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
... eigenvalues Ek . The set k is complete , and the k may always be taken to be orthogonal and normalized [ in accordance with ( 1.1.10 ) ] , k | ¥ ‡ ¥ , dx ~ = ( V , | Y1 ) = 8kl ( 1.1.11 ) N 0 We denote the ground - state wave function 4 ...
... eigenvalues Ek . The set k is complete , and the k may always be taken to be orthogonal and normalized [ in accordance with ( 1.1.10 ) ] , k | ¥ ‡ ¥ , dx ~ = ( V , | Y1 ) = 8kl ( 1.1.11 ) N 0 We denote the ground - state wave function 4 ...
Page 5
... eigenvalues of  . For example , if Ψ is normalized , expectation values of 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 ...
... eigenvalues of  . For example , if Ψ is normalized , expectation values of 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 ...
Page 6
... eigenvalues also satisfy ( 1.2.8 ) , but the corresponding methods for determining approximate and Ēk encounter orthogonality difficulties . For example , given 1 , Ē , is not necessarily above E1 , unless 1 is orthogonal to the exact 1 ...
... eigenvalues also satisfy ( 1.2.8 ) , but the corresponding methods for determining approximate and Ēk encounter orthogonality difficulties . For example , given 1 , Ē , is not necessarily above E1 , unless 1 is orthogonal to the exact 1 ...
Page 12
... electron basis functions , in terms of which orbitals are expanded and many - electron wave functions are expressed . This transforms the mathe- matical problem into one ( or more ) matrix eigenvalue 12 1.3 DENSITY - FUNCTIONAL THEORY.
... electron basis functions , in terms of which orbitals are expanded and many - electron wave functions are expressed . This transforms the mathe- matical problem into one ( or more ) matrix eigenvalue 12 1.3 DENSITY - FUNCTIONAL THEORY.
Page 13
... eigenvalue problems of high dimension , in which the matrix elements are calculated from arrays of integrals evaluated for the basis functions . If we call the basis functions Xp ( r ) , one can see from ( 1.1.2 ) what the necessary ...
... eigenvalue problems of high dimension , in which the matrix elements are calculated from arrays of integrals evaluated for the basis functions . If we call the basis functions Xp ( r ) , one can see from ( 1.1.2 ) what the necessary ...
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.