Confusion about comparing the charge densities of benzene and fluorobenzene I understand that the functional group $\ce{-F}$ is an electron-withdrawing group. It is expected that the difficulties of an electrophile to attack the carbon atoms are $$\ce{PhH}&lt;\ce{2,4of PhF}&lt;\ce{3 of PhF}\tag{1}$$Therefore, I want to demonstrate it quantitatively by computing the charge densities of carbon atoms.
Using command # opt freq hf/3-21g pop=nbo geom=connectivity
and the molecule models in Gaussian 09,
I obtained the charge densities of $\ce{PhH}$ and $\ce{PhF}$. To my surprise, the result is:
$$\begin{array}c\text{molecule}&amp;\text{ortho}&amp;\text{meta}&amp;\text{para}\\\ce{PhH}&amp;-0.239&amp;-0.239&amp;-0.239\\\ce{PhF}&amp;-0.306&amp;-0.222&amp;-0.261\end{array}$$
By observing this result, the fact that the electrophilic substitution of $\ce{PhF}$ is likely to occur in o- and p- is verified, or the right half of $(1)$ is verified.


  But why would the charge density of position 2,4 of $\ce{PhF}$ is more negative than that of benzene, given the fact that $\ce{-F}$ decreases rate of the electrophilic substitution reactions?  


My speculation
i) $(1)$ may be false.
ii) The NBO charge densities between two different molecules cannot be compared.
iii) The charge density cannot indicate the difficulty of the attacking of electrophile.

Which one, or something else, can explain this strange observation? Can another method to order electron-withdrawing ability of some functional groups computationally be suggested?
This is the way of directing the electrophiles to the ortho and para places  of the benzene cycle. As you see the ortho and para places are more negatively charged.That's true. It is due to the ability to donate its electron pair to the benzene cycle.

But an electronegative element can attract the electron cloud to it. Fluorine is the most electonegative element, so it has a greater ability to attract the electron cloud of the benzene cycle. So that makes it relatively  resistant to an incoming electrophile.

This does not say that it is not a  ortho-para director. It's a ortho-para director but it deactivates the ortho and para places of the benzene cycle.