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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... formula where Since, furthermore, each particular measurement of the energy gives one of the eigenvalues of H, we immediately have The energy computed from a guessed Ψ is an upper bound to the true groundstate energy E0. Full ...
... formula where Since, furthermore, each particular measurement of the energy gives one of the eigenvalues of H, we immediately have The energy computed from a guessed Ψ is an upper bound to the true groundstate energy E0. Full ...
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... The normalization 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.
... The normalization 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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... integrating, one obtains the formula for “orbital energies “ Summing over i and comparing with (1.3.2), we find where. with f(X1) an arbitrary function. The matrix ε consists of where Im is the ionization energy associated with removal of.
... integrating, one obtains the formula for “orbital energies “ Summing over i and comparing with (1.3.2), we find where. with f(X1) an arbitrary function. The matrix ε consists of where Im is the ionization energy associated with removal of.
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... is called the restricted HartreeFock method (RHF), the N orbitals ψi are taken to comprise N/2 orbitals of form orbitals of form . The energy formula (1.3.2) becomes where while the HartreeFock equations (1.3.8) now read with the operator.
... is called the restricted HartreeFock method (RHF), the N orbitals ψi are taken to comprise N/2 orbitals of form orbitals of form . The energy formula (1.3.2) becomes where while the HartreeFock equations (1.3.8) now read with the operator.
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... state is the electron density for that state. This quantity will be of great importance in this book; we designate it by ρ(r). Its formula in terms of Ψ is This is a nonnegative simple function of three variables, x,
... state is the electron density for that state. This quantity will be of great importance in this book; we designate it by ρ(r). Its formula in terms of Ψ is This is a nonnegative simple function of three variables, x,
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