In the end is it depending what the Smithsonian is willing to pay ;-)
Here a side where you can find some info from the american market. http://www.aphotoeditor.com/category/pricing-negotiating/
Especially interesting is maybe the post's:
"Reportage for advertising use" (take a look to the estimate number 2 and 3)
and also to "Nature preserve Guidebook"

I would think what i had to invest to get the image (look to the first post) plus a license fee depending if it should be a exclusive license (means only Smithsonian can use the image) or non exclusive. Also here you can take a look to the 3. estimate in the first post but consider that this images are only licensed over 2 years to the company.
Send an offer, but not to low, and hear what they saying. I always use a term like "negotiable" in such offers/estimates.

Regards
Thomas

The art of losing isn't hard to master. E. Bishop