Physical interpretation of orthogonal Hilbert space transformations in tight-binding systems with nonorthogonal bases

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 3, 2005, Pages

  Rittenhouse, S T ^a   Johnson, B L ^a  

^a WESTERN WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELEMENT;

ARTICLE; ELECTRON TRANSPORT; GEOMETRY; MATHEMATICAL ANALYSIS; QUANTUM MECHANICS; THEORETICAL STUDY;

EID: 15444371754     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.035118     Document Type: Article

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15. This assumption is based on the fact that the individual basis states |n〉 must be square-integrable (centered on site n), and therefore the overlap integrals must decay at least exponentially. The assumption in the text implies a cutoff imposed on the decay.
16. In addition, for many cases of experimental interest, the value of s itself is very small, and the decay of the hopping terms is quite rapid. For example, if s=0.1, and for typical values of t and ε, (i.e., t in the range 2 to 5 eV, and ε of order 10 eV) the hopping energies will drop off by a factor of 10 from n=1 to n=2, and by a factor of 100 from n=1 to n=3.
17. This assumption reduces the problem to the most fundamental level where basis overlap influences the physics. In addition, it is reasonable from the point of view of metallic leads coupling molecular systems, since an orthogonal tight-binding scheme is reasonable for leads. The molecular orbital structures can reasonably be modelled via the assumption of overlap (even in the case of weak coupling), since the bonding is via a different mechanism.