SQL 2012 :: Partitioning Large Table On Nullable Date

I have a very large table that I need to partition. Ideally the table will write to three filegroups. I have defined the Partition function and scheme as follows.

CREATE PARTITION FUNCTION vm_Visits_PM(datetime)
AS RANGE RIGHT FOR VALUES ('2012-07-01', '2013-06-01')
CREATE PARTITION SCHEME vm_Visits_PS
AS PARTITION vm_Visits_PM TO (vm_Visits_Data_Archive2, vm_Visits_Data_Archive, vm_Visits_Data)

This should create three partitions of the vm_Visits table. I am having a few issues, the first has to do with adding a new clustered index Primary Key to the existing table. The main issue here is that the closed column is nullable (It is a datetime by the way). So running the following makes SQL Server upset:

ALTER TABLE dbo.vm_Visits
ADD CONSTRAINT [PK_vm_Visits] PRIMARY KEY CLUSTERED
(
VisitID ASC,
Closed
)
ON [vm_Visits_PS](Closed)

I need to define a primary key on the VisitId column, but I need to include the Closed column in order to partition on it.how I would move data between partitions on a monthly basis. Would I simply update the Partition function, or have to to some sort of merge, split, or switch function?