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 v
... quantities of great intuitive appeal , mostly long well - known to chemists in one guise or another . These include the electronegativity of Pauling and Mulliken , the hardness and softness of Pearson , and the reactivity indices of ...
... quantities of great intuitive appeal , mostly long well - known to chemists in one guise or another . These include the electronegativity of Pauling and Mulliken , the hardness and softness of Pearson , and the reactivity indices of ...
Page 6
... quantity [ ( Y | Â │Y ) – E ( Y | Y ) ] without constraint , with E the Lagrange multiplier . This gives 8 [ ( Y | Â │Y ) – E ( Y | Y ) ] = 0 . ( 1.2.8 ) One must solve this equation for Ψ as a function of E , then adjust E until ...
... quantity [ ( Y | Â │Y ) – E ( Y | Y ) ] without constraint , with E the Lagrange multiplier . This gives 8 [ ( Y | Â │Y ) – E ( Y | Y ) ] = 0 . ( 1.2.8 ) One must solve this equation for Ψ as a function of E , then adjust E until ...
Page 14
... quantity will be of great importance in this book ; we designate it by p ( r ) . Its formula in terms of is p ( 11 ) = N √ · · · [ 1 ¥ ( X1 , X2 , 2 1 XN ) 2 ds1 dx2 dxN ( 1.5.1 ) This is a nonnegative simple function of three ...
... quantity will be of great importance in this book ; we designate it by p ( r ) . Its formula in terms of is p ( 11 ) = N √ · · · [ 1 ¥ ( X1 , X2 , 2 1 XN ) 2 ds1 dx2 dxN ( 1.5.1 ) This is a nonnegative simple function of three ...
Page 15
... δυ ( 2 ) δυ ( Γ . ) j + k WI Σ [ [ ... ] yo yo ds2 dx dx3 ⋅⋅ dxn ] [ ƒ · · · √ ч ° * ° ds , dx1⁄2 dx3 · · ( E - E ) dxN ( 1.5.9 ) This quantity is called the linear response function . The 1.5 15 ELEMENTARY WAVE MECHANICS.
... δυ ( 2 ) δυ ( Γ . ) j + k WI Σ [ [ ... ] yo yo ds2 dx dx3 ⋅⋅ dxn ] [ ƒ · · · √ ч ° * ° ds , dx1⁄2 dx3 · · ( E - E ) dxN ( 1.5.9 ) This quantity is called the linear response function . The 1.5 15 ELEMENTARY WAVE MECHANICS.
Page 16
Robert G. Parr, Yang Weitao. This quantity is called the linear response function . The symmetry represented in ( 1.5.9 ) is important . If a perturbation at point 1 produces a density change at point 2 , then the same perturbation at ...
Robert G. Parr, Yang Weitao. This quantity is called the linear response function . The symmetry represented in ( 1.5.9 ) is important . If a perturbation at point 1 produces a density change at point 2 , then the same perturbation at ...
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.