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Quantal Density Functional Theory 2004 ed., v.XIII [Kõva köide]

  • Formaat: Hardback, 270 pages, kõrgus x laius x paksus: 234x156x15 mm, kaal: 559 g, biography
  • Ilmumisaeg: 13-Jan-2004
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540408843
  • ISBN-13: 9783540408840
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  • Formaat: Hardback, 270 pages, kõrgus x laius x paksus: 234x156x15 mm, kaal: 559 g, biography
  • Ilmumisaeg: 13-Jan-2004
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540408843
  • ISBN-13: 9783540408840
Teised raamatud teemal:
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

Arvustused

"Gives physical insight because it renders the many-fermion problem in as close to a classical mechanical and electrodynamical form as can be imagined... It is an interesting, unconventional, and useful contribution to the DFT literature. " -- INT. J. QUANTUM CHEM. "This book shows how in an entirely new way, it becomes plausible to use the wave function within the broad context of DFT, thus redirecting the present computational approach of attempting to approximate the presently unknown, and thus largely mysterious, HK energy functional of the density. The claim is that the simplicity of the equations of DFT is retained on the one hand, while on the other hand, ridding them of their mystery, as contained in the Kohn-Sham (KS) local potential ... The book describes all quantum systems, including atoms and molecules, in terms of the fields inherent to the systems deriving from their quantal sources. Indeed, an innovation of QDFT is to identify all such fields, and to explicitly write their dependence upon the various quantal sources. The result is a description of quantum chemistry that is as close to a classical description as one may imagine... "All readers interested in how DFT fits within the larger theoretical structure of quantum theory will profit from this book. It marshals an effective argument for the existence of a specifically Q-DFT view of the density as cardinal object of quantum theory. To accept that argument in its entirety is to see Q-DFT as the fulfillment of the HK theorem promise, to turn the density into all the quantum properties of a chemical system. That in turn could lead to a conceptual and computational revolution within quantum chemistry, the like of which has not been seen since the original HK and KS papers of some 40 years ago." - J. CHEM. EDUCATION (L. Massa, CUNY)

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