Improvement of the LCAO MO

As we have seen the MO calculations of the last paragraph yielded a bond distance which was 25% too long and a dissociation energy which was 37% too low. How could the accuracy be improved  

Comparison of the probability densities calculated for the approximate wavefunction P+ with those calculated from the exact wavefunction P shows that the probability density in the low-energy region near and in between the two nuclei is underestimated by some 40%. No wonder then that the calculations fail to reproduce the true strength of the bond  

The simplest way to increase the probability density near the nuclei is to modify the Is orbitals  

When the two nuclei are far apart, the best value for f is obviously equal to 1.0. In the other limiting situation, i.e. when the internuclear distance approaches zero, the Ht molecule is 

The calculations are carried out as outlined in the preceding section. Thus E is calculated from equation (7.10)  

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