Another form of the transmission function

作者：Rosenfeld Vladimir R^*

来源：Journal of Mathematical Chemistry, 2013, 51(10): 2639-2643.

DOI：10.1007/s10910-013-0239-3

• Molecular electronics
• Transmission function
• Molecular graph
• Characteristic polynomial
• Spectral theory of graphs
• Theorem of Kolmykov

The transmission function describes the passage of the electric current from one point of an electric circuit to another. By now, this is also applied to molecules which are potential candidates for uses in the molecular electronics. We mean the modern branch of electronics which has a goal of reducing the sizes of its devices down to molecular ones and planning indeed to apply single molecules as conducting wires and functional components of microcircuits. For calculating the transmission function, some authors utilize the well-known idea of representing a molecule by a (molecular) graph, which allows them to apply for treating the latter also powerful methods of spectral graph theory. For instance, we refer to the paper by Fowler et al. (Chem Phys Lett. 465 2008) 142-146, where one such expression for this function is given. Our objective is to demonstrate that the same calculational result can be obtained using a different set of characteristic polynomials of graphs (which also slightly reduces a mathematical notation). Specifically, we apply one theorem of Kolmykov to the basic formula derived by these authors.

• 出版日期2013-11