# Chemical bonding and dipole moment

We know that ammonia undergoes amine inversion. Why doesn't the dipole moment decrease in ammonia, since the direction of the dipole changes to the opposite direction every time there's inversion?

Shouldn't the effective dipole moment become zero?

• Come to think of it, the effective dipole moment of anything is essentially zero, because the molecules rotate all the time, so the direction of dipole changes to the opposite every now and then. Nov 6 '16 at 18:00
• Probably due to the preservation of symmetry - not a true "inversion". See this Wikipedia article on molecular symmetry: "Similarly, ammonia (NH3) has two equivalent pyramidal (C3v) conformations which are interconverted by the process known as nitrogen inversion. This is not an inversion in the sense used for symmetry operations of rigid molecules, since NH3 has no inversion center. Rather it is a reflection of all atoms about the centre of mass (close to the nitrogen), which happens to be energetically feasible for this molecule. Nov 7 '16 at 1:02
• The 'inversion' in ammonia is also called an 'umbrella' motion as seen when one is opened the wrong way on a windy day; C3v changes to D3h to C3v to pointing the other way and back again. Inversion in the symmetry sense is replacing x, y, z by -x, -y, -z. The 'effective' or long time average dipole should really be zero as you suggest because during the vibration, the H atoms more from one side of the N atom to the other, so the dipole goes to zero at halfway in the motion and has the opposite sense every half cycle. A dipole assumes the molecule has its canonical structure. Nov 7 '16 at 8:54

Ivan Neretin is correct in stating that no particle in a (nondegenerate) state can have a permanent electric dipole moment in the laboratory frame. In fact, a permanent dipole moment would require a violation of time (T) and parity (P) symmetry. This is because any such dipole should be directed along the angular momentum vector of the molecule and time-reversal and parity operators have a different effect on the rotational angular momentum and direction of the dipole.

What chemists call a permanent dipole moment refers to the dipole moment in the molecular point group to which the molecule belongs. Only when a polar molecule is subjected to an electric field (e.g. an EM wave or DC field), this field will mix rotational states of opposite parity in such a way that the molecule "orients" itself in the field. You can only speak of the inversion of ammonia in the presence of an electric field (the eigenstates of the Hamiltonian are time independent in the absence of a field or other perturbing force).

Although degenerate states could in principle have a permanent dipole moment, it was shown by Klemperer et al. (J. Phys. Chem. 1993,97, 2413) that the degeneracy of these states is removed by higher-order terms in the Hamiltonian.

• Of course a molecule can have a dipole, e.g. $\ce{HCl}$ but in the gas phase (or solution) thermal motion in the ensemble of molecules has them pointing in all possible directions so the overall experimentally measured dipole is zero. Applying an external field breaks the symmetry and the average dipole can be measured and from this the true one. In small molecules in gas phase quantum effects are more obvious & restrict orientation. You can quite easily measure the inversion frequency of ammonia by observing its spectrum and its about $0.7 \pu{cm^{-1}}$ Nov 8 '16 at 13:53
• A molecule only has a permanent dipole in the molecule fixed-frame, not in the laboratory fixed frame. It is more fundamental than an effect of averaging over the motion of the molecules (and it took me quite some time to understand). The concept of a molecular fixed frame is a consequence of the Born-Oppenheimer approximation where the nuclei are considered to move in the effective potential of the electrons.
– Paul
Nov 8 '16 at 15:22
• If you consider beyond BO wavefunctions, you'll see that this concept indeed breaks down. Of course you can measure the inversion of ammonia, but you'll need a EM field, otherwise you cannot speak of inversion at all.
– Paul
Nov 8 '16 at 15:22
• The BO approx does allow us to imagine potential energy surfaces, and its generally applicable. However, experiment (x-ray diffraction) does show molecules have real shapes: atoms don't just wander around on the surface, not at normal energies anyway. So BO approx is good. As I mentioned dipole are only measurable in the presence of a field (e.g. directed force) to break spherical symmetry. This is how we get to molecule frame from lab frame. Your last comment seems to imply that an em field causes the inversion instead of measuring the effect. The tunnelling (inversion) occurs anyway. Nov 8 '16 at 17:14
• It makes no sense to speak about the inversion in the absence of a field. If you solve the SE for the double well potential of the ammonia molecule you find eigenstates that do not depend on time, i.e., there is no transition from one state to the other. Only when you introduce a field and couple the different parity states it makes sense to speak of the inversion. See for instance the treatment of Townes and Schawlow.
– Paul
Nov 8 '16 at 22:04