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Analysis

The first question we may address is the relationship between the bond modulus and the equilibrium bond length tex2html_wrap_inline2591 . If we take the logarithm of Equation gif we obtain

equation973

A graph of tex2html_wrap_inline2918 against tex2html_wrap_inline2920 is shown in Figure gif. If the regression coefficient is calculated for this plot we obtain a value of -0.38 which is statistically insignificant at a level of significance of 10%. Thus, there is no statistical evidence of a correlation between tex2html_wrap_inline2918 and tex2html_wrap_inline2920 and hence we can conclude that the bond modulus is independent of tex2html_wrap_inline2591 in this model.

  figure982

The values of k are plotted against tex2html_wrap_inline2940 in Figure gif. The regression coefficient for these data is 0.72 which is statistically significant at a level of significance of 1%. Thus, we can conclude that there is a correlation between the bond modulus and overlap population. The best fit line for the data is

equation993

We can see that the best fit line does not pass through the origin, but there is a small, negative value for the y-axis intercept. This is not unreasonable, as the previous investigation in Section gif showed that the minimum overlap population we can expect between two bonded atoms is approximately 0.19e. Hence, we would expect the bond modulus to reach zero before the overlap population.

   figure996
Figure: Graph of bond modulus against Mulliken overlap population. The best fit line tex2html_wrap_inline2946 is plotted for comparison.

This analysis has shown that there is a linear relationship between overlap population and bond modulus within the harmonic approximation. The correlation between these values is not ideal which may be because population analysis takes no account of the detailed electronic structure of the bond and the model does not consider factors such as anharmonic effects. However, results show that the overlap population may be used as an approximate measure of the bond modulus.


next up previous contents
Next: Spin Population Analysis Up: Overlap Population as a Previous: Simple Molecules

Matthew Segall
Wed Sep 24 12:24:18 BST 1997