Killing is said to fracture one's soul and Voldemort uses this to create horcruxes.
I always assumed that it was because of the evil intention and the act of killing someone was what caused the soul to split.
Does killing by accident also cause one's soul to splinter?
If you are talking splitting the soul for the purpose of making a Horcrux, then, yes, intent is involved. A person intends to deliberately split their soul through the act of homicide, in order to make a Horcrux.
"I do think that the strict definition of "Horcrux," once I write the [Harry Potter Encyclopedia], will have to be given, and that the definition will be that a receptacle is prepared by Dark Magic to become the receptacle of a fragmented piece of soul, and that that piece of soul was deliberately detached from the master soul to act as a future safeguard, or anchor, to life, and a safeguard against death." J.K. Rowling - POTTERCAST - THE LEAKY CAULDRON 12.23.07
Let's look at something objectively: It was Harry's touch that killed Professor Quirrell. Did Harry know that his touch would harm Professor Quirrell to that degree? No. Did Harry intend to kill Quirrell? No, of course not. There was no intention to kill Quirrell on Harry's part; Harry was defending his own life. It was not even in the category of accident, as Harry had no idea what would happen when he touched Quirrell. Yet, in Deathly Hallows, in the chapter King's Cross, Dumbledore says to Harry:
‘So the part of his soul that was in me ...’
Dumbledore nodded still more enthusiastically, urging Harry onwards, a broad smile of encouragement on his face.
‘... has it gone?’
‘Oh, yes!’ said Dumbledore. ‘Yes, he destroyed it. Your soul is whole, and completely your own, Harry.’
If Harry had had his soul split by the death of Quirrell, even when the fragment of Voldemort's soul left Harry, Harry's own soul still should have been split after Voldemort's fragment left it. Yet Harry's soul is whole and untainted.
I'm going to wager a guess that the following characters did not have their souls split either: Molly Weasley for killing Bellatrix Lestrange; Dumbledore for killing his sister Ariana, were it that he was indeed the one who struck her down; Mad-Eye Moody for (presumably) killing Death Eaters at the height of the First Voldemort War; Order members for killing Death Eaters at the Battle of Hogwarts; Snape for killing Dumbledore; and Harry for ultimately killing Voldemort during their final duel.
It's the difference between I'm killing so others can live versus I'm killing to kill or I'm killing for pleasure or power.
Repairing the soul is not as simple as feeling remorse; this indicates to me that intent plays a huge part in whether or not one's soul splits. I think it depends what kind of killing is done. Full-blown pre-meditated murder? Soul splits. Accidental and fully unintentional homicide? Soul does not split.
‘Remorse,’ said Hermione. ‘You’ve got to really feel what you’ve done. There’s a footnote. Apparently the pain of [trying to put your soul back together] can destroy you.'
Deathly Hallows - page 89 - chapter 6, The Ghoul In Pyjamas
So it's not like, I don't think, one can kill someone, feel some obligatory remorse, and then the soul's intact again with no trouble.
Not necessarily. Most likely, no.
Dumbledore heavily implied to Snape that Snape's soul would be at no risk from Killing Dumbledore on purpose, since this would - while legally still be murder, never mind accidentall killing - ethically and morally justifiable. The difference is manyfaceted, but for Potter universe purposes, most likely tied to feeling remorse over the killing.
Your soul can heal if you are remorseful of the act that split it. So, if you accidentally kill a person, regardless of the degree of recklessness you displayed that would result in the killing, the two halves of your soul would recombine if you were sorry that you did it. In addition, it's implied there is an incantation involved to actually create the Horcrux; Harry is an exceptional case because Voldemort didn't mean to make him a Horcrux. The requirement of a spell to make the Horcrux thus requires prior intent not only to kill, but to make a Horcrux.
