I have something akin to and need to change the single quotation marks to double quotation marks. I tried :s/\\\'.*\\\'/\
:s/\\\'.*\\\'/\
You need to put round brackets around the part of the expression you wish to capture.
s/\'\(.*\)\'/"\1"/
But, you might have problems with unintentional matching. Might you be able to simply replace any single quotes with double quotes in your file?