Why Hydrogen(H2) bond length is 74 pm? (Hydrogen Potential energy with bond length Curve)

Hydrogen potential Energy Curve:

Potential energy curve for H2 will look like as shown below.

Form the curve it is clear that Potential energy for Hydrogen decreases with increase in bond length upto 74 pm and increase in bond length beyond this value increases the potential energy.

As at 74 pm bond length H2 is having the lowest energy of -432 kJ/mol., it is the most desirable state and H2 atom will be stable at this bond length. So at stable conditions H2 bond length is 74 pm.

Typical Bond length and Potential energies are given below

 ( These values are calculated using GAUSSIAN software with UHF/STO-3G base)

d (A0)   P.E(Cal/mol)

0.4   -0.904361397

0.5   -1.042996276

0.6   -1.101128243

0.7   -1.117349035

0.8   -1.110850397

0.9   -1.09191404

1     -1.066108648

1.1   -1.036538874

1.3   -0.973110614

1.5   -0.910873553

1.7   -0.854337625

1.9 -0.805332843

2.1 -0.76417765

2.3 -0.73035332

2.5 -0.702943599

2.7 -0.68094076

2.9 -0.663404741

3.1 -0.649505776

3.3 -0.638519434

3.7 -0.622881774