Hello. It should be written as:
"The accident happenned due to the negligence of the driver".
Here is why:
Put the Subject ("The Accident") first, then the verb ("happened"), followed by the object.
That order S-V-O is usually how English is written.
Quite different from Korean where it is S - O - V (Subject - Object - Verb). English will sound backwards to you.
I Hope that helps :)