Charge separation efficiencies in artificial photosynthetic systems: Application to molecularly based electronic devices

We present exact calculations of the quantum efficiency in a general kinetic model for charge separation in artificial photosynthetic systems. The kinetic models we employ consist of a light absorber covalently linked to a linear chain of TV sites. The electron is initially excited at the light absorber and subsequently migrates along the molecular chain by virtue of a random distribution of hopping rates. Decay processes are included at each site which simulate the recombination of the electron with the hole at the light absorber. An exact expression is obtained for the quantum yield for this general model of photosynthetic charge separation. From this expression we show that (1) redox biases play a sensitive role in determining the quantum yield of electrons, (2) because the e^--hole recombination rates fall off exponentially with distance, e-hole recombination beyond the nearest neighbor to the light absorber is negligible, and (3) the distribution of electron hopping rates may cause the quantum yield to decay faster than 1/N even when e ^--hole recombination at multiple sites is included. The implications of these results on the experimental design of molecular electronic devices is discussed. Further, we show how the expression for the quantum yield can be used to construct the exact transit time, the moments of the transit time, and the exact expressions for the site probabilities for an arbitrarily disordered one-dimensional system when the particle is placed initially at the origin.