By J.R. Sabin (Eds.)
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Additional info for Advances in Quantum Chemistry
This arrangement is illustrated in Fig. 1b. The escape rate matrices now can be modeled as ½G1 ij Z G1 dij di1 ; (26) ½G2 ij Z G2 dij din ; (27) where once again G1 and G2 are now the escape rates to the source and emitter contacts. Using equation (18), we can calculate the transmission function: T Z G1 G2 Q1n Z G1 G2 jGr1n j2 : (28) This is a well-known result [16–25], the transmission of a molecular chain is related to the 1Kn element of the Green function. Using equation (12), we can also calculate the local DOS and the DOS: 2pNði; EÞ Z G1 Q1i C G2 Qni ; 2pNðEÞ Z ðG1 C G2 Þ X Q1i : (29) (30) i In equation (30) we used the fact that our molecular Hamiltonian is mirror symmetric.
In order to show the large changes of the functions, the plot is semi-logarithmic. Inspection of Fig. 2 confirms our conclusions: The DOS and the transmission function show the six resonance peaks within the molecular band. The transmittance function does not change significantly within the band, but it drops sharply at the band edge. The diminishing transmission function outside of the band is mainly a consequence of the drop in the transmittance, not in the DOS. We now investigate the long chain limit.
This is also true for PðEÞ. Of course, to the extent that we find the results for jmki and Em(k) wanting, we can 2 ^ and/or terms of order W^ to PðEÞ. ^ add terms of order W^ to S, (Vertex corrections may also be important). 2. Total energy expression ^ With a converged GðEÞ we can calculate the total energy of the system. Writing x 0 Z ðr 0 ; z 0 Þ; x Z ðr; zÞ; for space-spin coordinates, the total energy is given by  ð dE 1 1^ ^ expðiDEÞTr T^ C V^ C C^ C SðEÞ GðEÞCR Etot ZKi 2p 2 2 ð ð dE 1^ 1^ ^ ^ ^ expðiDEÞ dx x T C V C C C SðEÞ GðEÞ x CR; ZKi 2p 2 2 (15) (16) with DZ0C.