There are photosynthetic organisms that use retinal-rhodopsin complex. However, the mechanism of photosynthesis is different in these organisms than those that employ chlorophyll dependent photosystems. In these organisms, the light causes the rhodopsin-like membrane proteins to pump proton out of the cell and create a proton gradient which in turn is used by the ATP synthase to make ATP.
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This mechanism of "photosynthesis" is not as efficient as the chlorophyll dependent one (page 22, Baltscheffsky, 1997†). Moreover, it does not produce NADPH.
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† Baltscheffsky, Herrick. _Origin and evolution of biological energy conversion_. New York etc: VCH, 1996. Print. ISBN: 978-0-471-18581-9