Remarks on Correlation in Disordered Chains

If one has a disordered polymer, one expects that some or all of the states are localized, depending on the degree of disorder. This Anderson localization, which was shown with the help of a tight-binding Hamiltonian, also takes place at the Hartree-Fock level (see Section 4.2 and the work of Day et starting at the band edges and 

FIGURE 5.12. Localized and delocalized states in two bands in a not very strongly disordered chain. The mobility edges are indicated by arrows (L indicates localized states and D delocalized ones). 

In order to test the relative weight of the difficult L- D or D L excitations as compared to the others, a model calculation was recently performed on a H2 molecule ring introducing disorder by varying the intermolecular distances. The number of H2 molecules was 11, and a minimal STO-3G basis set was used for the calculation. In this way one obtains a simple two-band model with one completely filled and one unfilled band. 

Standard geometries were used for the ordered systems, and distance variations were obtained from a random number generator with a Gaussian probability distribution. The degree of disorder was then measured by the standard deviation a of the Gaussian distribution. 

The criterion for localization of the orbitals to be used here is that proposed by Day et namely to calculate the quantity 

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