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. |
From inside the book
Results 1-5 of 45
Page v
... many - electron systems , and useful predictions of facts about molecules are now routinely made from quantum - mechanical calculations based on orbital theories and their systematic extensions . Thus , we have restricted and ...
... many - electron systems , and useful predictions of facts about molecules are now routinely made from quantum - mechanical calculations based on orbital theories and their systematic extensions . Thus , we have restricted and ...
Page 4
... electrons are fermions , also must be antisymmetric with respect to interchange of the coordinates ( both space and spin ) of any two electrons . There are many acceptable indepepdent solutions of ( 1.1.1 ) for a given system : the ...
... electrons are fermions , also must be antisymmetric with respect to interchange of the coordinates ( both space and spin ) of any two electrons . There are many acceptable indepepdent solutions of ( 1.1.1 ) for a given system : the ...
Page 5
... energy by Ψ0 and E0 . Here I dx means integration over 3N spatial coordinates ... Many measurements average to ( A ) ; particular measurements give particular ... electron wave functions will give the true ground state and energy E [ Y ] ...
... energy by Ψ0 and E0 . Here I dx means integration over 3N spatial coordinates ... Many measurements average to ( A ) ; particular measurements give particular ... electron wave functions will give the true ground state and energy E [ Y ] ...
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
... electron - nucleus attraction integrals , ( 1.3.41 ) ( 1.3.42 ) * ( A \ pq ) = √x ; ( ) == x , ( , ) dr , 1 ( 1.3.43 ) and electron ... many interacting electrons is never a single determinant or a simple combination of a few deter- minants ...
... electron - nucleus attraction integrals , ( 1.3.41 ) ( 1.3.42 ) * ( A \ pq ) = √x ; ( ) == x , ( , ) dr , 1 ( 1.3.43 ) and electron ... many interacting electrons is never a single determinant or a simple combination of a few deter- minants ...
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 |
Other editions - View all
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.