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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... 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.
... 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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... 12)] are also invariant to such a transformation (Roothaan 1951, Szabo and Ostlund 1982, page 120). That is to say, if we let where U is a unitary matrix, then (1.3.23) becomes where This exhibits the considerable freedom that.
... 12)] are also invariant to such a transformation (Roothaan 1951, Szabo and Ostlund 1982, page 120). That is to say, if we let where U is a unitary matrix, then (1.3.23) becomes where This exhibits the considerable freedom that.
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... matrix ε. Since the matrix ε is Hermitian, one may choose the matrix U to diagonalize it. The corresponding orbitals λm, called the canonical HartreeFock orbitals, satisfy the canonical HartreeFock equations, Equation (1.3.31) is ...
... matrix ε. Since the matrix ε is Hermitian, one may choose the matrix U to diagonalize it. The corresponding orbitals λm, called the canonical HartreeFock orbitals, satisfy the canonical HartreeFock equations, Equation (1.3.31) is ...
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... matrix ε of (1.3.29) is a circulant matrix (diagonal elements all equal, every row a cyclic permutation of every other). Localized HartreeFock orbitals (Edmiston and Ruedenberg 1963) are orbitals with maximum selfrepulsion or minimum ...
... matrix ε of (1.3.29) is a circulant matrix (diagonal elements all equal, every row a cyclic permutation of every other). Localized HartreeFock orbitals (Edmiston and Ruedenberg 1963) are orbitals with maximum selfrepulsion or minimum ...
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... matrix eigenvalue problems of high dimension, in which the matrix elements are calculated from arrays of integrals evaluated for the basis functions. If we call the basis functions χp(r), one can see from (1.1.2) what the necessary ...
... matrix eigenvalue problems of high dimension, in which the matrix elements are calculated from arrays of integrals evaluated for the basis functions. If we call the basis functions χp(r), one can see from (1.1.2) what the necessary ...
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