A very effective way to start learning what computational chemistry can and cannot do is to start doing hands on tutorials of concrete examples. Last week, at the I2CAM workshop on photovoltaics, Jeff Reimers ran a hands on workshop where participants calculated photochemical properties associated with charge separation and recombination in a specific donor-acceptor molecule. Here is the tutorial sheet and you can run Jeff's CNDO (Complete Neglect of Differential Overlap) [something like a Hubbard model..] code on the nanohub.
Besides being hands on, and very chemically focused, I also like the tutorial because it discusses solvent effects, kinetics, and Marcus-Hush theory.
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