The connection between the rapture and the Day of the Lord

Immediately after the rapture God will bring his wrath on the earth. That is called the day of the Lord.
Matthew 24:30-31 the rapture
24:43 a thief in the night

I Thessalonians 4:13-18 the rapture
5:2 the day of the Lord will come like a thief in the night."

II Peter 3:4 the rapture
3:10 "day of the Lord will come like a thief."

There is no separation between the rapture and the day of the Lord. Matthew 24:29 tells us they will both occur after the great tribulation.