Wagner and AC. What's the connection between them?

I think the Opera is no Accident just for a track.... it has a connection but it is only a partial one and so it is not like every scene from Das Rheingold  will apply and those themes which do are in a loose way.

But indeed there are bound to be a few connections for certain, and the David Renouncing Love certainly fits.

Just as an aside, I found it interesting that when David plays Das Rheingold, Weyland states that sounds a bit thin without the orchestra (paraphrasing here).  For David himself, he finds it sufficient... he sets himself apart (center stage, so to speak), and has little desire to play with others...

In the Novelization, David actually gives some information about the particular piece he is playing: He says: "The gods have rejected mankind as weak, cruel, and filled with greed, so they are leaving the Earth forever and entering their perfect home in the heavens-the fortress of Valhalla."

So basically it's an allegory for the engineers being disappointed in their creation and them forsaking mankind to never return. Valhalla here being Paradise or Planet 4.

David continues: "But every step they take is fraught with tragedy because the gods are doomed. They are fated to die in a cataclysmic fire destined to consume not only them, but Valhalla itself."

So clearly, this is exactly what David does to the engineers and the entire planet while he's at it.

"They are as venal as the humans they have rejected, and their power is an illusion."

The last sentence mirrors Davids sentiments toward humans and the engineers.

So in the end, the exact piece that David is playing perfectly fitted the character and I believe that's why it was chosen.

Oh, and as for why Weyland choses Wagner, it seems to be the composer of choice for megalomanias...