why does the engine run rough on idle and smoth when the air conditioner is on?

Often times when the A/C is turned on, the engine computer will boost the idle speed, because the A/C pump is about a 20 hp load. When the A/C is off, then the idle speed will not boosted. Have the throttle body inspected and cleaned if need, and have the base idle re-set. Do you ever get any check engine light on? If so, have those codes traced, that will also be a big help.