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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... minimization of the functional E[Ψ] with respect to all allowed Nelectron wave functions will give the true ground state Ψ0 and energy E[Ψ0] = E0; that is, Formal proof of the minimumenergy principle of (1.2.3) goes as follows. Expand Ψ ...
... minimization of the functional E[Ψ] with respect to all allowed Nelectron wave functions will give the true ground state Ψ0 and energy E[Ψ0] = E0; that is, Formal proof of the minimumenergy principle of (1.2.3) goes as follows. Expand Ψ ...
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... Minimization of (1.3.2) subject to the orthonormalization conditions now gives the HartreeFock differential equations where in which the Coulombexchange operator ĝ(x1) is given by Here and Lagrange multipliers (in general complex) ...
... Minimization of (1.3.2) subject to the orthonormalization conditions now gives the HartreeFock differential equations where in which the Coulombexchange operator ĝ(x1) is given by Here and Lagrange multipliers (in general complex) ...
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... minimization of tr leads to the Nelectron ground state energy and the ground state if it is not degenerate, or an arbitrary linear combination (convex sum) of all degenerate ground states if it is degenerate. Thus, the search in (2.3.27) ...
... minimization of tr leads to the Nelectron ground state energy and the ground state if it is not degenerate, or an arbitrary linear combination (convex sum) of all degenerate ground states if it is degenerate. Thus, the search in (2.3.27) ...
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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