Physical Systems Why Do We Need Multiscale Methods

Modern computational chemistry research frequently examines problems that require treating multiple-length and time scales. It is instructive to consider first two example systems that exemplify the need to develop methods for handling multiple scales. These two examples come from recent research projects in the author s group they are limited in scope but representative of challenging computational problems in biophysics and nanoscience. 

Electron transport through nanoscale devices is often handled at the Landauer theory level, where the electrons are assumed to move coherently from one electrode to the other without inelastic collisions. The current can be determined by computing the transmission function T(E, V), which depends on energy for a given applied voltage. The functional form of T(E, V) arises from the quantum states of the molecule that is coupled to the two electrodes. The most general computational methods used to compute those states have employed Green s function techniques to obtain the current self-consistently.  

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