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A tri-atomic molecule should have 3 vibrational degrees of freedom (one for each "end" atom vibrating on its bond with the central atom and one for the flexing of the bonds like scissors opening and closing). If it is non-linear, it should also have a three rotational degrees of freedom. All molecules (including a triatomic one) will have 3 degrees of freedom for translational motion. All totaled, it will have 3+3+3 = 9 degrees of freedom. Note that this does not address the question of independence of the degrees of freedom - for example - if the two "end" atoms are identical, not all the rotational degrees of freedom are independent.

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