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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... give a coherent account of the theory as it stands today without special regard for the historical development of the subject. The table of contents indicates the specific topics covered. We emphasize systems with a finite number of ...
... give a coherent account of the theory as it stands today without special regard for the historical development of the subject. The table of contents indicates the specific topics covered. We emphasize systems with a finite number of ...
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... 〈Â〉; particular measurements give particular eigenvalues of Â. For example, if Ψ is normalized, expectation values of kinetic and potential energies are given by the formulas and The square brackets here denote that Ψ determines T and.
... 〈Â〉; particular measurements give particular eigenvalues of Â. For example, if Ψ is normalized, expectation values of kinetic and potential energies are given by the formulas and The square brackets here denote that Ψ determines T and.
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... gives one of the eigenvalues of H, we immediately have The energy computed from a guessed Ψ is an upper bound to the ... give the true ground state Ψ0 and energy E[Ψ0] = E0; that is, Formal proof of the minimumenergy principle of (1.2.3) ...
... gives one of the eigenvalues of H, we immediately have The energy computed from a guessed Ψ is an upper bound to the ... give the true ground state Ψ0 and energy E[Ψ0] = E0; that is, Formal proof of the minimumenergy principle of (1.2.3) ...
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... gives One must solve this equation for Ψ as a function of E, then adjust E until normalization is achieved. It is ... give welldefined best approximations and Ē0 to the correct Ψ0 and E0. By (1.2.3), Ē0 ≥ E0, and so convergence of the ...
... gives One must solve this equation for Ψ as a function of E, then adjust E until normalization is achieved. It is ... give welldefined best approximations and Ē0 to the correct Ψ0 and E0. By (1.2.3), Ē0 ≥ E0, and so convergence of the ...
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... gives the HartreeFock differential equations where in which the Coulombexchange operator ĝ(x1) is given by Here and Lagrange multipliers (in general complex) associated with the constraints of (1.3.7). Also, so that e is Hermitian ...
... gives the HartreeFock differential equations where in which the Coulombexchange operator ĝ(x1) is given by Here and Lagrange multipliers (in general complex) associated with the constraints of (1.3.7). Also, so that e is Hermitian ...
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