@JohanLiebert Thanks! I think instead of moving the entire iodine atoms from the plane we can cause disturbance only to the electron cloud in a way dipole moment is non-zero. This would eliminate the need for cis-trans isomerism. However, I'm not sure. As far as I can tell the structure looks planar.

I like your point which says the hydrogen atoms cause this distortion to the cloud which seems possible.

@YusufHasan Thanks! If I had understood your explanation properly, you too say that the dipole moment is due to the distorted electron cloud (instantaneous dipoles). So it seems as this is fluctuating, the direction of dipole moment cannot be ascertained. But what did you mean by "...it is not exactly polarizability at play here..."? And, what does "here" refer to? Is that the 1,4-diiodobenzene or other 1,4-dihalobenzenes? If it's the former, I think, I didn't fully get it.

@WilliamR.Ebenezer are you from India?