Do bacteria exist which live exclusively on non-organic matter? Are there bacteria which consume exclusively non-organic matter? Meaning that they do not require organic matter from other organisms to stay alive and reproduce? A completely pacifistic bacterium. Or phrased differently, are there bacteria which can stay alive and reproduce indefinitely with only non-organic matter present (plus sunlight or thermal vents etc.)? I'm asking specifically, to name one or more bacteria species which can do this.

Sulfate reducing bacteria get their energy converting sulfate to hydrogen sulfide. They are relatively common and may have been the source to turn some oil/gas deposits "sour". Specifics in Wikipedia.