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The splitting of water is an endergonic (non-spontaneous) reaction, and thus would require energy (chemical work to be done) in order to happen.
In Photosystem II, an enzyme catalyzes this splitting, but where does it get the energy from? Does it use ATP?
Catalysis is about reducing the free energy barrier (aka. activation energy) of a reaction, so it does not require any energy. In photolysis (e.g. splitting water) you get the energy from the absorbed photons.
The exact process is called the Joliot-Kok cycle:
So the photon separates the charges on the P680, after that the activated P680 activates the Yz intermedier, which forces the enzyme to the next step (Sx) in the reaction.
The overall process comprises three types of reaction sequences: (a) light-induced charge separation leading to formation of the radical ion pair P680+QA(-) ; (b) reduction of plastoquinone to plastoquinol at the QB site via a two-step reaction sequence with QA(-) as reductant and (c) oxidative water splitting into O2 and four protons at a manganese-containing catalytic site via a four-step sequence driven by P680+ as oxidant and a redox active tyrosine YZ acting as mediator.
So the process does not involve ATP or NAD or something like that just the "redox active tyrosine YZ". ATP and NADPH are created after the PS2 part of photosynthesis.
The photolysis of water is about storing the energy coming from the photons (light) in ATP and NADPH. In the Calvin cycle the cells use the stored energy to reduce CO2 into carbohydrates. For instance glucose can be delivered to the cells in the root, which can use it as food.
The electrones which are generated from splitting water are later used to split CO2.
The general formula is:
The Photosystem II does the first part of the reaction by splitting up water and transferring electrons to plastoquinone and also by generating H+ ions. Water gets oxidized (spends electrons) in this reaction, CO2 in the end is reduced (receives electrons). 4 photons are needed for splitting 1 water molecule and 8 photons to liberate one molecule of oxygen. For green plants the energy for this reaction comes completely from light. In the process the energy of the electrons is also used to generate ATP, not to use it. A more detailed view can be found in the schematic diagram "Z-scheme" in the Wikipedia page on photosynthesis:
The figure shows the flow of the electrons and the points when they are brought to higher energy levels by light. The energy of the light is then converted in a proton gradient which is then used to generate ATP.
Its also possible to exchange the role of the oxygen with sulphur, the energy source is then usually heat. This is done by sulphur reducing bacteria in the deep sea in the vicinity of black smokers.
Water oxidation chemistry of photosystem II
Light is indeed the energy required for the process to occur! The photosystem chlorophyll involved is P680. The light energy excites an electron to a higher level, and this electron is captured by pheophytin, forming P680+. The redox potential for P680+ is huge, 1.3V, and it becomes a very strong oxidizing agent, regenerating it's lost electron from water during the oxygen-evolving process. The electron that went to pheophytin ends up transferring to QA, then to QB (these are involved elsewhere).
So now, the P680+ oxidizes this redox-active tyrosine residue called Yz by taking an electron. This forces the Yz into a radical state Yz*. As the article goes on to provide, data showed the Yz hydroxyl group pKa to be greater than 9, meaning it should be protonated at physiological pH. As a result, in concert with the electron transfer outlined above, a proton is donated from Yz* to a nearby base: histidine 190. In this manner, Yz* is capable of quickly oxidizing the nearby tetranuclear manganese cluster. An oxygen-evolving complex is formed by Yz, Mn4, Ca, Cl, and a couple of additional amino acids. Yz oxidizes the manganese cluster resulting in transition states denoted S1-S4:
The heavily oxidized Mn cluster then oxidizes water to return to an S0 state, forming O2 as a part of the process.
The authors detail:
We propose that O–O bond formation occurs in the S4 state via nucleophilic attack on an electron-deficient MnV=O species by a Ca2-bound water molecule... O–O bond formation begins by bringing the second substrate water closer to the MnV=O in an SN2-like reaction (S4 state in figure 2). We propose that this occurs through contraction of the Mn–Cl bond upon formation of the high-valent MnV=O moiety.
In conclusion, we see light powers the reaction, but it is mediated by protein. The net reaction is an oxidation of a metalloenzyme complex which essentially rips the hydrogens off of water molecules to return to it's standard state. The article used for this answer was the best explanation, with a lot of details, that I could personally find, but it is from 2002. If someone has a more accurate explanation let me know!
Other two of them are describing very details and these are good answers.
Lights are the energy source, activating the enzymes to split $\ce{H_2O}$. When a chlorophyll in photosystem II reaction center absorbs light energy, an electron is released. This is the activated state energized by lights and has enough energy/ability to suck up electrons from $\ce{H_2O}$.
$\ce{2H_2O \rightarrow 4H^+ + 4e^- + O_2}$
