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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... 7.4 Localdensity and Xα approximations 7.5 The integral formulation 7.6 Extension to nonintegral occupation numbers and the transitionstate concept 8. The KohnSham method: Elaboration 8.1 Spindénsityfunctional theory.
... 7.4 Localdensity and Xα approximations 7.5 The integral formulation 7.6 Extension to nonintegral occupation numbers and the transitionstate concept 8. The KohnSham method: Elaboration 8.1 Spindénsityfunctional theory.
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... integral 〈ΨHF|ΨHF〉 is equal to 1, and the energy expectation value is found to be given by the formula (for example, see Parr 1963) where These integrals are all real, and J ij ≥ Kij. The HartreeFock approximation.
... integral 〈ΨHF|ΨHF〉 is equal to 1, and the energy expectation value is found to be given by the formula (for example, see Parr 1963) where These integrals are all real, and J ij ≥ Kij. The HartreeFock approximation.
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Robert G. Parr, Yang Weitao. These integrals are all real, and J ij ≥ Kij ≥ 0 The Jij are called Coulomb integrals, the Kij are called exchange integrals. We have the important equality This is the reason the double summation in (1.3.2) ...
Robert G. Parr, Yang Weitao. These integrals are all real, and J ij ≥ Kij ≥ 0 The Jij are called Coulomb integrals, the Kij are called exchange integrals. We have the important equality This is the reason the double summation in (1.3.2) ...
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... integrals will be: overlap integrals, kinetic energy integrals, electronnucleus attraction integrals, and electronelectron repulsion integrals, Sometimes these are all computed exactly, in which case one says that one has an ab initio ...
... integrals will be: overlap integrals, kinetic energy integrals, electronnucleus attraction integrals, and electronelectron repulsion integrals, Sometimes these are all computed exactly, in which case one says that one has an ab initio ...
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... integral HellmannFeynman theorem (formula), and the integrated HellmannFeynman theorem (formula) (Epstein, Hurley, Wyatt, and Parr 1967). The derivative ∂Ĥ/∂λ is written as a partial derivative to emphasize that the integral 〈Ψ| ∂Ĥ ...
... integral HellmannFeynman theorem (formula), and the integrated HellmannFeynman theorem (formula) (Epstein, Hurley, Wyatt, and Parr 1967). The derivative ∂Ĥ/∂λ is written as a partial derivative to emphasize that the integral 〈Ψ| ∂Ĥ ...
Contents
Densityfunctional theory | |
The chemical potential | |
Chemical potential derivatives | |
ThomasFermi and related models | |
Basic principles | |
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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