The Pentagon has spent millions of dollars, according to three new reports, on secret projects to investigate extrasensory phenomena and to see if the sheer power of the human mind can be harnessed to perform various acts of espionage and war - penetrating secret files, for example, locating submarines or blowing up guided missiles in midflight. The Pentagon denies that it is spending money on psychic research. The assertions to the contrary appear in a trio of new books, one just published and two scheduled to be released this spring, and in a series of interviews in which past Pentagon officials and scientists who study the paranormal have discussed what they contend is the military's decades-long psychic quest. What emerges is a picture of [the Pentagon] trying to master such esoteric arts as ESP (extrasensory perception), telepathy (thought transfer), clairvoyance (seeing things that are out of sight), and psychokinesis (mental influence over objects or events) - all in the name of the national defense. A Pentagon spokesman went so far as to deny that the Department of Defense today ''spent a nickel'' on psychic research, but he also suggested that he could not acknowledge the existence of highly classified projects. The most detailed study of an actual set of psychic experiments comes from The Mind Race, by Russell Targ and Keith Harary.