Here it's this one. I think.
*Edit* JJ beat it to me, but here's the Portkey version.
Harry Potter and the Fifth Element by
Bexis
Summary: Harry's summer and sixth year. Examines H/Hr in context of his unwanted wealth and fame, and her need for independence, requiring them to save one another's lives. H struggles for magical control over a mysterious fifth element, receives an inheritance and finds OC summer romance. Hr knows everything and nothing. The brain encounter changes R. D is dispossessed and vengeful. CC is not what she seems. Featuring H/Hr affinity, Auror training, poor parenting, goblins, kidnapping, death, a crash, a fire, an explosion, bribery, funerals, testimony, battles, tarot, pensieves, and eventually secret marriage, Stonehenge, a succubus, love potion, triads, and Druidism. The war against Voldemort spreads to the Continent and becomes a liberation struggle.
I come with a fic that starts of with the mystery of HBP's OOCness between Hermione and Harry, an adopted daughter, and words from the author: "And remember, her name isn't Herms, Hermy, 'mione or Nee, her name is Hermione... Deal with it.".
Harry Potter and the Lost Demon
FF.net Summary
ost HBP. HHr. Harry and Hermione's odd behavior during their 6th year explodes into a maelstrom of chaotic, bitter emotions, caused by a strange 'illness.' Help comes from a young, orphaned girl who is much more than she appears.
On Portkey the same fic is posted as Harry Potter and the Demon's Soul (No link, NC-17 rating).
Portkey Summary: Decidedly AU - During their sixth year, Harry and Hermione drifted apart. Jealousy, indifference and intolerance plagued their relationship until the funeral of their Headmaster. On the train home, Harry suffers from a strange illness and Hermione begins acting erratically, fighting a battle between wanting to punch Harry and wanting to snog him senseless. A mysterious Japanese orphan gets thrust into their lives, whose secrets may hold the key to life, love, and ultimately, the final battle. Excerpt from Ch. 50: ôIÆm not entirely sure,ö answered Harry, not knowing how the cultural difference mattered to their conversation, ôIÆd think itÆs something like 150 years or soà probably similar to just before the muggle industrial revolution.ö ôSo, do you know what orphanages in London were like 150 years ago?ö asked Ragnok pointedly. HarryÆs face fell into a hateful frown as he said, ôWorkhouses? Are you trying to tell me that the orphans at HavershamÆs were forced to work for wizarding businesses? Kotone and the rest of those kids were being used as slave labor?ö ôThatÆs exactly what IÆm telling you, Lord Potter.ö
