Caring sometimes needs to happen silently at a distance. I have never used smiling as intent to nullify negativity in others. However I have done the process in reverse.

As a Counselor (mental health) my job as overnight person was to wake people up for the day and for am medication monitoring - a task I intensely loathed. So, preceding the task I would do a negative dump in the office - by silently swearing aloud in a whisper, etc. Then I could be cheerful and firm in rousing people from their slumber. And it surprised me every week during more overnight rotation.