Conceptual density functional theory for electron transfer and transport in mesoscopic systems

Molecular and supramolecular systems are essentially mesoscopic in character. The electron self-exchange, in the case of energy fluctuations, or electron transfer/transport, in the case of the presence of an externally driven electrochemical potential, between mesoscopic sites is energetically driven in such a manner where the electrochemical capacitance (C_{[small mu, Greek, macron]}) is fundamental. Thus, the electron transfer/transport through channels connecting two distinct energetic (ΔE_{[small mu, Greek, macron]}) and spatially separated mesoscopic sites is capacitively modulated. Remarkably, the relationship between the quantum conductance (G) and the standard electrochemical rate constant (k_r), which is indispensable to understanding the physical and chemical characteristics governing electron exchange in molecular scale systems, was revealed to be related to C_{[small mu, Greek, macron]}, that is, C_{[small mu, Greek, macron]} = G/k_r. Accordingly, C_{[small mu, Greek, macron]} is the proportional missing term that controls the electron transfer/transport in mesoscopic systems in a wide-range, and equally it can be understood from first principles density functional quantum mechanical approaches. Indeed the differences in energy between states is calculated (or experimentally accessed) throughout the electrochemical capacitance as ΔE_{[small mu, Greek, macron]} = β/C_{[small mu, Greek, macron]}, and thus constitutes the driving force for G and/or k_r, where β is only a proportional constant that includes the square of the unit electron charge times the square of the number of electron particles interchanged.