A partial match is Psychic Academy (2002).
Psychic Academy follows the life of Ai Shiomi, a boy with psychic powers, also known as "aura power" in modern-day Japan. This ability has emerged in the world, but not all people have it. Aura power itself allows certain elements such as fire, water, ice, wind, lightning, earth, and light to be used by those who have the ability. Which type of power they can use depends on their aura and what they are taught.
As Ai struggles with his new school, a life he is not sure he wants; a crazy rabbit takes him as his student. His feelings for Orina and Myuu begin to develop and contrast as the school year progress. Ai also makes discoveries about his rare light aura. To further complicate things, a group of researchers try to artificially awaken the dormant aura genes within all humans, heedless of the danger and damage to society it might cause.
- characters with elemental powers;
- released in early 2000s;
- has fighting scenes;
- from TVTropes it appears Aura-seeing is something that can be achieved and reveals emotional states:
The color of a person's aura reveals their emotional state, even if they are normal people. When Ai learns to see these auras (something which would normally take months of hard work), his master immediately suggest they pick up some girls with it.
Not really a match:
- as far as I can see there's no particular black robes, rather regular clothes. Also almost no clothes for some girls;
- not sure about the clans;
- I'm also not sure if one could forget the level of NSFW stuff shown in that.
Opening below, warning NSFW underdressed teenage girls:
Found with the Google query
anime "see * auras" which returned What is this anime where people manifest special powers from element-based auras? on Anime.SE.