Geometry lone-pair directionality

Thylor R, Kennard O, Vereichel W (1983) Geometry of the N-H—0=C hydrogen bond. 1. Lone-pair directionality. J Am Chem Soc 105 5761-5766... 

The question of the exact geometry of hydrogen bonds (distances, angles, lone-pair directionality) has been reviewed [194]. 

A general equation can be derived that describes the variation in direction of the valence electron density about the nucleus. The distortion from sphericity caused by valence electrons and lone-pair electrons is approximated by this equation, which includes a population parameter, a radial size function, and a spherical harmonic function, equivalent to various lobes (multipoles). In the analysis the core electron density of each atom is assigned a fixed quantity. For example, carbon has 2 core electrons and 4 valence electrons. Hydrogen has no core electrons but 1 valence electron. Experimental X-ray diffraction data are used to deri e the parameters that correspond to this function. The model is now more complicated, but gives a better representation of the true electron density (or so we would like to think). This method is useful for showing lone pair directionalities, and bent bonds in strained molecules. Since a larger number of diffraction data are included, the geometry of the molecular structure is probably better determined. 

Much of our current knowledge of intermolecular interactions has been derived from the study of crystal structures. For example, it was not until an extensive survey of 1509 N—H---0=C hydrogen bonds in CSD structures that the O lone pair directionality of this key interaction was first recognized [31]. Another example is the detailed study of hydrogen bond geometries in 15 globular proteins carried out by Baker and Hubbard [32] and these hydrogen bond definitions, derived nearly 30 years... 

Figure 2.43 H-bonding results from a balance of favorable electrostatics and orbital interactions. The stereoelectronic aspect is reflected in the preferred geometries when a large covalent aspect is present. Lone pairs that play a primary role in directionality are shown in blue, lone pairs that play a secondary role (i.e. for O-compounds) are in black. The second lone pair at S is not shown because it plays only a minor role (see Chapter 5 and ref. 75 fora more detailed discussion).

In molecules such as H2O, the composition of the four hybrid orbitals (two bonding and two lone pairs) on the O atom will be slightly different In such cases, the actual percent composition of each hybrid orbital will be dictated by the molecule s geometry. For sp" hybridized orbitals (n= I -3), the relationship between the bond angle (0) and the decimal percent s-character (S) is given by Equation (10.8). For hybrids that also contain some d-orbital character, the relationship between the bond angle and directionality of the hybrid orbitals is somewhat more complex and is not discussed in this textbook. 

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