As I am learning about the valence bond theory, the model of hydrogen that Heitler and London created, seems to make sense. But, the theoretical and the experimental results are not the same.

Experimental results:

For the molecule to form, the distance between atoms should be $r=74.1~\mathrm{pm}$

and the energy on the other hand $E= -4.474~\mathrm{eV}$.

The theoretical results are this way:

$r= -\frac{1}{4}~\mathrm{pm}$ and $E= 89.9~\mathrm{eV}$

My question is, is it known why these deviations occurred?

Or is this considered as a correct calculation with approximation?


1 Answer 1


I think you have some typo or flaw in your question. "E = 89.9 pm" doesn't make sense. You are saying energy equals a length. The edited version "E = 89.9 eV" has energy units, but the theory never predicted such as large value. And "r = -1/4 pm" doesn't make sense either. Distance can't be negative. Also, even it were positive 1/4 pm, the theory never predicted such a small magnitude value.

The initial calculations of Heitler and London were:

r = 80pm
E = -2.4 eV

A major source of error was inability to compute integrals. Additionally, the calculations neglect ionic contributions.

See Computational Imperatives in Quantum Chemistry for a historical overview.

  • $\begingroup$ Yes it was a mistake.. $\endgroup$ Nov 14, 2015 at 14:27
  • $\begingroup$ The first paragraph should really have been a comment to the question. $\endgroup$
    – Jan
    Nov 14, 2015 at 16:23
  • $\begingroup$ @Jan the answer needs to emphasize that the values in the question (even after the edits) have no relationship to Heitler and London. $\endgroup$
    – DavePhD
    Nov 16, 2015 at 12:38
  • $\begingroup$ @DavePhD Yes; but I was explicitly referring to the bit ‘$E = 89.9~\mathrm{pm}$’. That’s not really relevant at all, that was a b** typo of some sort that shouldn’t (imho) be addressed in answers but in comments. The bit after that, stating the original values, is fine by me. $\endgroup$
    – Jan
    Nov 17, 2015 at 16:40

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