This is what we should start from!
45 gallons is 36" x 12" x 24" H. Too tall tank for so small 110W light fixture.
You should be looking for a lamp with at least 96W x 36" long power compacts there, bur 24" tall tank might need stronger lights.
I had succesfully kept anemone under power compacts but my tak was shallow 30 gallon: 36" x 12" x 16" and I had 2 tubes 96W each. You have 8 inches more height to deal with it.
In my opinion such a tall tank will probably require HQI. Or, with weaker light I would give up the anemones thing and make it less light seahorses tank or something like that.