What's the noun for motivelessly? Here's the word you're looking for.
motive
(obsolete) An idea or communication that makes one want to act, especially from spiritual sources; a divine prompting. [14th-17th c.]
An incentive to act in a particular way; a reason or emotion that makes one want to do something; anything that prompts a choice of action. [from 15th c.]
(obsolete, rare) A limb or other bodily organ that can move. [15th-17th c.]
(law) Something which causes someone to want to commit a crime; a reason for criminal behaviour. [from 18th c.]