Invoke deity is a technique in Slash'EM Extended that was introduced in version v65. Every character can use it right from the start of the game. Technically, it is granted by the player character's race, but every race is set to have it.
If the player character has a positive alignment record, their deity may heal some of their hit points and decrease the prayer timeout. However, characters with a negative alignment record will be damaged and have their prayer timeout increased instead. If the alignment record reads exactly zero, nothing happens. Using this technique breaks atheist conduct, and it will then have a timeout of about 3000 turns, so it should only be used if it's really necessary.
The Imperial race cannot use this technique at all, and it doesn't work in the Gehennom either since the player's god isn't available. None of the possible harmful effects will anger the player's god though.