I submitted this as my written extra credit for my arithmancy, charms, and defense NEWTs. My scores weren't broken down precisely enough to tell if they gave me fewer points for it because it was split three ways, or if I got full credit on each test. Maybe those proctors don't even talk to each other to notice that I duplicated it, the way the Ministry is run.
The class of charms nicknamed "Apologies" to contrast them with the Unforgivable curses can be more accurately termed as spells that use the power of soulfire. "Soulfire" is, itself, something of a term of art. It refers to power that is external to the caster, seemingly channeled from celestial realms. This is in opposition to the "hellfire" that powers the Unforgivables, which is the infernal force that makes them impossible to block with magic.
Unlike the more common class of spells, both Apologies and Unforgivables require the caster to achieve a particular mindset that is sympathetic with the energies of the beyond required to enact the spell. Our theory is that this involves attuning one's very soul to the correct dimension through use of this emotion, as evidenced by soulless creatures being unable to cast even Unforgivables.
But this is a digression for the Department of Mysteries to weigh in on. Suffice it to say that in order to cast any of these spells, the caster must essentially use emotion to create a proper resonance to channel additional energy from outside the inner magical well.
The first Apology is a well-known charm, the patronus. This spell, with the incantation Expecto Patronum, summons a silvery positive energy which, in complete use, turns into a protector imago (but which might only form a shield or even a mist if partially cast). This field tends to uplift the spirits of those nearby, and wards off creatures of negative energy, such as dementors. Fully realized castings, referred to as "corporeal" (even though they are still intangible), can have a near-physical effect on dark creatures.
While it has long been thought that one needs a strong "happy memory" to cast the spell, this is a bit of a misunderstanding. The actual emotion involved is the feeling of being safe, or of providing safety for others. Since this feeling is often part of happy memories, and so few individuals can manage to cast the spell, it is only recently that the specifics were determined. This emotion of safety feeds the intention of the spell.
The patronus is the counterpart to the fiendfyre curse, which also summons an imago in the form of cursed fire. Through investigating the arithmancy of both spells, we were able to isolate the factors that channeled exterior energy and compare them against the three Unforgivables. Replacing the "hellfire core" of the arithmantic diagram with the corresponding "soulfire core" from the patronus, and updating the interface elements between these cores and the rest of the spell matrix, we were able to create three new charms. (See the attached arithmantic diagrams.)
The second Apology is the empowering charm, or libertas. It is the counterpart to the domination curse (the imperius), and essentially serves as a counter to that spell and several other mental effects such as the confundus. Being affected by the charm augments the target's own strength of will, enabling the mind to more easily fight off exterior influence. It also provides a brief rush of confidence.
Silvery-blue in appearance and with the incantation Libero, the charm requires pride in the target to cast. This may serve to make it less useful as a general prophylactic against mind-controlled subjects entering controlled spaces, as experiments in the last year at the Ministry have determined that the emotion must be fairly strong. Few people, it turns out, are able to summon a meaningful pride in all their coworkers, let along perfect strangers.
The third Apology is the exorcism charm, or excoriatus. It is the counterpart to the torture curse (the cruciatus), but does not counter that spell. Instead, the charm directs a scouring stream of energy at the target's soul. This can serve to remove exterior influences, particularly spiritual possession. It does not remove most curses, though it is possible that it can reduce the long-term effects of curses if applied quickly enough after application (research ongoing). Due to its effect of essentially directing a strong current of energy that seeks out cracks between the soul and the spirit of a possessing entity, it also seems as effective deterrent to individuals that, through use of dark magic, have "cracked" souls. These individuals suffer incapacitating feelings of guilt and shame at their actions, and may be unable to successfully cast curses for a short time after being affected by the spell. Currently, it is unknown what extended exposure would do to a sufficiently morally bankrupt individual.
Familiar to muggles as television static, the stream of spell energy is a dense collection of silver sparks. Its incantation is Excorio, and the emotion to cast it is hope. Specifically, this hope is the feeling that the future will be better than today, and that good will overcome evil. To the best of my knowledge, the spell has not been widely tested (as it was only finished a few months ago), but it may serve as a useful nonlethal offensive spell for aurors to use on dark wizards. Unlike other incapacitating spells, it is as unblockable as the Unforgivables.
Finally, the fourth Apology is simply known as the soulfire charm, the counterpart of the killing curse. It does counter that spell, if cast quickly enough after death (before the soul has left the body). This spell has only been completed very recently, and our team was obviously unable to test the killing curse except accidentally (which I, myself, was hit by it). Thus, it is unclear what the allowable time limit is to restore a victim of the killing curse, or the peculiarities of how both spells affect targets not considered to have souls. In addition to its ability to revive a target, the spell's offensive application destroys dementors and likely other entities primarily composed of dark magic (e.g., wraiths).
Manifesting as a reddish-orange bolt shot through with silver, the incantation for the spell is Hoc Est Corpus. It requires a feeling of love to cast. Those of us that have tested it primarily used romantic love, but familial love and even deep friendship might be sufficient. Likely, the sensation is tied to willingness to give up one's own life for the object of affection, given its ability to call a target back from recent death. The emotion does not have to be felt toward the target, though it may help with the revivification version of the spell. Given the recent defection of the dementors of Azkaban, it may be as important for Britain's aurors to learn this spell as any other. It does not appear to have any significant short-term effect on a living target that is not made of dark magic, but research has so far not been extensive on this subject.
Two members of our research team anticipate working in the Department of Mysteries after graduation, so new research is likely to be published quickly as it's relevant to other Ministry staff.