The innodb_system data file 'ibdata1' must be writable even with full permissions set

i'm trying to change the datadir in mysql, i created a new directory with the user mysql as a owner, i know am not supposed to set the permission to 777. but even with this full permission still getting the same error in the log file whenever i try to start the mysql service.

[InnoDB] The innodb_system data file 'ibdata1' must be writable

user@user:~$ ls -l /database2/mysql | grep ibdata1 
-rwxrwxrwx 1 mysql mysql 12582912 Jan 15 15:24 ibdata1

any solution ?