calculating degrees of freedom chemistry

Therefore it's not a 'degree of freedom' which counts against the 3 N total.

But for linear molecules like C O 2, one of those rotations (around the axis of the molecule) doesn't actually change the position of the atoms. For most larger molecules, there's three different degrees of rotational freedom: rotation around each of the x, y, z directions. Likewise, it's standard to subtract out the whole molecule rotation. So you have 3 N total degrees of freedom, but you can set aside 3 of them as translation of the whole molecule in each of the x, y, z directions, leaving ( 3 N − 3 ) degrees of freedom.

The standard breakdown of degrees of freedom subtracts out global movement in each of the three directions. The important thing when doing so is that the number of independent degrees of freedom are preserved: it's just that what a particular degree of freedom does to the atoms changes. Instead, we can make combinations of different degrees of freedom. Now, having independent degrees of freedom for each atom isn't all that useful. These come about because when each atom moves, it has three independent degrees of freedom: its position in each of the x, y, z directions. There are always 3 N total independent degrees of freedom for a molecule, where N is the number of atoms.

Calculating degrees of freedom chemistry