Sham Model

The Hohenberg-Kohn Existence Theorem

The Hohenberg-Kohn Theorem

The Hohenberg-Kohn Theorem for Degenerate Ground States

The Hohenberg-Kohn Theorem for Relativistic -Particle Systems

The Hohenberg-Kohn Variational Theorem

The Hulthen-Kohn variational principle

The Kohn-Sham Approach

The Kohn-Sham Auxiliary System of Equations

The Kohn-Sham Equations

The Kohn-Sham Method

The Kohn-Sham Model

The Kohn-Sham Molecular Orbital Model

The Kohn-Sham Potential is Local

The Kohn-Sham Single-particle Equations

The Kohn-Sham construction

The Kohn-Sham scheme

The Kohn-Sham system of non-interacting electrons

The Second Hohenberg-Kohn Theorem Variational Principle

The complex Kohn method

Time-dependent Kohn-Sham

Time-dependent Kohn-Sham equation

Time-dependent Kohn-Sham method

Time-dependent Kohn-Sham potential

Towards Linear Scaling Kohn-Sham Theory

Two important Hohenberg-Kohn theorems

Unrestricted Kohn-Sham approach

Variational principles Hulthen-Kohn

Variational principles complex Kohn

Wave function Kohn-Sham

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