Which singlet dihalocarbene has the strongest carbon-halogen bond? There are three singlet carbenes - difluorocarbene, dichlorocarbene and dibromocarbene. Which has the strongest carbon halogen bond?


Obviously backbonding is a point to be considered, as carbene is an electron deficient species. As fluorine is the most easiest to overlap with, the $\ce{C-F}$ bond will be strongest.

But I am not able to get that whether it is possible for the singlet carbene to overlap or share electron density with empty d-orbitals on chlorine and bromine atoms? 

And which is more probable, backbonding from halogens to carbene empty orbital, or the other way round (from carbene filled orbital to vacant d-orbitals)?
Singlet carbene is zwitteronic, meaning the $\mathrm{sp^2}$ orbital is doubly occupied resulting in a negative $\mathrm{sp^2}$ orbital and a slightly positive empty $\mathrm{p}$ orbital. Therefore it attracts electron on one orbital and repulses them around another orbital. The huge reactivity of the singlet carbene comes from this zwitterionic character.

Below is the picture electrostatic potential of on the left a singlet carbene with doubly occupied sp2 orbital and the right triplet carbene.



It can be argued in many ways how a halogen stabilizes the singlet state of carbene.

Two explanation usually used are:


Electronegative species increase the $\mathrm{s}$ character of σ orbital (Bent's Law).   
Electron donation from the electron pairs into the empty carbene $\mathrm{p}$ orbital.


Though the second one is usually used, I suggest you follow the first (more physical). Adding electron negative substituents increases the s character of the doubly occupied sigma in-plane orbital of carbene stabilizing it, significantly decreasing the energy of the system. Following this concept you can see that flourine should provide the maximum stabilization and so on.

$$\ce{F} &lt; \ce{Cl} &lt; \ce{Br} \ldots$$