The tight-binding version of the source-and-sink potential (SSP) model of ballistic conduction can be cast in a graph-theoretical form where the transmission through a molecular wire depends on four characteristic polynomials: those of the molecular graph and the vertex-deleted subgraphs with one or both of the molecular vertices contacting the electrodes removed. This gives an explicit function for the dependence of transmission on energy, one that is well adapted for qualitative description of general classes of conductors and conduction behavior. It also leads directly to a selection-rule criterion for conduction in terms of counting zero roots of the polynomials, which for benzenoids and graphenes is shown to subsume literature approaches based on Kekulé structure counting, bond order, and frontier-orbital matching. As explicitly demonstrated here, the SSP transmission function agrees with that derived by the Green’s function (GF) method.
Conference
International Conference on Physical Organic Chemistry (ICPOC-20), International Conference on Physical Organic Chemistry, ICPOC, Physical Organic Chemistry, 20th, Busan, Korea, 2010-08-22–2010-08-27
References
1 E. N. Economou. Green’s Functions in Statistical Physics, Springer, Berlin (1990).Search in Google Scholar
2a 10.1063/1.468314, V. Mujica, M. Kemp, M. A. Ratner. J. Chem. Phys.101, 6849 (1994).Search in Google Scholar
2b 10.1063/1.468315, V. Mujica, M. Kemp, M. A. Ratner. J. Chem. Phys.101, 6856 (1994).Search in Google Scholar
3 10.1063/1.2715932, F. Goyer, M. Ernzerhof, M. Zhuang. J. Chem. Phys.126, 144104 (2007).Search in Google Scholar PubMed
4 10.1063/1.2804867, M. Ernzerhof. J. Chem. Phys.127, 204709 (2007).Search in Google Scholar PubMed
5 10.1063/1.3119299, P. Rocheleau, M. Ernzerhof. J. Chem. Phys.130, 184704 (2009).Search in Google Scholar PubMed
6 10.1016/j.cplett.2008.05.062, B. T. Pickup, P. W. Fowler. Chem. Phys. Lett.459, 198 (2008).Search in Google Scholar
7 10.1016/j.cplett.2008.09.048, P. W. Fowler, B. T. Pickup, T. Z. Todorova. Chem. Phys. Lett.465, 142 (2008).Search in Google Scholar
8 10.1063/1.3124828, P. W. Fowler, B. T. Pickup, T. Z. Todorova, T. Pisanski. J. Chem. Phys.130, 174708 (2009).Search in Google Scholar PubMed
9 10.1063/1.3182849, P. W. Fowler, B. T. Pickup, W. Myrvold, T. Z. Todorova. J. Chem. Phys.131, 044104 (2009).Search in Google Scholar PubMed
10 10.1063/1.3272669, P. W. Fowler, B. T. Pickup, T. Z. Todorova, W. Myrvold. J. Chem. Phys.131, 244110 (2009).Search in Google Scholar PubMed
11 I. Gutman, O. E. Polyansky. Mathematical Concepts in Organic Chemistry, Springer, Berlin (1986).10.1007/978-3-642-70982-1Search in Google Scholar
12 10.1021/nl101688a, T. Markussen, R. Stadler, K. S. Thygesen. Nanoletters.Search in Google Scholar PubMed
13 10.1063/1.2049249, M. Ernzerhof, M. Zhuang, P. Rocheleau. J. Chem. Phys.123, 134704 (2005).Search in Google Scholar PubMed
14 G. C. Solomon, D. Q. Andrews, R. P. van Duyne, M. A. Ratner. Chem. Phys. Chem.10, 257 (2009).Search in Google Scholar
15 T. Hansen, G. C. Solomon, D. Q. Andrews, M. A. Ratner. J. Phys. Chem.131, 257 (2009).Search in Google Scholar
16 A. L. Cauchy. In Oeuvres Complètes d’Augustin Cauchy, Paris: Gauthier-Villars et fils, 1882–1974, (IIe Série) Tome 9, p. 174, Exer. de math. 4 (1829).Search in Google Scholar
17 H. Sachs. Publ. Math. (Debrecen)11, 119 (1964).10.5486/PMD.1964.11.1-4.15Search in Google Scholar
18 S. Fajtlowicz, P. John, H. Sachs. Croat. Chem. Acta78, 195 (2005).Search in Google Scholar
19 10.1016/j.cplett.2004.12.102, T. Morikawa, S. Narita, D. J. Klein. Chem. Phys. Lett.402, 554 (2005).Search in Google Scholar
20 10.1063/1.1744701, N. S. Ham, K. Ruedenberg. J. Chem. Phys.29, 1215 (1958).Search in Google Scholar
21 10.1063/1.1744702, N. S. Ham. J. Chem. Phys.29, 1229 (1958).Search in Google Scholar
22 10.1002/hlca.19620450538, E. Heilbronner. Helv. Chim. Acta155, 1722 (1962).Search in Google Scholar
23 10.1021/ja800638t, K. Yoshizawa, T. Tada, A. Staykov. J. Am. Chem. Soc.130, 9406 (2008).Search in Google Scholar PubMed
24 10.1063/1.3119299, P. Rocheleau, M. Ernzerhof. J. Chem. Phys.130, 184704 (2009).Search in Google Scholar PubMed
25 10.1063/1.3330900, Y. X. Zhou, M. Ernzerhof. J. Chem. Phys.132, 104706 (2010).Search in Google Scholar PubMed
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