One of my favorite times to record is at 2 AM. Regardless of my energy level, there's always a relaxed, quiet sound to the recordings I make then. Here's an example.
Recordings I make then are usually challenges, seeing as most of my recent recording spaces contain people sleeping at that hour. I have to keep quiet, and that's a challenge for me because singing quietly isn't my strength. I was recording my newest release at two AM and I ran into an interesting problem related to that.
The song that I was working on at the time, "Someone Else's Problem", is a very angry song. Had I been able to record it at top volume, it would have turned out far differently than it turned out on the final take. The forced quietness of it all makes it sound almost sarcastic and angry instead of raw rage. Combining the 2 AM sound with the anger created something cool.
If I want to nail a song in one take and am full of emotions, the best time in my experience to record is midafternoon. Many entire albums of mine were recorded straight through in midafternoon along with notable songs like my covers "Heroes" (David Bowie)
and "Letters From The Sky" (Civil Twilight).
The key here is the emotion behind it. Since my songs are almost always tracked live with one microphone, the entire thing really depends on emotions. If I record a song and don't feel it, the take can be musically and structurally spot on, but will seem flat and stale. I'm usually deep in my emotions by the time I record something. It shows.
The emotions still come out at 2 AM, they just come out differently due to environmental constraints. That's part of the magic of recording.