Talking about the breakup with the guy you need to start just personally. No instant messengers, SMS, phone calls and other methods of communication will have no effect. Will precipitate, a sense of reciprocity. So make an appointment and tell him you want to discuss an important issue.
Do not start a conversation about the gap immediately after the greeting. Sit in a secluded place where no one will disturb you. Then in a short sentence affirmative tone bragging about breaking. Possible wording: "We break up" "We need to leave." Most likely, the young man thinks about it and won't argue. Otherwise, no matter what arguments he might put forward, no matter what was asked, stay adamant. To leave means to part.
Then state the reasons for the gap. If the case is the shortcomings of man: infidelity, aggression, jealousy - frankly, I can't live with them. Do not believe the promises to improve, but do not show the cynicism. If the reason is another, Express it. Do not offer out of the situation and do not listen to his proposals. If the conflict reached the gap, even this conversation will not change anything.
Some time not to mess with a young man. If you work together or are engaged in other General business, General meetings, act like nothing happened, but try to avoid his touch. Be polite and friendly.