There has been a lot of back-and-forth on this question in the last 30 years or so. I've tried to summarize the current historical consensus here. It is a tricky issue to unpack, in part because there wasn't one chain of decision-making involved. Most historians today do not think that the bomb was dropped just to scare the Soviet Union, but there were some of Truman's advisors who saw this as a secondary benefit to dropping the bomb.

The best book on the tricky relationship between the USA and USSR at the end of the war is Tsuyoshi Hasegawa's Racing the Enemy: Truman, Stalin, and the Surrender of Japan. For the best discussion of exactly how Stalin reacted to the bomb, I recommend Michael Gordin's Red Cloud at Dawn: Truman, Stalin, and the End of the Atomic Monopoly.

There you go:

http://www.dannen.com/decision/

They have a ton of sources on the decision to drop the bomb.

In the Potsdam conference both Truman and Churchill were confused about that Stalin wasn't scared at all. They initially presumed he didn't get it.

Harry S. Trueman:

On July 24 I casually mentioned to Stalin that we had a new weapon of unusual destructive force. The Russian Premier showed no special interest. All he said was he was glad to hear it and hoped we would make "good use of it against the Japanese."

Harry S. Truman, Year of Decisions (Garden City, NY: Doubleday and Company, 1955) p. 416.

Winston Churchill:

I was perhaps five yards away, and I watched with the closest attention the momentous talk. I knew what the President was going to do. What was vital to measure was its effect on Stalin. I can see it all as if it were yesterday. He seemed to be delighted. A new bomb! Of extraordinary power! Probably decisive on the whole Japanese war! What a bit of luck! This was my impression at the moment, and I was sure that he had no idea of the significance of what he was being told. Evidently in his immense toils and stresses the atomic bomb had played no part. If he had the slightest idea of the revolution in world affairs which was in progress his reactions would have been obvious. Nothing would have been easier than for him to say, "Thank you so much for telling me about your new bomb. I of course have no technical knowledge. May I send my expert in these nuclear sciences to see your expert tomorrow morning?" But his face remained gay and genial and the talk between these two potentates soon came to an end. As we were waiting for our cars I found myself near Truman. "How did it go?" I asked. "He never asked a question," he replied. I was certain therefore that at that date Stalin had no special knowledge of the vast process of research upon which the United States and Britain had been engaged for so long...

Winston Churchill, Triumph and Tragedy (Boston: Houghton-Mifflin, 1953) pp 669-70.

Charles Bohlen (interpreter):

Three days after the successful test blast, after consulting his advisers and Churchill (the British had cooperated in the project), Truman decided it would be wise to tell Stalin the news. Explaining that he wanted to be as informal and casual as possible, Truman said during a break in the proceedings that he would stroll over to Stalin and nonchalantly inform him. He instructed me not to accompany him, as I ordinarily did, because he did not want to indicate that there was anyting particularly momentous about the development. So it was Pavlov, the Russian interpreter, who translated Truman's words to Stalin. I did not hear the conversation, although Truman and Byrnes both reported that I was there.

Charles E. Bohlen, Witness to History 1929-1969 (New York: W. W. Norton, 1973) pp. 247-248.

But Stalin did, in fact, already have all the special knowledge that there was to procure.

G.K.Zhukov:

I do not recall the exact date, but after the close of one of the formal meetings Truman informed Stalin that the United States now possessed a bomb of exceptional power, without, however, naming it the atomic bomb.

As was later written abroad, at that moment Churchill fixed his gaze on Stalin's face, closely observing his reaction. However, Stalin did not betray his feelings and pretended that he saw nothing special in what Truman had imparted to him. Both Churchill and many other Anglo-American authors subsequently assumed that Stalin had really failed to fathom the significance of what he had heard.

In actual fact, on returning to his quarters after this meeting Stalin, in my presence, told Molotov about his conversation with Truman. The latter reacted amost immediately. "Let them. We'll have to talk it over with Kurchatov and get him to speed things up."

I realized that they were talking about research on the atomic bomb.

It was clear already then that the US Government intended to use the atomic weapon for the purpose of achieving its Imperialist goals from a position of strength in "the cold war." This was amply corroborated on August 6 and 8. Without any military need whatsoever, the Americans dropped two atomic bombs on the peaceful and densely-populated Japanese cities of Hiroshima and Nagasaki.

Georgii Konstantinovich Zhukov, The Memoirs of Marshal Zhukov (New York: Delacorte Press, 1971) pp. 674-675.

Kurchatov was the head of the Soviet bomb project since 1943.