Must every diatomic molecule always have an equilibrium bond length? That is, is there always a distance between two nuclei such that the Coulomb attraction between the electron and protons counterbalances perfectly the electric repulsion between the protons?
$\begingroup$
$\endgroup$
9
-
2$\begingroup$ I wonder what the alternative would be. Would the atoms come closer together, feel repulsion, move apart, feel attraction, move together? How do we even measure the distance of two particles that are too small to see? $\endgroup$– Karsten ♦Commented Sep 24, 2022 at 21:48
-
1$\begingroup$ Hmm, for polyatomic molecules this isn't true - there are molecules that don't keep one equilibrium position - fluxional molecules. $\endgroup$– MithoronCommented Sep 24, 2022 at 21:55
-
1$\begingroup$ Taking the English maybe too literally one could just about read "an equilibrium bond length" as "a single equilibrium bond length", i.e. can we devise a system where there are multiple minima? Otherwise I can't think what physically the question could actually mean. $\endgroup$– Ian BushCommented Sep 24, 2022 at 21:58
-
$\begingroup$ @IanBush There could be hysteresis. $\endgroup$– Karsten ♦Commented Sep 24, 2022 at 22:00
-
1$\begingroup$ @Mithoron the more I think about it the more I think the most likely scenario in a diatomic is a weakly bound system where the BO approximation is breaking down - i.e. at elongated bond lengths an excited but still bound state becomes lower in energy than the "ground state". Not my area, no idea if it is observed. $\endgroup$– Ian BushCommented Sep 25, 2022 at 7:17
|
Show 4 more comments
1 Answer
$\begingroup$
$\endgroup$
2
[OP] Must every diatomic molecule always have an equilibrium bond length?
The bond length depends on "what the electrons are doing". For example, $\ce{H2}$ and $\ce{H2+}$ have different bond lengths (the latter is a molecular ion, so maybe outside of the scope of the question). Also, if you are looking at an excited electronic state, the bond length will be different from that of the electronic ground state. It also depends on the temperature, and with that, the vibrational state. The atoms will always oscillate. For higher vibrational states, the average bond length will be longer (anharmonic oscillator).
[OP] That is, is there always a distance between two nuclei such that the Coulomb attraction between the electron and protons counterbalances perfectly the electric repulsion between the protons?
The main repulsive force for 2nd period and heavier atoms is the not repulsion of protons, but the quantum-mechanical effects keeping electrons apart (Pauli exclusion), see What repulsion keeps non-hydrogen atoms at a distance: between inner shells or between nuclei?. Aside from that, the question is
- whether there is always a distance where the atoms experience neither a repulsive nor an attractive force (i.e. a potential energy minimum),
- whether there is a single minimum, and
- whether the atoms arrange such that they are in the minimum position.
The first part is easy to answer - it depends. For atoms that form a given molecule, there is a potential energy minimum different from infinite distance. When two atoms can't form a molecule (at the given pressure and temperature), there is not.
The second part is easy to answer (with no) for molecules with more than two atoms. There are examples where multiple arrangements of atoms in space give rise to a potential energy minimum (rotation around single bonds and other conformers, various types of isomers). I am not aware of any examples for diatomic molecules (if the number of electrons is constant and we are in the ground state) where there is more than one minimum.
The third part is easy to answer, again. When there is kinetic energy available, molecules will not always be at equilibrium distance.
Lastly, here is a definition of equilibrium bond length for computational chemistry:
The equilibrium bond length for a diatomic molecule is defined as the separation that minimizes the total electronic energy; we can identify this as the minimum on our potential energy curves.
Source: Molssi
-
1$\begingroup$ I think that your last definition from Libretexts is not quite correct. Thermal motion does not come into it. It is the uncertainty principle that determines the minimum zero point energy and so the range of possible bond lengths that on average we may call the equilibrium length. Stronger bonds do not always have to correlate with bond length, I'm sure exceptions exits. An excited state can have a shorter bond length than a ground state, e.g. NO $\endgroup$ Commented Oct 1, 2022 at 8:48
-
$\begingroup$ @porphyrin I edited the answer, trying to address your points. $\endgroup$– Karsten ♦Commented Oct 2, 2022 at 14:10