Bloch equation Fock-space

Bloch Equation-Based Fock Space Theories... 

Another way is to start from the precursor of the Bloch equation, eq.(6.1.15), generalized to Fock space/69,76,93/ and use the Q and P projections for the n-valence sector. Writing the Fock space Bloch equation as... 

Bloch Equation Baaed Fock Space Theory ... 

Mukherjee/69/, use of the sufficiency conditions (7.3.9) amounts in effect to assuming that ft is a valence-universal wave-operator. In fact Haque has explicitly demonstrated/123/ that the use of a valence-universal ft in the Fock-space Bloch equation leads automatically to eqn (7.3.9) with the ad-hoc sufficiency requirement. We give the sketch of a general proof here, since it shows that the extra information content of a Fock-space ft, as opposed to a Hilbert space, can be used to advantage for ensuring the connectivity of the cluster amplitudes of S/93/. For a valence-universal ft, the Fock-space Bloch equation (6.1.15) leads to... 

We show below, following Mukherjee/91-94/, how a connected H can he obtained using a Valence-universal O which uses a normalization convention different from intermediate normalization. We start from the Fock-space Bloch Equation ... 

One can set up the equations for the k=1=1 valence- problem in a hierarchical manner. The valence sectors are defined in terms of particle-hole rank. Thus the Fock space Bloch equation would be... 

It may be shown that for the (0,1) sector of Fock-space, the values of the roots obtained by diagonalizing Hn s are independent of the active space used for the calculation. In other words, if two orbitals, a and b are taken as active, the resulting ionization potentials would be identical to those obtained from separate calculations with either a or 6 alone active. This is a very useful result because it means that we do not have to worry about choosing the right active space for a given calculation in order to get good results. However the proof of this invariance rests on the FSCC amplitudes and /7jv,eff satisfying the Fock-space Bloch equation 13. The approximate FSCCSDT methods described above do not satisfy Eq. 13, so the invariance is lost. 

We consider for simplicity the single-reference case and start with theFock-space relation (34) and the corresponding Fock-space Bloch equation... 

The photonic-Fock-space Bloch equation now becomes... 

The FSCC equations for a particular (m, n) sector of the Fock space are derived by inserting the normal-ordered wave operator into the Bloch equation (2.6). The final form of the FSCC equation for a complete model space includes only connected terms [11,35],... 

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. 

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