Why is an empty MongoDB database so big?

Depending on your version of MongoDB and configured storage engine, several data and metadata files will be preallocated on startup. This is the expected behaviour: an "empty" deployment still results in housekeeping and diagnostic data.

Based on your directory listing, you are running MongoDB 3.2 which defaults to using the WiredTiger storage engine. WiredTiger allocates up to 100MB per journal file, so your new deployment has ~300MB of preallocated journal files:

     100M    ./journal/WiredTigerLog.0000000003
     100M    ./journal/WiredTigerPreplog.0000000001
     100M    ./journal/WiredTigerPreplog.0000000002

Aside from journal files, other metadata that will be created in your dbpath (without you having explicitly created databases yet) will include:

• A local database with a capped collection called startup_log with some diagnostic information about each startup invocation of this instance of mongod. There will be an associated collection and index file for local.startup_log; the filenames are opaque but as the first files created I'm guessing in your example these might be:

   36K    ./collection-0-3697658674625742251.wt
   36K    ./index-1-3697658674625742251.wt
  

• Multiple WiredTiger metadata files. There will always be at least one database in a deployment since the local database is created by default for the startup_log:

  4.0K    ./WiredTiger
  4.0K    ./WiredTiger.lock
  4.0K    ./WiredTiger.turtle
  4.0K    ./WiredTigerLAS.wt
   16K    ./_mdb_catalog.wt
   36K    ./sizeStorer.wt
   44K    ./WiredTiger.wt
  

• A diagnostic.data directory; this is for periodic sampling of server status metrics:

  168K    ./diagnostic.data/metrics.2016-06-10T11-17-58Z-00000
  72K    ./diagnostic.data/metrics.2016-06-10T10-19-31Z-00000
  

When you create a new database, MongoDB create space for the oplog.

The oplog (operations log) is a special capped collection that keeps a rolling record of all operations that modify the data stored in your databases.