Why did the Germans fall behind the Americans in the development of the atomic bomb after an initial lead?

There is a relevant new publication on the topic:

Popp (2016) "Misinterpreted Documents and Ignored Physical Facts: The History of ‘Hitler's Atomic Bomb’ needs to be corrected"

"It is shown that until the end of the war the German physicists did not know that an atomic bomb can only be made with fast neutrons, except Heisenberg, who, however, discovered it rather late, did not communicate it clearly and did not study any bomb physics. The physically correct interpretation of the documents reveals that the German physicists worked unsuccessfully on a reactor, which would have been a prerequisite for a plutonium bomb. But they did not know how to build a bomb because they never worked on a realistic bomb theory."

I would say there were two main reason...

First off, they miscalculated badly on how much uranium it would take to make a bomb. Thus their calculations for how long time it would take to stockpile and enrich enough uranium was much too long. (German scientists captured by the USA and secretly under surveillance, were surprised by how little uranium was needed when they heard about the American bombs.)

Second, the Germans knew they needed a quick victory. They knew they couldn't stand against all the resources available to the USA for long, once the USA went on a war-footing and put all resources into making weapons. Partly due to the assumption about the amount of uranium needed, the Germans thus concluded that it would take too long to make an atomic-bomb. They wouldn't be able to create such a bomb for several years; and by then they would either 1)have had to already have won the war or 2)being overwhelmed by a fully militarized USA - in either case, a German atomic bomb wouldn't impact the result. Thus money, resources and scientists were allocated to other projects, while the atom-bomb was put on a back-burner.

IMHO there is no doubt the Germans could've succeeded and probably should have tried. They after all made some rather stunning invention; like V1, V2, jet-engines and rocket-planes... Imagine combining an a-bomb with a rocket. But by the time it was obvious the war would drag on, they'd lost too much time in the research of an a-bomb.

First, a correction on Deuterium; it is a hydrogen atom with a neutron as well as a proton in its nucleus, giving it an atomic mass of ~2 instead of ~1. Heavy water is a molecule with one hydrogen and one deuterium atom bonding to the oxygen, instead of two regular hydrogen bonding to the oxygen. It's chemical formula is DHO, (or sometimes colloquially but incorrectly D2O) compared to the H2O of regular water.

Now to the main point: Another reason for the inability of the Germans in WWII to develop the atomic bomb (as well as their inability to perfect numerous other possible weapon systems) is their determination to expend resources on everything. The economic resources of Germany were likely more than sufficient to build an atomic bomb faster; or to perfect a jet fighter sooner; or to complete the V1 and V2 programs a year earlier; but not to attempt all of the above and numerous others simultaneously while resource-starved.

This was also a direct question in an interview with J. Robert Oppenheimer's biographer Ray Monk, which he chose to answer thus (approx. 16' into the program):

One of the aspects of the Manhattan project that is often not emphasized as much as it should is the sheer scale of the industrial operation. Two whole towns were created for doing nothing but producing fissile material, in Hanford in Washington and Oak Ridge in Tennessee. And the Germans did not have that, and that I think was the main reason why their project got nowhere.

The interview also contains several other interesting references e.g. to Werner Heisenberg's role as well as this quote by Winston Churchill :)

The reason we won the war is that our Germans were better than their Germans.