Hi Elizabeth,
Am researching David Beaton Bethune of Scotland, are they the one and the same?
From what I deducted his son, Richard, left in 1625 or 1630. The Clearances I believe you are referring to are around 1745 after the Jacobite uprising. Look through the church records in Scotland and the ship records of immigrants during this time.
Hope this helps a little,
Jan Leishman