We use Perfect infinitives:
1) After link verbs like
seem and
appear to refer to a previous time period (an ordinary to-infinitive will usually refer to the present or future):
- There seems to have been some sort of mistake.
2) After passive reporting verbs:
- They are said to have arrived.
- The suspect is reported to have been at home at the time of the incident.
3) After phrases expressing emotions and feelings:
- I'm sorry to have kept you waiting.
- She was felt not to have met the standards required.
4) After modals:
- Who would have thought?
- She might have seen it before.