Why is cis-1,2-diflouroethene more stable than trans-1,2-dichloroethene?
Answers
This is mainly due to The lone pair of chlorine atoms being involved in resonance with the double bond, as it does so positive charge appears on one chlorine and negative on another. A cis geometry allows for a stabilizing interaction (attraction) between these positive and negative charges, which makes this resonance form a greater contributor to the resonance hybrid than it is for the trans isomer.
From MO perspective
Fleming (2009) provides an explanation which I feel is more convincing. Essentially, the idea is that extra stabilisation in the cis form is derived from the interaction between the antiperiplanar C−H σ and the low-lying C−Cl σ∗ MOs. Jan provides more details on this here when he explains the cause of a similar effect responsible for the gauche conformation being favoured in 2-fluoroethanol. Another phenomenon that Fleming touches on which he uses the same explanation for is the preference for the gauche conformation in 1,2-difluoroethane. It is also explained in the same paragraph on p. 89.
The same explanation can be used for 1,2-dichloroethene. This is because chlorine is also a rather electronegative atom, although less so than fluorine. Thus, we can still expect the C−Cl σ∗ MO to be low enough in energy to interact with the the C−H σ MO.
You can refer from here--
Fleming, I. Molecular Orbitals and Organic Chemical Reactions. John Wiley & Sons, Ltd. United Kingdom, 2009.