PREDICTING THE PATH OF ELECTRONIC TRANSPORT THROUGH A MOLECULAR DEVICE VIA A MOUNTAIN-PASS ALGORITHM

The so-called “mountain-pass” theorem allows for the finding of a critical point on the path between two points on a multidimensional contour where the maximal elevation is minimal. By implementing the “elastic string algorithm”, it is possible to not only find the critical point, but to compute the mountain-pass itself on a finite-dimensional contour. For a given molecule that sits between two probes making up a nanostructure device, we propose that the mountain-pass will be a likely path of electron transport through the molecule, the contour being the electronic potential of the molecule. This potential along this path will be used as the input potential for SETraNS, a 1D Wigner-Poisson electron transport solver in order to explore the current-bias characteristics of such the molecule in such a device. In order to calculate the mountain pass, the elastic string algorithm is used to set up a constrained non-linear optimization problem which is, in turn, solved via a Monte Carlo method. We will compute the mountain-pass for a well-known test contour in order to show the validity of this approach. The procedure developed here is to be combined with conformational analysis via the molecular modeling program AMBER and the quantum transport program SETraNS in order to predict molecular function. When achieved, this combined procedure will allow for the better design and implementation of nanoscale molecular devices for application such as sensing, switching and data processing.