What is the equilibrium distance between two hydrogen atoms?

[Rade]

From another forum an interesting question comes to mind:
Suppose a universe made of only two hydrogen atoms {[P+]e-}. What would be the exact distance of separation where the total of all attractive and repulsive forces would balance ? Thus if < than this distance, union of the two atoms to form hydrogen molecule results.

 

[Gokul43201]

Suppose a universe made of only two hydrogen atoms ...

This is the assumption we make when we do the standard calculation for the H-H bond length.

Or is there some Cosmological twist to this?

Thus if < than this distance, union of the two atoms to form hydrogen molecule results.

This is incorrect. When the atoms are at the separation where the net force is zero, we say that a hydrogen molecule has formed.

 

[Rade]

This is the assumption we make when we do the standard calculation for the H-H bond length.Or is there some Cosmological twist to this?This is incorrect. When the atoms are at the separation where the net force is zero, we say that a hydrogen molecule has formed.

Thank you. It is known that the H-H bond length is 0.77 Angstrom. So, it is exactly at this length that the net force between the two atoms = 0.0, that is, this is where all EM and gravity forces balance to allow the hydrogen molecule to be formed--is this a correct understanding ?

 

[Gokul43201]

Thank you. It is known that the H-H bond length is 0.77 Angstrom. So, it is exactly at this length that the net force between the two atoms = 0.0, that is, this is where all EM and gravity forces balance to allow the hydrogen molecule to be formed--is this a correct understanding ?

Gravity is weak enough that it doesn't figure in the calculation.

 

[quetzalcoatl9]

in quantum chemistry, we call this the "gas phase" calculation, we often times do dimers as well to get a fairly good idea of the intermolecular potential in pairwise terms

actually, NIST gives an experimentally-measured equilibrium bond distance of 0.741 A:

http://srdata.nist.gov/cccbdb/exp2.asp?casno=1333740

my own Hartree-Fock+MP2/631G* calculations give the same number

the forces at work here are electrostatic

 

[Rade]

Thank you all. I would like to take this thread one step further. From above we know that H-H bond forms when the two atoms come within 0.741 A. Suppose in this universe from Post #1 the two atoms by chance come within 1.0 A of each other, or perhaps closer, but never as close as 0.741 A. How do electrostatic forces alone result in union, given, that gravity is not involved ? That is, how do we overcome the coulomb repulsion of the protons to allow union ? It almost seems that, in a universe of only two hydrogen atoms, they could never form union without some "outside" force involved (that is, outside the boundary conditions of the two atoms)--the coulomb would always keep them apart. Is there a place for action of quantum gravity here, whatever that may be ? Please let me know where I error.

 

[Gokul43201]

You're forgetting about the electrons on those atoms. Simplistically modeled, electron cloud1 attracts proton2 and electron cloud2 attracts proton1. But the electron clouds and the protons repel each other. The attraction exceeds the repulsion for all separations greater than the bond length (0.741A), and conversely for separations smaller than this. The reason for a non-zero net force at any given separation is due to the non-zero polarizability of the H-atom that gives it a dipole moment when in the vicinity of another atom.

 

[Rade]

... The attraction exceeds the repulsion for all separations greater than the bond length (0.741A), and conversely for separations smaller than this...

Thank you for your response. But now another questions arises. Do you really mean "all separation" distances ? How would the mechanism you explain above result in "attraction exceeds repulsion" if the two hydrogen atoms were say 2 meters apart ? So, I guess I ask, at what limit of separation distance between the two atoms does the mechanism of "attraction exceeds repulsion" kick into gear ?

 

[Gokul43201]

Thank you for your response. But now another questions arises. Do you really mean "all separation" distances ?

Yes, I do.

How would the mechanism you explain above result in "attraction exceeds repulsion" if the two hydrogen atoms were say 2 meters apart ?

In no different a manner than if they were 2A apart, only the difference, or net force, would be way smaller.

So, I guess I ask, at what limit of separation distance between the two atoms does the mechanism of "attraction exceeds repulsion" kick into gear ?

It's always there for any separation, even if the atoms are 2 lightyears apart, but as the atoms get closer, the difference gets significant. The separation where this any "kicking in" happens depends on what you consider significant.

See first figure and explanation here:
http://www.chem.ucalgary.ca/courses/351/Carey5th/Ch02/ch2-2-1.html

 

[Rade]

...It's always there for any separation, even if the atoms are 2 lightyears apart, but as the atoms get closer, the difference gets significant...

This comment brings forth another set of questions. Suppose the hypothetical universe is a circle with diameter of 2 lightyears. Now, place the two hydrogen atoms at each end of the circle opposite each other, 2 lightyears apart. Does not theory predict no EM attraction between the two atoms for 2 years (730 days) since it is photons that mediate the EM force and they cannot travel faster than c ? Next, what is the origin of the photons that will result in the EM attraction when it does occur after 730 days, is it from the two atoms, or from the space-time between the two atoms, or both, or neither ?