Repeated diagonalization technique

Indeed, the techniques of repeated diagonalization of the Hamiltonian on a large basis set and the search for resonance states from the numerical features of the roots upon variation of the function space may lead to reliable conclusions for models or for certain cases of ground shape resonances or of low-lying states of simple systems for which the chosen function space happens to describe the inner part of the resonance accurately. However, it was evident in the late 1960s that such methods had (have) certain limitations when it comes to the MEP in complex, polyelectronic systems. For example, for complex spectra of polyelectronic systems the root-identification criteria may not always lead to physically correct results, even qualitatively. Thus, in spite of careful (and computationally costly) examination, resonance states may be missed or roots may be wrongly attributed to resonances that do not exist. 

The variational condition determining the coefficients cJt is cubic in the unknowns, but iterative techniques permit these coefficients to be determined by repeated use of matrix diagonalization methods. Under most conditions it is possible to choose an iterative process facilitating convergence there is much RHF experience, and inordinate difficulties are not usually experienced. Because of the occupancy assumptions, it is possible without loss of generality to take the RHF spatial orbitals as orthogonal, and this is an important feature simplifying the calculations. 

TMs effective design, made out of coloured card (cardboard), is variation I of the Double sat Cut Away technique, repeated many times on a diagonally pleated sheet of card. The repeated use of even the simplest Cut Away form (here, a semicircle), can create patterns of gyeat beauty. Suspended from a thread and allowed to rotate, the ever-changng pattern of //gjhf and shade across the planes adds greatly to the effect. 

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