Desperance is a psychotropic substance that, when administered, causes an extreme level of hopelessness and depression in the individual (the word "Desperance" supposedly means "hopelessness"). Once the individual reaches that state of mind, he/she becomes extremely susceptible to mind control.
Desperance is encountered in Forward the Foundation. When Hari Seldon decides to deal with strength with the remnants of the Joranumite Conspiracy, he sends Raych Seldon as a spy to infiltrate the movement. Despite undergoing several procedures to change his physical appearance, Raych is immediately recognized by Neferti, the leader of the remaining Joranumite Conspirators, due to the fact that Raych had infiltrated the movement during its initial growth, without hiding his identity, and had told Jo-Jo Joranum that Eto Demerzel was a robot. Joranum's decision to make this information public, ironically, only served to bring an end to the first phase of the Joranumite Conspiracy.
After recognizing Raych for who he was, Neferti and his men surreptitiously administer Desperance to Raych, and eventually, controlling his mind, make him one of the new gardening recruits at the Imperial Palace, with the eventual goal of having him assasinate Hari Seldon, who by that point had become First Minister.
Seldon only escapes the attempt thanks to Manella Dubanqua, who later becomes Raych's wife.
After the ordeal, it is revealed that Raych would probably need an extended time to be cured of Desperance's full effects, meaning the drug probably affects the mind for a very extended period of time, if ingested over a long period of time. It is also important to note that in and of itself, Desperance is not a mind control drug, but merely allows for a state of mind that allows for mind control.