FAILURE BY SMT FLC TO SET ALTIMETER DSNDING THROUGH FL180 RESULTS IN ALT OVERSHOOT WHICH TRIGGERS TCASII ALERT IN ANOTHER ACFT.

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WE WERE ADVISED BY ATC TO OBTAIN CURRENT WX AT OUR DEST AND TO INFORM HIM WHEN WE HAD COMPLETED THAT TASK. I AND THE FO AGREED THAT HE WOULD OBTAIN THE WX AND I WOULD MONITOR CTR FREQ AND CONTINUE FLYING THE ACFT. SHORTLY AFTER THE FO BEGAN GETTING THE WX; ATC AMENDED AN EARLIER CLRNC AND INSTRUCTED US TO DSND FROM FL200 TO 16000 FT. THEY ALSO ADVISED US OF OPPOSITE DIRECTION TFC AT 11 O'CLOCK POS AND 10 MI CLBING TO 15000 FT. I ACCEPTED THE DSCNT CLRNC AND BEGAN DSNDING USING THE AUTOPLT. I SET THE ALT SELECT AT 16000 FT AND DSNDED AT APPROX 1800 FPM. TO MY BEST RECOLLECTION I WAS NOT GIVEN A CURRENT ALTIMETER SETTING WITH THE AMENDED CLRNC FROM ATC. SIMULTANEOUSLY I BEGAN SEARCHING FOR THE TFC AT MY 11 O'CLOCK POS. AS THE AUTOPLT STARTED TO LEVEL OFF AT 16000 FT MY FO COMPLETED OBTAINING THE ABR WX AND SET HIS ALTIMETER. IT WAS IMMEDIATELY NOTED THAT I WAS DSNDING THROUGH 16000 FT. I HAD THE TFC IN SIGHT AND INITIATED A CLB AND ASKED THE FO TO RESET MY ALTIMETER. ATC ADVISED US THAT WE WERE 400 FT LOW AND THE TFC HAD DEVIATED BECAUSE OF TCASII ALERT. CONTRIBUTING FACTORS INCLUDED: DSNDING TOWARDS A CLBING ACFT ON ROUGHLY A RECIPROCAL BEARING TO OUR COURSE. AN EXTREMELY DEEP LOW PRESSURE SYS CONTRIBUTED TO HIGHER THAN NORMAL ALTIMETER ERROR; 29.92 SET VERSUS 29.16 ACTUAL. HIGH COCKPIT WORKLOAD; MONITORING RADAR; 1 PLT GETTING WX AT DEST BECAUSE CTR WAS TOO BUSY; LOOKING FOR TFC; DEVIATING FOR WX AND AN INITIATED DSCNT AND AMENDED CLRNC. POSSIBLE CREW FATIGUE AS THEY HAD BEEN CALLED OUT AT XX40 THAT MORNING. CRM; AS A RESPONSIBILITY OF THE CAPT; SHOULD HAVE BEEN BETTER.