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Consider this sentence:

One can observe a sharp fall in/of the IL’s electrostatic potential occurs/occurring in/at the center of bulk water.

Is it "occurs" or "occurring". The sentence explains an observation. I could also remove "occurs". However, I don't know which is correct if I want to add a verb to this case.

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Which word you would choose here depends on the meaning you are trying to convey.

If the intended meaning is that the electrostatic potential always falls in bulk water, then you might say:

One can observe a sharp fall in the IL’s electrostatic potential that occurs at the center of bulk water.

If the intended meaning is that right now, as you are reading the sentence, you could measure the bulk water and see the electrostatic potential falling, then you might say:

One can observe a sharp fall in the IL’s electrostatic potential occurring at the center of bulk water.

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