Oracle SQL Statement alter index and add partition

I have an index in which I have to remove one column and reindex back for rebuild:

ALTER INDEX <index_name> REBUILD;

Is it possible to add partition when I rebuild an index. Partition will be based on one of the column index which is a datetime field. Something like:

ALTER INDEX <index_name> REBUILD, PARTITION BY RANGE(COLLECTIONTIME) INTERVAL     (INTERVAL '15' MINUTE)
(PARTITION INITIAL_PARTITION VALUES LESS THAN (DATE '2014-10-10') );

Not sure how to write the sql statement for it. Anyone can help?

Also, if it is possible will the existing records will also be partitioned?