Auto Populate Discussion Group

I have user groups that are organizational departments (User Groups) which employee (end users) are members.  I would like Clarizen to create a new group  membership link between the employees in specific organizational departments to a New Discussion Group.  If a new employee is added to the  one of the organizational department (User Group) they would also be added to the New Discussion Group.

Example:

If User is Member of Department A, Department B, Department C, Department D then Add user to Discussion Group A1.