The Lewis structure should have a central #"P"-"P"# bond with 2 #"Cl"# atoms and a lone pair on each #"P"# atom.
#"Cl"-stackrelcolor(blue)(··)("P")-stackrelcolor(blue)(··)("P")-"Cl"#
#color(white)(mml)|color(white)(mm)|#
#color(white)(mm)"Cl"color(white)(ml)"Cl"#
Each #"P"# atom is #"sp"^3# hybridized, so #"P"_2"Cl"_4# has a structure similar to that of ethane, with lone pairs replacing a #"C-H"# bond on each carbon.
According to VSEPR theory, the lone pairs will repel each other.
Hence, the most stable structure is like the staggered conformation of ethane with the lone pairs anti to each other.
This structure is confirmed by the infrared and Raman spectra of #"P"_2"Cl"_4# in the solid, liquid, and gaseous states.
Thus, the #"P→Cl"# bond dipoles on one #"P"# atom should cancel the bond dipoles on the other atom.
#"P"_2"Cl"_4# is a nonpolar molecule.
