Density-Functional Theory of Atoms and MoleculesThis book is a rigorous, unified account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. Containing a detailed discussion of the chemical potential and its derivatives, it provides an understanding of the concepts of electronegativity, hardness and softness, and chemical reactivity. Both the Hohenberg-Kohn-Sham and the Levy-Lieb derivations of the basic theorems are presented, and extensive references to the literature are included. Two introductory chapters and several appendices provide all the background material necessary beyond a knowledge of elementary quantum theory. The book is intended for physicists, chemists, and advanced students in chemistry. |
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Results 1-5 of 82
Page viii
... kinetic - energy functional 149 7.4 Local - density and Xa approximations 152 7.5 The integral formulation 157 7.6 Extension to nonintegral occupation numbers and the transition - state concept 163 8. The Kohn - Sham method ...
... kinetic - energy functional 149 7.4 Local - density and Xa approximations 152 7.5 The integral formulation 157 7.6 Extension to nonintegral occupation numbers and the transition - state concept 163 8. The Kohn - Sham method ...
Page 3
... energy , Ψ = Ψ ( x1 , x2 , . . function , xnd Ĥ is the Hamiltonian operator , A = in which N N Ž ( −¿ ▽ ? ) + Σ v ( x ) + Ž i = 1 i = 1 Za v ... kinetic energy operator , ↑ = N 3 1. Elementary wave mechanics 1.1 The Schrödinger equation.
... energy , Ψ = Ψ ( x1 , x2 , . . function , xnd Ĥ is the Hamiltonian operator , A = in which N N Ž ( −¿ ▽ ? ) + Σ v ( x ) + Ž i = 1 i = 1 Za v ... kinetic energy operator , ↑ = N 3 1. Elementary wave mechanics 1.1 The Schrödinger equation.
Page 4
Robert G. Parr, Yang Weitao. where is the kinetic energy operator , ↑ = N Î Σ ( -17 ) i = 1 N ( 1.1.5 ) Vne = Σ v ( ri ) ( 1.1.6 ) i = 1 is the electron - nucleus attraction energy operator , and Vee = Σ ( 1.1.7 ) i < jij is the ...
Robert G. Parr, Yang Weitao. where is the kinetic energy operator , ↑ = N Î Σ ( -17 ) i = 1 N ( 1.1.5 ) Vne = Σ v ( ri ) ( 1.1.6 ) i = 1 is the electron - nucleus attraction energy operator , and Vee = Σ ( 1.1.7 ) i < jij is the ...
Page 5
... kinetic and potential energies are given by the formulas and T [ Y ] = { ' Î ' ) = { ¥ * Î ¥ dx V [ Y ] = ( V ) = { ¥ * V ¥ dx ( 1.1.13 ) ( 1.1.14 ) The square brackets here denote that Ψ determines T and V ; we say that T and V are ...
... kinetic and potential energies are given by the formulas and T [ Y ] = { ' Î ' ) = { ¥ * Î ¥ dx V [ Y ] = ( V ) = { ¥ * V ¥ dx ( 1.1.13 ) ( 1.1.14 ) The square brackets here denote that Ψ determines T and V ; we say that T and V are ...
Page 7
... energy E [ N , v ] and other properties of interest . Note that in this statement there is no mention of the kinetic - energy or electron- repulsion parts of Ĥ , because these are universal in that they are determined by N. We say that ...
... energy E [ N , v ] and other properties of interest . Note that in this statement there is no mention of the kinetic - energy or electron- repulsion parts of Ĥ , because these are universal in that they are determined by N. We say that ...
Contents
3 | |
20 | |
3 Densityfunctional theory | 47 |
4 The chemical potential | 70 |
5 Chemical potential derivatives | 87 |
6 ThomasFermi and related models | 105 |
Basic principles | 142 |
Elaboration | 169 |
Functionals | 246 |
Convex functions and functionals | 255 |
Second quantization for fermions | 259 |
The Wigner distribution function and the h semiclassical expansion | 265 |
The uniform electron gas | 271 |
Tables of values of electronegativities and hardnesses | 276 |
The review literature of densityfunctional theory | 281 |
Bibliography | 285 |
9 Extensions | 201 |
10 Aspects of atoms and molecules | 218 |
11 Miscellany | 237 |
Author index | 319 |
Subject index | 325 |
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Common terms and phrases
Appendix atoms and molecules Bartolotti bond calculations canonical ensemble Chem chemical potential components constrained-search convex coordinates correlation energy corresponding defined density functional theory density matrix density operator density-functional theory determined dp(r dr₁ dr₂ Dreizler eigenstates eigenvalues electron density electronegativity electrostatic energy functional equilibrium exact Exc[p exchange energy exchange-correlation external potential formula Ghosh given gives gradient expansion grand canonical ensemble grand potential ground ground-state energy Gunnarsson Hamiltonian hardness Hartree-Fock Hohenberg-Kohn integral interaction kinetic energy Kohn Kohn-Sham equations Lett Levy Lieb local-density approximation Lundqvist minimization minimum molecular N-electron Nalewajski noninteracting number of electrons obtain orbitals P₁ parameter Parr particle Perdew Phys quantum r₁ r₂ reduced density Sham softness Sp(r spin theorem Thomas-Fermi theory total energy v-representable values variational principle Vee[P Veff(r wave function x₁ Y₁
Popular passages
Page i - FRS THE INTERNATIONAL SERIES OF MONOGRAPHS ON CHEMISTRY 1. JD Lambert: Vibrational and rotational relaxation in gases 2. NG Parsonage and LAK Staveley: Disorder in crystals 3. GC Maitland, M. Rigby, EB Smith, and WA Wakeham: Intermolecular forces: their origin and determination 4. WG Richards, HP Trivedi, and DL Cooper: Spin-orbit coupling in molecules 5. CF Cullis and MM Hirschler: The combustion of organic polymers 6. RT Bailey, AM North, and RA Pethrick: Molecular motion in high polymers 7.
Page 287 - Becke, AD (1993): Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648-5652 8.
Page 293 - Molecular orbital theory of orientation in aromatic heteroaromatic, and other conjugated molecules.
Page 296 - Correlation energy correction as a density functional. A model of the pair distribution function and its application to the first- and second-row atoms and hydrides. Chem. Phys.
Page 295 - B 12: 2111-2120. Golden, S. (1957a). Statistical theory of many-electron systems. General considerations pertaining to the Thomas-Fermi theory. Phys. Rev. 105: 604615. Golden, S. (1957b). Statistical theory of many-electron systems. Discrete bases of representation. Phys. Rev. 107: 1283-1290. Golden, S. (1960). Statistical theory of electronic energies. Rev. Mod. Phys. 32: 322-327. Goldstein, JA and Rieder, GR (1987). A rigorous modified Thomas-Fermi theory for atomic systems.
Page 294 - Behavior of the chemical potential of neutral atoms in the limit of large nuclear charge.
Page 47 - His main assumption is that the electrons are distributed uniformly in the six-dimensional phase space for the motion of an electron at the rate of two for each h* of 6-volume.
Page 287 - Completely numerical calculations on diatomic molecules in the localdensity approximation. Phys. Rev. A 33: 2786-2788.