Julius and Ethelhel Rosenberg were charged convicted and executed specifically for

Under Section 2 of the Espionage Act of 1917 50 US code 32 which is now 18 US code 794 the Rosenbergs were convicted of espionage. They maintained their innocence during the trail and their family did as well for years after their execution. However after the fall of the USSR more information has become available from inside Russia that the Rosenbergs were spies for the USSR and passed much secret information to the Soviets about the atomic bomb as well as other military secrets.