ACR MLG ON DIVERSION TO ALTERNATE FLEW WRONG TRACK.

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I WAS COPLT NOT FLYING ON FLT MSP DIRECT DFW. WE RECEIVED A MESSAGE TO CONTACT DISPATCH ON COMMERCIAL RADIO FREQ. DISPATCH INFORMED US DUE TO ACFT ACCIDENT AT DFW WE SHOULD DIVERT TO OKC AND GET FUEL AND BY THAT TIME THE ARPT SHOULD BE RE-OPENED. WE INFORMED ATC OF OUR INTENTIONS TO GO TO OKC. ATC INFORMED US THEY WERE NOW ACCEPTING TFC AT DFW. I TUNED IN THE OKC VOR TO REF WHERE WE WERE AT. THE CAPT THEN RETURNED TO TRYING TO CONTACT DISPATCH THAT WE COULD GET INTO DALLAS. DURING THIS TIME ATC GAVE US DIRECT OKC. I WAS BUSY DOING MY REQUIRED DUTIES FOR A DIVERSION; UPDATING ACARS; ETA; ARR FUEL; ETC; PLUS THE DSCNT CHK HAD NOT BEEN COMPLETED. I THEN INCORRECTLY TOLD THE CAPT THAT I HAD OKC TUNED ON MY RADIO WHEN ACTUALLY IT WAS BPR. BECAUSE OF ME BEING BUSY I DID NOT NOTICE THE NEW HDG THE CAPT HAD TAKEN UP WHICH WAS SOUTHERLY WHEN WE SHOULD HAVE BEEN GOING NW. AFTER SEVERAL MINS WE REALIZED OUR MISTAKE AND AT THE SAME TIME ATC CALLED AND WONDERED WHAT THE HECK WE WERE DOING. WE TOLD THEM THAT WE HAD TUNED THE WRONG FREQ AND WERE NOW PROCEEDING DIRECT OKC. THE MAJOR CAUSE OF THIS INCIDENT WAS MY MISTAKENLY TELLING THE CAPT I HAD OKC ON MY VOR. CONTRIBUTING FACTORS WERE THE CAPT NOT DOUBLE CHKING THE OKC FREQ AND IDENTING; INDECISION ON WHETHER OR NOT TO DIVERT; NOT SURE WHO WAS FLYING THE ACFT AND WHO WAS RUNNING THE RADIOS. SUPPLEMENTAL INFO FROM ACN 93571: I TUNED MY VOR THE SAME AS HIS ALL INDICATIONS LOOKED THE SAME AND I FAILED TO AURALLY IDENT IT. WE THEN RECEIVED A LEFT TURN AWAY FROM OKC FOLLOWED BY DIRECT OKC. INITIAL LEFT TURN AWAY FROM OKC WAS DISORIENTING TO BOTH CREW MEMBERS.