We don't have picture windows in our current house but years ago, when we did, they used to eat mountain ash berries and then fly into the windows. I don't know if the two were related; we wondered if the berries were slightly toxic and made them a bit loopy. I think they were mainly trying to fly into the reflected trees/open sky in the glass.

Maybe putting a loudly-patterned curtain in the window to help disguise the reflection would work? The neighbors might object to orange-and-blue paisley but if it saves some bird necks . . . eh.