by accident vs purposefully

by accident

adj
  • Accidental; as the result of some unforeseen happening or series of events; unexpected; resulting from an event without the foresight, expectation, aid, or design of the person by whose agency it was caused; unintentional. 

adv
  • As the result of some undesigned, unintended, unrelated, natural, or random occurrence; as the unexpected and unforeseen result of formerly unrelated factors. 

  • By chance; unexpectedly; as the result of an unrelated series of events. 

  • Accidentally; unintentionally; without meaning to; as the result of an event not expected, aided, or willingly planned. 

purposefully

adv
  • In a purposeful manner. 

  • On purpose, purposely, deliberately. 

How often have the words by accident and purposefully occurred in a corpus of books? (source: Google Ngram Viewer )