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How the angle of a water molecule is measured?

The bond angle for water was first determined by vibrational and rotational analysis of its infrared absorption spectra. How is bond angle extracted?

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I wish there was an easy answer, but this is actually somewhat complicated, and to some extent is more art than science. There are several simple models that are used to predict molecular geometry, one of the most common is the VESPR model. Based on this model, one can begin to perform calculations of energy associated with different vibrational modes of the molecule. It is the comparison of calculated vibrational modes using the non-relativistic Schrodinger equation to those values observed in spectroscopic data that verify that the model is correct. It turns out rather surprisingly that many simple molecules can have a structure determined by simple models such as VESPR. However, as the molecules become increasingly complex, numerical simulation techniques are required, especially in the cases of complex proteins.

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