Quantal Density Functional Theory (2004. 290 p. w. 50 figs.)

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Quantal Density Functional Theory (2004. 290 p. w. 50 figs.)

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  • 製本 Hardcover:ハードカバー版/ページ数 290 p.
  • 商品コード 9783540408840

基本説明

Contents: Introduction.- Schrödinger Theory from the Perspective of Classical Fields Derived from Quantal Sources.- Quantal Density Functional Theory.- The Hohenberg-Kohn Theorems and Kohn-Sham Density Functional Theory.- and more.

Full Description


Density functional theory is an important and widely used tool in many-body physics that has found applications in atomic, molecular, solid-state and nuclear physics. It is used principally to determine the electronic structure of these complex systems. Sahni has developed a new approach, termed quantal density functional theory, which simplifies the process of solving the computational problem and at the same time, gives insight into the underlying quantum mechanics. Further, the book describes Schrodinger theory from the new perspective of fields and quantal sources. It also explains the physics underlying the functionals and functional derivatives of traditional DFT

Table of Contents

    Introduction                                   1  (7)
Schrodinger Theory from the Perspective of 7 (42)
`Classical' Fields Derived from Quantal
Sources
Time-Dependent Schrodinger Theory 7 (1)
Definitions of Quantal Sources 8 (4)
Electron Density p(rt) 9 (1)
Spinless Single--Particle Density 9 (1)
Matrix γ(rr't)
Pair--Correlation Density g(rr't), and 10 (1)
Fermi--Coulomb Hole ρxc(rr't)
Current Density j(rt) 11 (1)
Definitions of `Classical' Fields 12 (2)
Electron--Interaction Field 12 (1)
εee(rt)
Differential Density Field D(rt) 12 (1)
Kinetic Field Z(rt) 13 (1)
Current Density Field J(rt) 13 (1)
Energy Components in Terms of Quantal 14 (2)
Sources and Fields
Electron-Interaction Potential Energy 14 (1)
Eee(t)
Kinetic Energy T(t) 15 (1)
External Potential Energy Eext(t) 16 (1)
Pure State Differential and Integral 16 (2)
Virial Theorems
The Quantum--Mechanical `Hydrodynamical' 18 (1)
Equations
The Internal Field of the Electrons and 19 (4)
Ehrenfest's Theorem
The Harmonic Potential Theorem 23 (1)
Time-Independent Schrodinger Theory: 24 (6)
Ground and Bound Excited States
Coalescence Conditions 26 (1)
Asymptotic Structure of Wavefunction 27 (3)
and Density
Examples of the Field Perspective: The 30 (13)
Ground and First Excited Singlet State of
the Hooke's Atom
Wavefunction, Orbital Function, and 31 (3)
Density
Fermi--Coulomb Hole Charge Distribution 34 (2)
ρxc(rr')
Hartree, Pauli--Coulomb, and 36 (3)
Electron--Interaction Fields eH(r),
Exc(r), Eee(r) and Energies EH, Exc, Eee
Kinetic Field Z(r) and Kinetic Energy T 39 (1)
Differential Density Field D(r) 40 (2)
Total Energy E and Ionization Potential 42 (1)
I
Expectations of Other Single-Particle 42 (1)
Operators
Schrodinger Theory and Quantum Fluid 43 (6)
Dynamics
Single--Electron Case 43 (2)
Many--Electron Case 45 (4)
Quantal Density Functional Theory 49 (50)
Time--Dependent Quantal Density 50 (13)
Functional Theory
Quantal Sources 51 (3)
Fields 54 (3)
Total Energy and Components in Terms of 57 (3)
Quantal Sources and Fields
Effective Field Feff(rt) and 60 (3)
Electron-Interaction Potential Energy
υee(rt)
Sum Rules 63 (2)
Integral Virial Theorem 63 (1)
Ehrenfest's Theorem 63 (1)
Torque Sum Rule 64 (1)
Time-Independent Quantal Density 65 (6)
Functional Theory
Quantal Sources 66 (1)
Fields 67 (1)
Total Energy and Components 67 (1)
Effective Field Feff(r) and 68 (1)
Electron-Interaction Potential Energy
υee(r)
Sum Rules 69 (1)
Highest Occupied Eigenvalue εm 70 (1)
Endnote 70 (1)
Application of Q--DFT to the Ground and 71 (15)
First Excited Singlet State of the
Hooke's Atom
S System Wavefunction, Spin--Orbitals, 71 (1)
and Density
Pair--Correlation Density; Fermi and 72 (5)
Coulomb Hole Charge Distributions
Hartree, Pauli, and Coulomb Fields 77 (2)
εH(r), εx(r),
εc(r) and Energies EH, Ex, Ec
Hartree WH(r), Pauli Wx(r), and Coulomb 79 (2)
Wc(r) Potential Energies
Correlation-Kinetic Field Ztc(r), 81 (4)
Energy Tc, and Potential Energy Wtc(r)
