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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... Hamiltonian operator, in which is the “external” potential acting on 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 ...
... Hamiltonian operator, in which is the “external” potential acting on 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 ...
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... Hamiltonian terms not to cause blowups in ĤΨ there. The specific cusp condition is (for example, see Davidson 1976, page 44) where is the spherical average of ρ(rα). Another important result is the longrange law for electron density ...
... Hamiltonian terms not to cause blowups in ĤΨ there. The specific cusp condition is (for example, see Davidson 1976, page 44) where is the spherical average of ρ(rα). Another important result is the longrange law for electron density ...
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... electrons is fixed. For a general discussion of functional derivatives, see Appendix A. 1.6. HellmannFeynman. theorems. and. virial. theorem Let λ be a parameter in the Hamiltonian and. HellmannFeynman theorems and virial theorem.
... electrons is fixed. For a general discussion of functional derivatives, see Appendix A. 1.6. HellmannFeynman. theorems. and. virial. theorem Let λ be a parameter in the Hamiltonian and. HellmannFeynman theorems and virial theorem.
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... Hamiltonian and Ψ(λ) be an eigenfunction of Ĥ. Then and These identities are the differential HellmannFeynman ... Hamiltonians acting on the same Nelectron wavefunction space, but they need not be related to each other by a parameter λ ...
... Hamiltonian and Ψ(λ) be an eigenfunction of Ĥ. Then and These identities are the differential HellmannFeynman ... Hamiltonians acting on the same Nelectron wavefunction space, but they need not be related to each other by a parameter λ ...
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... ) has been used. If the basis set is. Consider now a complete basis set {| fi〉} (for example, the eigenstates of some Hamiltonian), satisfying the orthonormality We also introduce a shorthand notation for the diagonal element.
... ) has been used. If the basis set is. Consider now a complete basis set {| fi〉} (for example, the eigenstates of some Hamiltonian), satisfying the orthonormality We also introduce a shorthand notation for the diagonal element.
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