“The optimal times to tweet are 12–3 p.m., with a peak best time at 5 p.m. During the workweek is the best, though some niches might have more active audiences on the weekend.
Wednesday at noon and 5–6 p.m.
Monday–Friday at 12–3 p.m. and 5 p.m.
Experiment with 2–3 a.m., 6–7 a.m., and 9–10 p.m.
When to tweet in general to increase retweets and clickthroughs:
5–6 p.m.
Noon specifically
3 p.m.”
– CoSchedule