Hydrogen electron density

For XH bonds, where X is any heavy atom, the hydrogen electron density is not thought to be centered at the position of the hydrogen nucleus but displaced along the bond somewhat, towards X. The MMh- force field reduces the XH bond length by a factor of 0.915 strictly for the purposes of calculating van der Waals interactions with hydrogen atoms. 

For such systems the constitutional isomerism order is k = 2. Consequently, the simplest ansatz for the description of a point-property of an allenic hydrogen atom conforming to the requirement of completeness only contains one-particle functions (A = 3 - 2). In Ref. 9 it has been shown that for the predictions of CNDO/S electron densities of allenic hydrogens indeed one-particle functions suffice that is, the hydrogen electron densities may be calculated according to Equation 33. 

In Equation 33 is a constant, 0 (R2) and 7 (R/) are ligand-specific parameters for the substituents attached to the ligand sites 2 or / = 3,4, respectively. These parameters have been determined from the CNDO/S hydrogen electron densities of monosubstituted allenes (a (H) = t (H) = 0). They are given in Table 5. From the numerical values one can see that substitution affects both the kinds of allenic hydrogen atoms to a comparable extent which again indicates the pronounced substituent effects across the whole allenic heavy-atom grouping. 

Parameters for the Predictions of Hydrogen Electron Densities of Allenes, Obtained from Monosubstituted Compounds RHC=C==CH2 (in 10" e) (9)... 

Concerning hydrogen electron densities one observes a close similarity for all the cumulenic hydrocarbons 11, 222, and 223. Their hydrogen electron densities are distinctly more positive than that of ethylene. Qualitatively, the equivalencies of the various carbon atoms in the cumulenes (and ethylene) are also reflected by their C nmr resonance positions (relative to TMS). 

For ketenes, however, such an alternating polarization is not observed. The alternating polarization within the allenic CH2 subunit is lucidly illustrated by the linear correlation (90n) of the (CNDO/S) tt electron density / cc(3 ) at C3 and the hydrogen electron density PhhO) at H3 which is determined essentially by TT interactions (9). 

Figure 38 Relation of the geminal proton-proton coupling constants in allenes to the squares of the hydrogen electron densities.

The electron densities are calculated from the coefficients of if i, 2 and 3 only because these are the occupied orbitals for the six-valence-electron system. The carbon atom is calculated to have 3.565 electrons (exclusive of those in the Is level), and each of the hydrogen atoms is calculated to have 0.812 electron. Since carbon in its neutral form has four electrons, its net charge in methyl cation is +0.435 (4—3.565). Each hydrogen atom has a charge of +0.188 (1-0.812). A sample calculation of hydrogen electron density is as follows ... 

These stmctures tend to have a lot of disorder. It is rare that any hydrogens can be observed in the final electron density maps. In fact, many groups of atoms (water molecules and some side chains) may be so disordered that it is usually difficult to determine positions for these groups. 

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