ACR MDT FREQ CHANGE WRONG DURING DEP FROM SUX.

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F/O LISTENED TO ATIS PRIOR TO 0X00 LCL TIME; PRIOR TO OPENING OF CTL TWR. ATIS SAID TO CONTACT MPS CENTER ON 124.1 FOR SUX WX AND IFR CLRNC. F/O WROTE 124.1 DOWN IN CLRNC SECTION OF LOAD MANIFEST. WE BEGAN TO TAXI AT 0X02 LCL TIME. F/O COPIED DOWN IFR CLRNC FROM SUX GND CTL WITH DEP CTL LISTED AS 124.6. F/O SET RADIOS UP FOR DEP AND MIS-SET SUX DEP CTL AS 124.7. TWR WAS CONTACTED AND WE RECEIVED A CLRNC TO TAKE OFF. CLBING THROUGH APPROX 2000' MSL SUX TWR TOLD US TO CONTACT DEP. F/O WAS FLYING ACFT. I SWITCHED FREQ (124.7) AND TRIED TO CALL; BUT OF COURSE RECEIVED NO ANSWER. I ASKED F/O IF HE WAS SURE THAT WE HAD THE RIGHT FREQ. HE LOOKED AT THE CLRNC AND SAW 124.1 WHICH HE HAD WRITTEN FROM EARLIER ATIS. HE TOLD ME; 'NO; WE SHOULD BE ON 124.1.' I SWITCHED FREQ AND CALLED OUT OF 2600' MSL FOR 5000' MSL TO SUX DEP CTL. MSP CENTER ACKNOWLEDGED OUR CALL BUT FAILED TO IDENTIFY THEMSELVES AS MSP CENTER. WE EXCHANGED SEVERAL XMISSIONS; WERE CLRED TO INTERCEPT THE ARWY AND CLB TO 17000' MSL. I STILL DID NOT REALIZE I WAS TALKING TO MSP CENTER INSTEAD OF SUX DEP CTL. WE RAN THE CLB CHKLIST AND OUT OF ABOUT 7000' MSL I HEARD MSP CENTER BEGIN COMMUNICATING WITH OTHER ACFT AND REALIZED I WAS ON MSP CENTER. CAREFUL PREPROGRAM WOULD HAVE HELPED PREVENT THIS. ALSO; IF MSP CENTER HAD IDENTIFIED THEMSELVES DURING OUR INITIAL CALLUP; WOULD HAVE HELPED. ALSO; THE USE OF VERY SIMILAR FREQS IN CLOSE PROX WAS A MAJOR FACTOR. FREQS SHOULD BE SPLIT SO DIFFERENT FREQS ARE USED.