Heitler-London hydrogen model 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?
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.