What is the Smithsonian Institution's most valuable possession? It's rarest possession?

The Smithsonian owns several rare and unique items. As to which is the most valuable that could be up for debate. Probably the item that could be sold for the greatest price at auction is the Hope Diamond.

The diamond has had several owners, including Washington socialite Evalyn Walsh McLean, who was often seen wearing it. New York gem merchant Harry Winston purchased the diamond in 1949, touring it for several years before donating it in 1958 to the Smithsonian National Museum of Natural History in the United States, where it is on permanent exhibition.

https://en.wikipedia.org/wiki/Hope_Diamond

The Hope Diamond is estimated to be worth around $325 million! By comparison, the Mona Lisa is estimated to be worth around $1 billion!

https://www.therichest.com/luxury/these-are-the-most-expensive-artifacts-in-the-world-as-of-2022/