Bond critical point density

The value of the electron density at this point, the bond critical point density pt,. 

The Diatomic Hydrides of Periods 2 and 3 6.9.1 Bond Critical Point Density... 

We assume that the bond critical point density is an approximate measure of the amount of density accumulated in the bonding region, that is, the amount of shared density. For bonds that are conventionally regarded as predominately covalent, pt, has a large value, and for bonds conventionally regarded as predominately ionic, pb has a low value. In a hypothetical purely ionic bond, the value of pb would be zero. 

As we have seen in earlier chapters, an important and much discussed bond property is the bond length. The length of a bond depends on its strength, and it therefore also depends on the bond critical point density and on the atomic charges. 

The strength of a bond increases with increasing bond critical point density pb and with increasing charges of the bonded atoms. 

The length of a bond decreases with increasing bond critical point density and increasing atomic charges, but increases with increasing coordination number of the atom to which it is bonded. 

Clearly not all these atomic and bond properties are independent of each other and it can be difficult to disentangle one from another. Nevertheless we will find these properties useful for discussing the properties of molecules, as we do for some typical molecules of the period 2 elements in this chapter. In particular, the amount of accumulated or shared density, which we assume is approximately measured by the bond critical point density, represents what is commonly called the covalent contribution to the bonding. The atomic charges represent what is commonly called the ionic contribution. 

Bonds between atoms with large charges and a small value of the bond critical point density are described as predominately ionic. 

Table 8.3 gives the experimental and calculated bond length and angles, and the calculated atomic charges, bonding radii, and the bond critical point densities, for the hydrides of the... 

Table 8.15 Bond Lengths, Bond Angles, Bond Critical Point Densities, and Atomic Charges for (HnX)20 Molecules...

Table 9.1 Calculated and Experimental Geometrical Parameters and Calculated Atomic Charges and Bond Critical Point Densities for the Period 3 Fluorides...

Table 9.3 gives the calculated and experimental bond lengths and bond angles and the calculated atomic charges and bond critical point densities for the hydrides of the period 3 el-... 

Figure 5. Three-dimensional isodensity envelopes of (a) SCI2, (b) H2O, and (c) Cl2. The outer envelope has the value of 0.001 au, the van der Waals envelope the inner one is the bond critical point density envelope (pb-envelope).

Clearly the concepts of ionic and covalent character have only an approximate qualitative significance. They cannot be defined and therefore measured in any quantitative way. Although they are widely used terms and have some qualitative usefulness if used carefully they have caused considerable misunderstanding and controversy. The AIM theory does, however, provide properties that we can use to characterize a bond quantitatively, such as the bond critical point density and the atomic charges. It seems reasonable to assume that the strength of a bond depends on both these quantities, increasing as pb and the product of the atomic charges increase. 

The concepts of ionic and covalent character of a bond are vague and ill defined. The well-defined AIM-derived quantities such as the integrated atomic charges and the bond critical point density provide a quantitative characterization of bonding (4). 

FIGURE 10. Three-dimensional isodensity envelopes of the bond critical point density (pb-envelope)... 

Another characteristic property of the electron density of 1 is its relatively high value at the centre e of the ring (more than 80% of that at the CC bond critical point). Density is smeared out over the ring surface and concentrated at its centre because of the occupation of the w0 -orbital (MO 8, 3a(, Figure 6), which has the character of a surface orbital . Cremer and Kraka9, n 13 have termed this phenomenon surface delocalization of electrons, to be distinguished from ribbon delocalization and volume delocalization of electrons (Figure 12)12. 

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