Have you ever felt like you were half asleep and more relaxed than usual? What chemicals in the brain cause this to happen?

It isn't just one chemical, it's more like a whole system.

Adenosine increases in your body through the day, making you more tired, your body clock takes cues from the environment to know when to sleep, and this leads to the release of melatonin when your body notices it is getting dark and closer to bedtime, and then cortisol kicks in when it's getting closer to the time you need to wake up.