No connection at all. Although coincidentally they both have geographic or place name origins. The Buchans held land in Aberdeenshire on the northeast coast of Scotland although there is a chance they were Welch in origin.
The name Buchanan comes from an area with the same name on the shores of Loch Lomond. Buchanans were originally MacAuslans after the prince of the same name who came over from Ireland in 1016, they took on the place name Buchanan in the 13th century.
President, Clan Buchanan Society International