3.3 Critical points in the electron density

Further analysing the first and second derivatives at the critical points validate the assumption of ionic bonding in the silatrane.

 

 

Table 5: Properties of the critical points in the chiral silatrane

Si(1) O(2)	bcp (3,-1)
coordinates	X = 4.24113875 Å	Y = -1.48450393 Å	Z = -0.45686378 Å
distance from	Si 1.27 Å	O 1.87 Å
$\rho(r)$	0.1203 e/a03
$\nabla^2(\rho(r))$	0.964 e/a05

Si(1) N(5)	bcp (3,-1)
coordinates	X = 3.15303269 Å	Y = -0.135561143 Å	Z = 0.158368394 Å
distance from	Si 1.56	N 2.54
$\rho(r)$	0.0497
$\nabla^2(\rho(r))$	0.148

The low electron density at the critical points and the positive Laplacian ( $\nabla^2\rho(r)$) are clear evidence that the bonds are more ionic than covalent. As one compares these results to those obtained by Gordon [12] there is a good agreement with results obtained on 6-31G(d) optimised structures, showing that the X-ray structure is a valid geometry for doing ab-initio calculations.

To connect the analysis to the concept of the bond order (which is more familiar to the preparative chemist), Bader has derived an expression to calculate the bond order n from the electron density $\rho$ at the bond critical point [16]:

$$n=\exp{6.458(\rho - 0.2520)}$$ (1)

Comparing the bond orders derived by Mulliken population analysis and calculated using equation (1) one finds that the silicon-oxygen bond is attributed a much more ionic character in the Bader analysis (table 6).

 

 

Table 6: Bond Order

bond	Mulliken derived	Bader
Si(1)-O(2)	0.897	0.427
Si(1)-N(5)	0.237	0.270