Several groups of bacteria can conduct anoxygenic photosynthesis: green sulfur bacteria (GSB), red and green filamentous phototrophs (FAPs e.g. Chloroflexia), purple bacteria, acidobacteriota, and heliobacteria.
Some archaea (e.g. Halobacterium) capture light energy for metabolic function and are thus phototrophic but none are known to "fix" carbon (i.e. be photosynthetic). Instead of a chlorophyll-type receptor and electron transport chain, proteins such as halorhodopsin capture light energy with the aid of diterpenes to move ions against a gradient and produce ATP via chemiosmosis in the manner of mitochondria.