## 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 5

... the observable A. Many measurements average to (A); particular

measurements give particular

expectation values of kinetic and potential energies are given by the formulas TV

-(r)=sworwa, ...

... the observable A. Many measurements average to (A); particular

measurements give particular

**eigenvalues**of A. For example, if \P is normalized,expectation values of kinetic and potential energies are given by the formulas TV

-(r)=sworwa, ...

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### 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

antisymmetric Appendix atoms and molecules Bartolotti bond calculations Chapter Chem chemical potential classical components constrained-search convex coordinates correlation energy corresponding defined density functional density matrix density operator density-functional theory determined differential discussion Dreizler eigenstates eigenvalues electron density electronegativity energy functional equal equilibrium exact exchange energy external potential formula functional derivative functional theory Gázquez Ghosh given gives grand canonical ensemble grand potential ground ground-state energy Gunnarsson Hamiltonian hardness Hartree–Fock method Hartree–Fock theory Hilbert Hohenberg–Kohn integral interaction kinetic energy kinetic-energy Kohn Kohn-Sham equations Kohn-Sham theory Lagrange multiplier Levy local-density approximation Lundqvist many-electron minimization minimum molecular N-electron noninteracting number of electrons obtain orbitals parameter Parr particle Perdew Phys problem properties quantity quantum Sham ſº softness space spin spin-polarized Table theorem Thomas–Fermi theory Thomas–Fermi–Dirac total energy Tſp v-representable variational principle wave function zero

### 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 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.