Final answer:
President Thomas Jefferson was instrumental in smoothing relations which led to the Louisiana Purchase, assigning envoys to negotiate the deal, and acquiring a territory that doubled the size of the U.S.
Step-by-step explanation:
The individual who averted war and smoothed relations that led to the Louisiana Purchase of 1803 was President Thomas Jefferson. He assigned Robert Livingston and James Monroe to negotiate the acquisition of land, which was crucial as it included control of New Orleans and the Mississippi River, vital for westward expansion and trade. Napoleon Bonaparte, facing difficulties in Europe and Haiti, was motivated to sell the Louisiana Territory. This resulted in the signing of the Louisiana Purchase Treaty and Conventions in Paris on April 30, 1803, which substantially doubled the size of the United States for $15 million. The deal symbolized a significant real estate transaction in American history and fulfilled Jefferson's vision of an agrarian republic.