Green matrix

G. Del Re and J. Ladik Adsorption of Molecules on Polymers. I. A General Analysis in Terms of the Green-Matrix Version of the Local-Impurity SCF Approach. Chem. Physics 49, 321-332 (1980). 

The Buckeye Tillite in Table 10.12 is an unsorted boulder clay composed of boulders, cobbles, aud pebbles in a fine-grained bluish-green matrix. Long (1965) published an excellent close-up picture of this tillite in his Fig. 8. The tillite is interbedded with water-deposited layers of sandstone and shale. The Buckeye Tillite occurs along the whole length of the northern escarpment and is also present on Treves... 

The Metrics Green Star, Green Circle and Green Matrix... 

The Green matrix of this system can be given, by analogy with expression (4.37), as... 

However, to do this for every state is practically impossible in the case of really long chains (N> 1000, where N is the number of sites). Therefore, a technique is needed that gives a rough idea as to whether or not the states are localized in a certain eneigy region without explicitly calculating them. Such a method based on the calculation of Green matrix elements of the chain will be examined in the next section. 

The best way to take into account also propagation during the iterations leading to self-consistency of a perturbation localized originally to one or a few cells is a general Green matrix formulation of the problem. " ... 

Dyson s equation defines the Green matrix for the system with a perturbation in the form... 

Calculate G°(E), the Green matrix of the unperturbed system, as defined in equation (4.111) for the elements of F , using as input the results of a Hartree-Fock band-structure calculation of the... 

It became evident from self-consistent cluster calculations that the core contributions to the matrix P remain constant during the iterations. Therefore, by the self-consistent Green matrix calculation, the core contribution was kept constant (frozen-core approximation). 

With the help of the HF band structures one calculates elements (8.22) of the Green matrix G(F k) in the region of the gap (where one expects exciton states). 

Application of the above-described method to different poly-mers " has yielded reasonably good agreement with experiment only (see the next section) if one employs a good basis set and substitutes into the Green matrix elements (8.22) not the HF one-electron eneigies, but rather the quasi-particle energies, which contain also correlation contributions at least in the second order of many-body perturbation theory (see Section 5.3). 

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