Total Energy and Ionization Potential 85 (1)
Quantal Density Functional Theory of 86 (13)
Hartree Fock and Hartree Theories
Hartree Fock Theory 87 (2)
The Slater--Bardeen Interpretation of 89 (1)
Hartree--Fock Theory
Theorems in Hartree--Fock Theory 90 (1)
Q--DFT of Hartree--Fock Theory 91 (3)
Hartree Theory 94 (2)
Q--DFT of Hartree Theory 96 (3)
The Hohenberg--Kohn Theorems and Kohn--Sham 99 (26)
Density Functional Theory
The Hohenberg--Kohn Theorems 100(7)
Inverse Maps and Constrained Search 105(2)
Kohn--Sham Density Functional Theory 107(4)
Time--Dependent Density Functional Theory 111(3)
Corollary to the Hohenberg--Kohn Theorem 114(11)
Time-Independent Case 115(5)
Time-Dependent Case 120(2)
Endnote 122(3)
Physical Interpretation of Kohn--Sham 125(28)
Density Functional Theory
Interpretation of the Kohn--Sham 126(4)
Electron--Interaction Energy Functional
EeeKS[ρ] and Its Derivative
υee(r)
Adiabatic Coupling Constant Scheme 130(7)
Q--DFT Within Adiabatic Coupling 131(2)
Constant Framework
KS--DFT Within Adiabatic Coupling 133(2)
Constant Framework
Q--DFT and KS--DFT in Terms of the 135(2)
Adiabatic Coupling Constant
Perturbation Expansion
Interpretation of the Kohn--Sham 137(1)
`Exchange' Energy Functional ExKS[ρ]
and Its Derivative υx(r)
Interpretation of the Kohn--Sham 138(1)
`Correlation' Energy Functional
EcKS[ρ] and Its Derivative
υc(r)
Interpretation of the KS--DFT of 139(1)
Hartree--Fock Theory
Interpretation of the KS--DFT of Hartree 140(1)
Theory
The Optimized Potential Method 141(5)
The Exchange--Only Optimized Potential 142(4)
Method
Physical Interpretation of the Optimized 146(7)
Potential Method
Interpretation of `Exchange--Only' OPM 147(6)
Quantal Density Functional Theory of the 153(14)
Density Amplitude
Density Functional Theory of the B System 154(4)
DFT Definitions of the Pauli Kinetic 157(1)
and Potential Energies
Derivation of the Differential Equation 158(3)
for the Density Amplitude from the
Schrodinger Equation
Quantal Density Functional Theory of the 161(5)
B System
Q--DFT Definitions of the Pauli Kinetic 164(2)
and Potential Energy
Endnote 166(1)
Quantal Density Functional Theory of the 167(20)
Discontinuity in the Electron--Interaction
Potential Energy
Origin of the Discontinuity of the 168(3)
Electron--Interaction Potential Energy
Expression for Discontinuity Δ in 171(3)
Terms of S System Eigenvalues
Correlations Contributing to the 174(1)
Discontinuity According to Kohn--Sham
Theory
Quantal Density Functional Theory of the 175(11)
Discontinuity
Correlations Contributing to the 177(3)
Discontinuity According to Q-DFT:
Analytical Proof
Numerical Examples 180(6)
Endnote 186(1)
Further Insights Derived Via Quantal 187(28)
Density Functional Theory
The Local Density Approximation in 189(16)
Kohn--Sham Theory
Derivation and Interpretation of 189(3)
Electron Correlations Via Kohn--Sham
Theory
Derivation and Interpretation of 192(6)
Electron Correlations Via Quantal
Density Functional Theory
Structure of the Fermi Hole in the 198(5)
Local Density Approximation
Endnote 203(2)
Slater Theory 205(10)
Derivation of the Exact `Slater 205(3)
Potential'
Why the `Slater Exchange Potential' 208(2)
Does Not Represent the Potential Energy
of an Electron
Correctly Accounting for the Dynamic 210(2)
Nature of the Fermi Hole
The Local Density Approximation in 212(3)
Slater Theory
Epilogue 215(6)
Asymptotic Structure of the 216(5)
Electron-Interaction Potential Energy in
the Classically Forbidden Region of Atoms
and Metal Surfaces
Asymptotic Structure in Atoms 216(1)
Asymptotic Structure at Metal Surfaces 217(4)
Appendices 221(24)
A.Proof of the Pure State Differential 221(4)
Virial Theorem
B. Proof of the Harmonic Potential Theorem 225(2)
C. Analytical Expressions for the 227(9)
Properties of the Ground and First
Excited Singlet States of the Hooke's Atom
C.1 Ground State (k = 1/4) 227(5)
C.2 First Excited Singlet State (k = 232(4)
0.144498; w = √k = 0.381029)
D. Derivation of the 236(2)
Kinetic--Energy--Density Tensor for
Hooke's Atom in Its Ground State
E. Proof of the S System Differential 238(2)
Virial Theorem
F. Derivation of the Pair--Correlation 240(5)
Density in the Local Density
Approximation for Exchange
References 245(8)
Index 253