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    $\begingroup$ X, Y, and Z can show the same positions all right. But there is no such oscillation that would change, say, just the X coordinate of one of the H atoms and nothing else. Everything is connected with everything, and we didn't like that. $\endgroup$ Commented Sep 4, 2019 at 13:42
  • $\begingroup$ Solving for the normal coordinates in the days of Herzberg wasn't trivial. (It's a 3N x 3N matrix after all) But yes, you have $3N-6$ normal displacements - one for each normal mode. $\endgroup$ Commented Sep 5, 2019 at 2:42