Can the light reaction of photosynthesis happen spontaneous in pools of water?
Photosynthesis is a lot more complex than just breaking down water

Yes, photosynthesis involves a reaction which partly involves absorbing photons and breaking down water. But overall it is far more complex than that as it also involves absorbing carbon dioxide and turning that into sugars and other molecules that plant can use a fuel. Breaking down water is a byproduct of that larger process as is the oxygen released by it.

The detail of the reaction involved is complex and consists of dozens of individual steps. It isn't as simple as absorbing a photon and splitting water. In fact, there are two separate and individually complex systems of proteins involved in the water-splitting part of the process: photosystem I absorbs light and generates higher energy electrons; photosystem II also absorbs light, breaks water molecules part and generates higher energy electrons. But these processes are so complex that we don't fully understand how they work (and our understanding of the structure of photosystem II was updated as recently as 2014). And that machinery is very complex involving dozens of individual proteins and components.

Given the complexity of the processes behind water-splitting in photosynthesis (which involves multiple photons and electrons) it should be clear that there is no easy way to perform the reaction. 

You don't just need photons and water molecules. You need some of the most complex molecular machinery we know of and multiple photons. Sunlight + water isn't going to achieve it.