Could you estimate the rate of reaction from the chemical structure of the reactants? If so, how?
As Paul J. Gans correctly pointed out in his comment, in general it is impossible.

In practice you can calculate reaction rates only for quite restrictive class of reactions - the unimolecular gas-phase reactions - using RRKM theory.
The whole potential energy surface is actually not needed, as far as I know, you just need to identify reactant, product, and transition state.
RRKM is based on few assumptions, with the first one being quite obvious: since we are talking about potential energy surfaces, the electronic motion and the nuclear motion is separated by the Born-Oppenheimer approximation.
The nuclear motion is also assumed to be well separated into rotational, vibrational, and translational one. The internal degrees of freedom are treated classically with quantum mechanical corrections. 

RRKM is quite useful for predicting gas phase dissociation and isomerization rates  under low pressure (low enough so that reaction can be safely assumed to be unimolecular). For that reason, this theory is ofthen used in mass-spectrometry, since the above mentioned conditions are quite often met here, but it is of no use for reactions in the condensed phase.