Harry S. Truman took over the post of the president of the United states when Roosevelt died in 1945. Truman was very detailed in his diary, and some facts about him and the office of the United States was well documented in is diary.
Truman's diary is a reputable source for understanding not just the act of dropping the atomic bomb, but also, the development of the bomb and the events leading to the dropping of the bomb. As the president of the United states, who gave the final order for the dropping of the bomb, which marked the end of world war II, it is only logical to see that accessing his diary, will give a reliable insight into the bomb dropping on Japan during world war II. Since his diary was handwritten by him, and he was at the center of the event, using Truman's diary as a source of understanding the events that lead to the bombing of Japan is the most logical thing to do.
An excerpt from the diary of July 25, 1945, at the Potsdam Conference meeting of allied powers near Berlin between  July 17 to August 2, 1945 is shown below.
[Potsdam]
July 25, 1945
We met at 11 a.m. today. That is Stalin, Churchill and the U.S. President. But I had a most important session with Lord Mountbatten & General Marshall before that. We have discovered the most terrible bomb in the history of the world. It may be the fire destruction prophesied in the Euphrates Valley Era, after Noah and his fabulous Ark.
Anyway we "think" we have found the way to cause the disintegration of the atom. An experiment in the New Mexico desert was startling — to put it mildly. Thirteen pounds of the explosive caused the complete disintegration of a steel tower 60 feet high, created a crater 6 feet deep and 1200 feet in diameter, knocked over a steel tower 1/2 mile away and knocked men down 10,000 yards away. The explosion was visible for more than 200 miles and audible for 40 miles and more.
This weapon is to be used against Japan between now and August 10th. I have told the Sec[retary]. of War, Mr. [Henry] Stimson to use so that military objectives and soldiers and sailors are the target and not women and children. Even if the Japs are savages, ruthless, merciless and fanatic, we as the leader of the world for the common welfare cannot drop this terrible bomb on the old Capitol [Kyoto] or the new [Tokyo].
He & I are in accord. The target will be a purely military one and we will issue a warning statement asking the Japs to surrender and save lives. I'm sure they will not do that, but we will have given them the chance. It is certainly a good thing for the world that Hitler's crowd or Stalin's did not discover the atomic bomb. It seems to me to be the most terrible thing ever discovered, but it can be made the most useful.
Diary source: http://web.mit.edu/course/21/21h.102/www/Primary%20source%20collections/World%20War%20II/Truman,%20Diary.html