Hydrogen atom fields

For XH bonds, where X isany heavy atom, the hydrogen electron den sity is ri ot th ough t to be cen tered at th e position of th e hydrogen n ueleus but displaced alon g th e bon d sorn ewhat, towards X. The MM+ force field reduces the XH bond length by a factor of 0.9 I 5 strictly for th e purposes of calculatin g van der Waals in teraction s with hydrogen atoms. 

In some force fields the interaction sites are not all situated on the atomic nuclei. For example, in the MM2, MM3 and MM4 programs, the van der Waals centres of hydrogen atoms bonded to carbon are placed not at the nuclei but are approximately 10% along the bond towards the attached atom. The rationale for this is that the electron distribution about small atoms such as oxygen, fluorine and particularly hydrogen is distinctly non-spherical. The single electron from the hydrogen is involved in the bond to the adjacent atom and there are no other electrons that can contribute to the van der Waals interactions. Some force fields also require lone pairs to be defined on particular atoms these have their own van der Waals and electrostatic parameters. 

In a united atomforce field the van der Waals centre of the united atom is usually associated v ilh the position of the heavy (i.e. non-hydrogen) atom. Thus, for a united CH3 or CH2 group the vem der Waals centre would be located at the carbon atom. It would be more accurate to associate the van der Waals centre with a position that was offset slightly from the carbon position, in order to reflect the presence of the hydrogen atoms. Toxvaerd has developed such a model that gives superior performance for alkemes than do the simple united atom models, particularly for simulations at high pressures [Toxvaerd 1990]. In... 

The hydrogen molecule ion is best set up in confocal elliptical coordinates with the two protons at the foci of the ellipse and one electron moving in their combined potential field. Solution follows in mueh the same way as it did for the hydrogen atom but with considerably more algebraic detail (Pauling and Wilson, 1935 Grivet, 2002). The solution is exact for this system (Hanna, 1981). 

The helium atom is similar to the hydrogen atom with the critical difference that there are two electrons moving in the potential field of a nucleus with a double positive charge (Z = 2) (Eig. 8-1). 

No nitration of thiazole occurs with the classical nitration reagents, even in forcing conditions (341-343). In a study concerning the correlation between the ability of thiazole derivatives to be nitrated and the HNMR chemical shifts of their hydrogen atoms, Dou (239) suggested that only those thiazoles that present chemical shifts lower than 476 Hz can be nitrated. From the lowest field signal of thiazole appearing at 497 Hz one can infer that its nitration is quite unlikely. Thiazole sulfonation occurs... 

For the hydrogen atom, and for the hydrogen-like ions such as He, Li, ..., with a single electron in the field of a nucleus with charge +Ze, the hamiltonian (the quantum mechanical form of the energy) is given by... 

The hydrogen atom presented a unique opportunity in the development of quantum mechanics. The single electron moves in a coulombic field, free from fhe effecfs of infer-elecfron repulsions. This has fwo imporfanf consequences fhaf do nof apply fo any atom wifh fwo or more elecfrons ... 

Each hydrogen atom in a unique chemical environment is shielded differently from the external field and has a slightly different resonance frequency. The chemical shift in ppm, 5, is defined as... 

Representative chemical shifts from the large amount of available data on isothiazoles are included in Table 4. The chemical shifts of the ring hydrogens depend on electron density, ring currents and substituent anisotropies, and substituent effects can usually be predicted, at least qualitatively, by comparison with other aromatic systems. The resonance of H(5) is usually at a lower field than that of H(3) but in some cases this order is reversed. As is discussed later (Section 4.17.3.4) the chemical shift of H(5) is more sensitive to substitution in the 4-position than is that of H(3), and it is also worth noting that the resonance of H(5) is shifted downfield (typically 0.5 p.p.m.) when DMSO is used as solvent, a reflection of the ability of this hydrogen atom to interact with proton acceptors. This matter is discussed again in Section 4.17.3.7. 

I.Guarneri, Relevance of classical chaos in quantum mechanics the hydrogen atom in a monochromatic field , Physics Reports 154 (1987) 77. 

---