Dear student,
The photosystem in anoxygenic bacteria is not similar to photosystem II of eukaryotic organism as the reaction centre of anoxygenic bacteria gets excited at 870 (purple sulphur bacteria) nanometer or 840 nanometer(green sulphur bacteria) and the pigment present is bacteriochlorophyll. Anoxygenic bacteria has single photosystem because the electron transport chain is cyclic and they do not produce oxygen. Electron gets excited and after completing the electron transport chain reaches the reaction centre again thus filling the deficiency of electron in the reaction centre. So, there is no need of oxygen evolving complex to provide electrons to the reaction centre.
Regards