Hyperatomics are part of the missile defense systems employed by Turan Tot Narut's people. They used these weapons against the USS Enterprise on Stardate 4401.9 in order to "sweep the ship the ship from their skies and the disease it carried". (a different philosophy than that of Turan Tot Narut's people in which showing one's bare face was not considered sinful)
The Enterprise's shields could resist their destructive power but made it impossible for a Landing Party led by Captain James T. Kirk to be transported up while the attack continued.
As their description implies, these weapons may be a type of atomic weapon superior in capabilities than those of regular atomic weapons. (TOS comic: "The Hidden Face")