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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... electron i, the potential due to nuclei of charges Zα. The coordinates xi, of electron i comprise space coordinates ri, and spin coordinates si . Atomic units are employed here and throughout this book (unless otherwise specified): the ...
... electron i, the potential due to nuclei of charges Zα. The coordinates xi, of electron i comprise space coordinates ri, and spin coordinates si . Atomic units are employed here and throughout this book (unless otherwise specified): the ...
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... spin coordinates are discrete. Because electrons are fermions, Ψ also must be antisymmetric with respect to interchange of the coordinates (both space and spin) of any two electrons. There are many acceptable independent solutions of ...
... spin coordinates are discrete. Because electrons are fermions, Ψ also must be antisymmetric with respect to interchange of the coordinates (both space and spin) of any two electrons. There are many acceptable independent solutions of ...
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... spin orbitals ψi(x), each a product of a spatial orbital and a spin function σ(s) = α(s) or β(s), the Slater determinant The HartreeFock approximation (Roothaan 1951) is the method whereby the orthonormal orbitals ψi are found that ...
... spin orbitals ψi(x), each a product of a spatial orbital and a spin function σ(s) = α(s) or β(s), the Slater determinant The HartreeFock approximation (Roothaan 1951) is the method whereby the orthonormal orbitals ψi are found that ...
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... gives no energy lowering over the restricted HF method. But there are important cases in which energy lowering is found. For example, the UHF description of bond breaking in H2 gives the proper dissociation products, while. Electron ...
... gives no energy lowering over the restricted HF method. But there are important cases in which energy lowering is found. For example, the UHF description of bond breaking in H2 gives the proper dissociation products, while. Electron ...
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... spin for the moment). It can also be equivalently “represented” by a momentumspace wave function that is the Fourier transform of Ψ(r). This, together with the quantum superposition principle, leads one to construct a more general and ...
... spin for the moment). It can also be equivalently “represented” by a momentumspace wave function that is the Fourier transform of Ψ(r). This, together with the quantum superposition principle, leads one to construct a more general and ...
Contents
Densityfunctional theory | |
The chemical potential | |
Chemical potential derivatives | |
ThomasFermi and related models | |
Basic principles | |
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Common terms and phrases
Appendix atoms and molecules Bartolotti bond calculations Chapter Chem chemical potential components constrainedsearch convex coordinates correlation energy corresponding defined density density functional theory density matrix density operator densityfunctional theory determined Dreizler eigenstates eigenvalues electron density electronegativity electronic structure electronic systems electrostatic equilibrium exact exchange energy exchangecorrelation energy external potential Fermi Fock formula Gázquez Ghosh given gives gradient expansion grand canonical ensemble grand potential ground groundstate energy Gunnarsson Hamiltonian hardness Hartree–Fock integral interaction kinetic energy kineticenergy Kohn Kohn–Sham equations Lagrange multiplier Langreth Lett Levy Lieb localdensity approximation Lundqvist manyelectron systems method minimization molecular Nalewajski Nelectron noninteracting Nrepresentable number of electrons obtain orbitals parameter Parr particle Perdew Phys problem properties Quantum Chem quantum chemistry reduced density matrix representation secondorder selfinteraction Sham softness spin spindensity spinpolarized theorem ThomasFermi theory timedependent total energy values variational principle wave function Wigner