e.21a These experimental and calculated magnitudes for the charges on oxygen and nitrogen in a standard NO2 group are almost identical, giving confidence in the accuracy and meaning of the terms Etotal, Ecovalent and Eionic, obtained from the N–O bond energy/bond order formula.
This result also suggests that any observed major variation from the standard N–O bond length of 1.227 Å may be used to estimate the strengths of external attractive or repulsive forces acting on the oxygen atoms of an NO2 group. A common attractive force found in crystals and operating at very short distances of only 2.2-2.8 Å is that due to H-bonding. It is shown below that such attractive H-bond forces give rise to N–O bond lengthening, which can be used to estimate the strength of the H-bond. In contrast, repulsive forces causing bond contraction seem to be mostly due to electronegative centres lying inside the normal van der Waals approach distance of about 3.4 Å.22
Hydrogen-bonding and long N–O bond lengths in NO2 groups
The oxygen atoms of an NO2 group are very weakly basic, the pKa for ArNO2H+ being approximately –11, which indicates that the group will be a poor H-acceptor. From sparse literature, it seems that H-bonding between a nitro group and known H-donors is weak in solution.23a,24,25 However, in crystals there are many instances in which the distance between a nitro oxygen acceptor atom and a hydrogen atom donor (HA) is very short, the hydrogen atom lying between donor and acceptor in such a way that the acceptor-hydrogen-donor angle is usually near to 180o. Typically, these close NO–H–A interactions in crystals are about 2.2-2.8 Å apart and are often noted generally as "hydrogen-bonds". In the present work, the only H-bonds considered to be significant are those, which have enthalpies greater than about 6-8 kJ.mol-1, particularly those involving alcohols, phenols, acids or amides.
There is little doubt that much of the energy for H-bonding arises through ionicity effects23h,3e but these do not need to be considered separately. Changes in N–O bond lengths are easily related to changes in the total bond energy (Etotal). Thus, Etotal (without H-bonding) > Etotal (with H-bonding) and the difference between them should be a measure of the enthalpy of the H- bond. From bond energy/bond order relationships, any reduction in Etotal should appear as an increase in length of the N–O bond.
Compounds 6-12 of Figure 1 exhibit longer than usual N–O bonds. The X-ray structural data for these compounds21 confirm that, in each case, one oxygen of a nitro group lies very close to a hydrogen atom of a good hydrogen donor. Table 1 lists these compounds, the relevant N–O bond lengths and Etotal for each N–O bond. In comparison with a standard N–O bond, the long N–O bonds in compounds 6-12 have smaller bond orders and smaller values for Etotal. By subtraction of Etotal(standard N–O bond) from Etotal(long N–O bond), H-bond enthalpies were calculated (Table 2).26 It is satisfying that these H-bond energies fall exactly in the range 8-46 kJ.mol-1 normally observed for typical H-bond enthalpies.23a,24
Entry 1 (Table 2) relates to dilituric acid 6, which is particularly interesting for its intramolecular hydrogen bond between a nitro group and an adjacent hydroxyl. From studies on H-bonding in ortho substituted aromatic compounds such an intramolecular bond to NO2 would
