The Institute building was also famous as the site of the headquarters of the Bolshevik party, and is currently the location of SPb governor and city administration.

However, I have a hard time figuring out where exactly this photo might've been taken. The long wall suggests the neighboring Smolny Convent rather than the Institute itself — but it turns out that some spaces behind the current Smolny building and inside the convent are walled off so hard that even Yandex doesn't have photos from there.