How well do molecules conduct electricity? What are the controlling factors? Recently, the conductance of short strands of DNA have been measured. The results show surprisingly high conductance. These are questions that the field of theoretical molecular electronics is trying to answer. The computational challenge is great. Besides conventional electronic structure, which should include parts of the electrode, one needs to compute a large number of quantum mechanical transmission coefficients. We discuss the prospects for performing this in O(N) complexity. Finally, the prospects for including electron correlation effects in O(N^2) complexity using TDDFT are mentioned.
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