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هارتری-فاک
22 1.10 The Pauli Exclusion Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.11 On the Numerical Solution of the Schrdinger Equation . . . . . . . . 25 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2 Ab-Initio Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.1 The Hartree-Fock Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.1.1 The Orbital Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.1.2 Accounting for the Pauli Exclusion Principle . . . . . . . . . . 30 2.1.3 The Variational Principle . . . . . . . . . . . . . . . . . . . . . . . . 31 2.1.4 A Direct Solution Procedure . . . . . . . . . . . . . . . . . . . . . . 32 2.1.5 The Hartree-Fock Approach . . . . . . . . . . . . . . . . . . . . . . 33 2.1.6 Post-Hartree-Fock Methods . . . . . . . . . . . . . . . . . . . . . . 34 2.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.1 The First Hohenberg and Kohn Theorem . . . . . . . . . . . . . 35 2.2.2 The Second Hohenberg and Kohn Theorem. . . . . . . . . . . 37
We describe in the next chapter the two most widely used: the Hartree-Fock (HF) method and the Density Func- tional Theory (DFT), the first of which can be applied only for a moderate number of electrons and it has been extensively used in the context of quantum chemistry to analyze the structure and behavior of molecules.
However, in the case of crystals, the number of electrons becomes too large to make their simulation possible by the direct solution of the Schrdinger equation or by using the Hartree-Fock technique.
Even if the use of separated repre- sentations in computational mechanics is quite unusual, its use has been extensively considered in the context of quantum chemistry; in particular, it is at the base of the Hartree-Fock method described in the next chapter.
Among them, those most usually employed are the Hartree-Fock and the Density Functional Theory, which we revisit in the present chapter.
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