On the role of the nonlocal Hartree-Fock exchange in ab initio quantum   transport: Hydrogen in Platinum nanocontacts revisited
  We propose a practical way to overcome the ubiquitous problem of the overestimation of the zero-bias and zero-temperature conductance, which is associated to the use of local approximations to the exchange-correlation functional in Density-Functional Theory when applied to quantum transport. This is done through partial substitution of the local exchange term in the functional by the nonlocal Hartree-Fock exchange. As a non-trivial example of this effect we revisit the smallest molecular bridge studied so far: a Hydrogen molecule placed in between Platinum nanocontacts. When applied to this system the value of the conductance diminishes as compared to the local-exchange-only value, which is in close agreement with results predicted from Time-Dependent Current-Density-Functional Theory. Our results issue a warning message on recent claims of perfect transparency of a Hydrogen molecule in Platinum nanocontacts. 
Y. Garcia and JC. Sancho-Garcia