Cognitive psychologist Dan Ariely notes on Reddit that the time of day we are most ready to cognitively engage hard tasks (the first two hours) is wasted with trivialities. (Source)
Ariely: One of the saddest mistakes in time management is the propensity of people to spend the two most productive hours of their day on things that don’t require high cognitive capacity (like social media). If we could salvage those precious hours, most of us would be much more successful in accomplishing what we truly want.
Q: What are those hours? I must know.
Ariely: Generally people are most productive in the morning. The two hours after becoming fully awake are likely to be the best.
Maria Popova has also analyzed working habits of writers and found successful writers work early in the day. (jpg)
First fully awake hours would be about two hours after waking. See Sleep Inertia
Creative Nights argues that night work is better suited to particular tasks.