Hartree-Fock approximation transition metal electronic structure

This chapter begins a series of chapters devoted to electronic structure and transport properties. In the present chapter, the foundation for understanding band structures of crystalline solids is laid. The presumption is, of course, that said electronic structures are more appropriately described from the standpoint of an MO (or Bloch)-type approach, rather than the Heitler-London valence-bond approach. This chapter will start with the many-body Schrodinger equation and the independent-electron (Hartree-Fock) approximation. This is followed with Bloch s theorem for wave functions in a periodic potential and an introduction to reciprocal space. Two general approaches are then described for solving the extended electronic structure problem, the free-electron model and the LCAO method, both of which rely on the independent-electron approximation. Finally, the consequences of the independent-electron approximation are examined. Chapter 5 studies the tight-binding method in detail. Chapter 6 focuses on electron and atomic dynamics (i.e. transport properties), and the metal-nonmetal transition is discussed in Chapter 7. 

Prior to this, it had already been established that even the simplest forms of DFT, based on the exchange-only Slater or Xa scheme, could give good descriptions of the electronic structure of metal complexes and a number of contemporary applications confirmed this. However, in combination with structure optimization, here at last was a quantum chemical method accurate enough for transition metal (TM) systems and yet still efficient enough to deliver results in a reasonable time. This was in stark contrast to the competition which was either based on the single-determinant Hartree-Fock approximation, which had been discredited as a viable theory for TM systems,or on more sophisticated electron correlation methods (e.g., second order Moller-Plesset theory) which are relatively computationally expensive and thus, for the same computer time, treat much smaller systems that DFT. 

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