Several early chapters of Dark Sun are devoted to Soviet spies in the US Manhattan project and their influence on the Russian bomb effort. It was immense. During the war the US shipped thousands of tanks, aircraft, ships, and even whole factories to Russia to support the war effort against Germany. They also shipped thousands of sealed suitcases, which contained tens of thousands of documents, many of them top secret. A flood of Soviet agents made the trip in the opposite direction, spreading out over the country. They had broad access to American technology and American industry. Evidently, someone important thought it was important enough to the war effort to allow that.
Air Force Major General Follette Bradley, who pioneered the Alsib Pipeline [the air route from Montana to Alaska to Siberia], would tell the New York Times:
Of my own personal knowledge I know that beginning early in 1942 Russian civilian and military agents were in our country in huge numbers. They were free to move about without restraint or check and, in order to visit our arsenals, depots, factories and proving grounds, they had only to make known their desires. Their authorized visits to military establishments numbered in the thousands. I also personally know that scores of Russians were permitted to enter American territory in 1942 without visa. I believe that over the war years this number was augmented at least by hundreds.
Rhodes, Richard. Dark Sun: The Making Of The Hydrogen Bomb (pp. 100-101). Simon & Schuster. Kindle Edition.
For the Manhattan project, the key spies were inside, with Klaus Fuchs being the most important. He was a talented physicist as well as a committed Communist from his teenage years, and he worked at the heart of two crucial efforts: the gaseous diffusion plant to separate fissionable U235 from U238 at Oak Ridge and the design of the explosive lenses that were the essential ingredient of the plutonium bomb.
The information gathered by the various spies was crucial to the Russian efforts, since the relative poverty and weakly developed technology in Russia made it impossible to carry out many of the experiments performed by the US, Britain, and Canada.
Rhodes has a lot of material on the spies, their psychology, and the tactics used to recruit them. Nearly all were motivated mainly by ideology. A common recruiting tactic used on the less committed was the appeal to a common enemy: Russia is our ally, we are just sharing information needed to confront the fascists. Israel has been known to use similar tactic on Americans.