You can use the Date property of the DateTime object – eg
DateTime midnight = DateTime.Now.Date;
So your code example becomes
private DateTime _Begin = DateTime.Now.Date;
public DateTime Begin { get { return _Begin; } set { _Begin = value; } }
PS. going back to your original code setting the hours to 12 will give you time of noon for the current day, so instead you could have used 0…
var now = DateTime.Now;
new DateTime(now.Year, now.Month, now.Day, 0, 0, 0);