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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Page 4
... energy operator . The total energy W is the electronic energy E plus the nucleus - nucleus repulsion energy That is , Vnn = Σ a < ß Z & ZB R & B W = E + Vnn E + Vnn ( 1.1.8 ) ( 1.1.9 ) It is immaterial whether one solves ( 1.1.1 ) for E ...
... energy operator . The total energy W is the electronic energy E plus the nucleus - nucleus repulsion energy That is , Vnn = Σ a < ß Z & ZB R & B W = E + Vnn E + Vnn ( 1.1.8 ) ( 1.1.9 ) It is immaterial whether one solves ( 1.1.1 ) for E ...
Page 8
... total electron - electron repulsion energy Voc = [ " Wit ( x ) ( 2 + = + ) 4 = ( x * ) dx ^ Vee = N HF F ( X ' ' i < jľij ' = 1⁄2 Σ ( J¡¡ – Ki ... total molecular energy including nuclear - nuclear repulsion 8 1.3 DENSITY - FUNCTIONAL THEORY.
... total electron - electron repulsion energy Voc = [ " Wit ( x ) ( 2 + = + ) 4 = ( x * ) dx ^ Vee = N HF F ( X ' ' i < jľij ' = 1⁄2 Σ ( J¡¡ – Ki ... total molecular energy including nuclear - nuclear repulsion 8 1.3 DENSITY - FUNCTIONAL THEORY.
Page 9
Robert G. Parr, Yang Weitao. For the total molecular energy including nuclear - nuclear repulsion , one has from ( 1.1.9 ) , N WHF = ε ; -Vee + Vnn i = 1 N = Σ Hi + Vee + Vnn = i = 1 ( 1.3.17 ) ( 1.3.18 ) Note that neither EHF nor WHF is ...
Robert G. Parr, Yang Weitao. For the total molecular energy including nuclear - nuclear repulsion , one has from ( 1.1.9 ) , N WHF = ε ; -Vee + Vnn i = 1 N = Σ Hi + Vee + Vnn = i = 1 ( 1.3.17 ) ( 1.3.18 ) Note that neither EHF nor WHF is ...
Page 14
... energy tends to remain constant for atomic and molecular changes that ... energies are an order of magnitude or more bigger , even if the self - exchange term ... total number of electrons , [ p ( r ) dr = N ( 1.5.2 ) There has been much ...
... energy tends to remain constant for atomic and molecular changes that ... energies are an order of magnitude or more bigger , even if the self - exchange term ... total number of electrons , [ p ( r ) dr = N ( 1.5.2 ) There has been much ...
Page 18
... energy components of Ĥ . The kinetic energy component , ↑ = Σ ( - { ▽ 2 ) i ( 1.6.8 ) is homogeneous of degree -2 in particle coordinates . The total potential energy component , -Σ Zα 1 για Για + Σ + Σ Tij α a < B ZaZB R & B ( 1.6.9 ) ...
... energy components of Ĥ . The kinetic energy component , ↑ = Σ ( - { ▽ 2 ) i ( 1.6.8 ) is homogeneous of degree -2 in particle coordinates . The total potential energy component , -Σ Zα 1 για Για + Σ + Σ Tij α a < B ZaZB R & B ( 1.6.9 ) ...
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.