Hydrogen bonding approximations

Note added in -proof. The application of the usual integral equation theories of the liquid state 2> to water has not been successful.1) A recent study by H. C. Andersen [J. Chem. Phys. 61, 4985 (1974)] promises to change this situation. Briefly, Andersen reformulates the well known Mayer cluster expansion of the distribution function 2> by consistently taking into account the saturation of interaction characteristic of hydrogen bonding. Approximations are selected which satisfy this saturation condition at each step of the analysis. Preliminary calculations (H. C. Andersen, private communication) indicate that even low order approximations that preserve the saturation condition lead to qualitative be-... 

A comparative analysis of the dimer interface between NOS isoforms is important since there are questions on significant variation in dimer stability between isoforms (84, 85). The dimer interface is extensive with approximately 2700 A of surface area buried per monomer. The interface contacts involve a mix of nonpolar and polar interactions, including hydrogen bonding. Approximately 60% of the interface in both iNOS and eNOS is hydrophobic, although the higher resolution eNOS... 

F. 7.21. The conformation of PrP and PrP . The prion proteins have two domains, an N-terminal region that binds four per chain, and a C-terminal region. In PrP, the C-terminal regions contain three substantial helices and two 3-residue p strands joined by two to three hydrogen bonds (approximately 40% a-helix and almost no P-sheet structure). It exists as a monomer. In PrP , the C-terminal region is folded into an extensive P-sheet. The overall structure is approximately 40 to 50% P-sheet, 20 to 30% a-hehces. This conformation promotes aggregation. 

A quick calculation confirms that electrophilic bromination of benzene is exothermic. A phenyl-hydrogen bond (approximately 112 kcal mol Table 15-1) and a bromine molecule (46 kcal moF ) are lost in the process. Counterbalancing this loss is the formation of a phenyl-bromine bond DH° = 81 kcal moF ) and an H-Br bond (DH° = 87.5 kcal moF ). Thus, the overall reaction is exothermic by 158 — 168.5 = —10.5 kcal moF (43.9 kJ moF ). 

Figure C3.2.5. Strongest tunnelling patliways between surface histidines and tire iron atom in cytochrome c. Steps in patliways are denoted by solid lines (covalent bonds), dashed lines (hydrogen bonds), and tlirough-space contacts (dotted lines). Electron transfer distance to His 72 is 5 A shorter tlian in His 66, yet tire two rates are approximately...

As shown m Figure 16 1 however the presence of an oxygen atom permits ethers to participate m hydrogen bonds to water molecules These attractive forces cause ethers to dissolve m water to approximately the same extent as comparably constituted alco hols Alkanes cannot engage m hydrogen bonding to water... 

The attraction for two neutral atoms separated by more than four Angstroms is approximately zero. The depth of the potential wells is minimal. For the AMBER force field, hydrogen bonds have well depths of about 0.5 kcal/mol the magnitude of individual van der Waals well depths is usually less. 

Many problems with MNDO involve cases where the NDO approximation electron-electron repulsion is most important. AMI is an improvement over MNDO, even though it uses the same basic approximation. It is generally the most accurate semi-empirical method in HyperChem and is the method of choice for most problems. Altering part of the theoretical framework (the function describing repulsion between atomic cores) and assigning new parameters improves the performance of AMI. It deals with hydrogen bonds properly, produces accurate predictions of activation barriers for many reactions, and predicts heats of formation of molecules with an error that is about 40 percent smaller than with MNDO. 

For large deformations or for networks with strong interactions—say, hydrogen bonds instead of London forces—the condition for an ideal elastomer may not be satisfied. There is certainly a heat effect associated with crystallization, so (3H/9L) t. would not apply if stretching induced crystal formation. The compounds and conditions we described in the last section correspond to the kind of system for which ideality is a reasonable approximation. 

Since polar solvents would be expected to stabilize polar forms, a retreat towards the hydroxy tautomer (71) would be predicted in solvents less polar than water, and in the vapour phase. This is borne out in practice at equilibrium both 2- and 4-hydroxypyridine (as well as the 3-hydroxy compound, which even in water exists as an approximate 1 1 mixture of OH and NH forms) exist as such, rather than as the pyridinones. However, the 2- and 4-quinolinones remain in the NH (keto) forms, even in the vapour phase. Hydrocarbon or other solvents of very low polarity would be expected to give results similar to those in the vapour phase, but intermolecular association by hydrogen bonding often leads to a considerably greater proportion of polar tautomers being present than would otherwise have been predicted (77ACR186, 78JOC177). 

Modem understanding of the hydrophobic effect attributes it primarily to a decrease in the number of hydrogen bonds that can be achieved by the water molecules when they are near a nonpolar surface. This view is confirmed by computer simulations of nonpolar solutes in water [15]. To a first approximation, the magnimde of the free energy associated with the nonpolar contribution can thus be considered to be proportional to the number of solvent molecules in the first solvation shell. This idea leads to a convenient and attractive approximation that is used extensively in biophysical applications [9,16-18]. It consists in assuming that the nonpolar free energy contribution is directly related to the SASA [9],... 

In addition, the frequency cooo, as well as the tunneUng distance can also be extracted from the same empirical data. Thus all the information needed to construct a PES is available. Of course, this PES is a rather crude approximation, since all the skeleton vibrations are replaced by a single mode with effective frequency cooo and coupling parameter C. From the experimental data it is known that the strong hydrogen bond (roo < 2.6 A) is usually typical of intramolecular hydrogen transfer. 

In this case the parameters C and Q are of order of unity, and therefore they correspond to the intermediate situation between the sudden and adiabatic tunneling regimes. Examples are mal-onaldehyde, tropolon and its derivatives, and the hydrogen-oxalate anion discussed above. For intermolecular transfer, corresponding to a weak hydrogen bond, the parameters C, Q and b are typically much smaller than unity, and the sudden approximation is valid. In particular, carbonic acids fulfill this condition, as was illustrated by Makri and Miller [1989]. 

Figure 2.2 The a helix is one of the major elements of secondary structure in proteins. Main-chain N and O atoms ate hydrogen-bonded to each other within a helices, (a) Idealized diagram of the path of the main chain in an a helix. Alpha helices are frequently illustrated in this way. There are 3.6 residues per turn in an a helix, which corresponds to 5.4 A (1.5 A pet residue), (b) The same as (a) but with approximate positions for main-chain atoms and hydrogen bonds Included. The arrow denotes the direction from the N-terminus to the C-termlnus.

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