Combining rule, intermolecular interaction

Natural mutation of amino acids in the core of a protein can stabilize the same fold with different complementary amino acid types, but they can also cause a different fold of that particular portion. If the sequence identity is lower than 30% it is much more difficult to identify a homologous structure. Other strategies like secondary structure predictions combined with knowledge-based rules about reciprocal exchange of residues are necessary. If there is a reliable assumption for common fold then it is possible to identify intra- and intermolecular interacting residues by search for correlated complementary mutations of residues by correlated mutation analysis, CMA (see e.g., http //www.fmp-berlin.de/SSFA). 

The justification for using the combining rule for the a-parameter is that this parameter is related to the attractive forces, and from intermolecular potential theory the attractive parameter in the intermolecular potential for the interaction between an unlike pair of molecules is given by a relationship similar to eq. (42). Similarly, the excluded volume or repulsive parameter b for an unlike pair would be given by eq. (43) if molecules were hard spheres. Most of the molecules are non-spherical, and do not have only hard-body interactions. Also there is not a one-to-one relationship between the attractive part of the intermolecular potential and a parameter in an equation of state. Consequently, these combining rules do not have a rigorous basis, and others have been proposed. 

Another difficulty in developing a molecular theory of liquid mixtures is the relatively poor knowledge of the intermolecular interactions between molecules of different species. While the intermolecular forces between simple spherical particles are well-understood, the intermolecular forces between molecules of different kinds are usually constructed by the so-called combination rules, the most well-known being the Lorentz and the Berthelot rules. 

We may now begin to explore the transferability and combination rules of force constants, partial charges, van der Waals parameters, etc., using the methods described above. The issue of the transferability of force field parameters is crucial to the practitioner of molecular mechanics applications. Is the carbonyl oxygen in an amide the same as in an acid —Are the intermolecular interactions between peptides the same as in model amide compounds Clearly, our ability to derive force fields from well-characterized model compounds and to transfer them to polymeric and biomolecular systems of interest depends substantially on our ability to answer such questions. 

Combination Rules.—The relation between simple empirical potential functions and the more fundamental and more detailed descriptions of intermolecular interactions is tenuous. Most simple potentials provide a convenient means by which the gross details of the interactions can be specified. As a result, one should not expect that the combination rules that provide the best representation for the dispersion or repulsive interactions will prove the most satisfactory for a given potential. A variety of empirical rules for combining pure-component potential parameters has been proposed the most widely used have been... 

Pena MD, Pando C, Renuncio JAR (1982) Combination rules for intermolecular potential parameters, n. Rules based on approximations for the long-range dispersion energy and an atomic distortion model for the repulsive interactions. J Chem Phys 76 333-339 Schnabel T, Vrabec J, Basse H (2007) Unlike Lennard-Jones parameters for vapor-liquid equilibria. J Mol Liq 135 170-178... 

The same intermolecular potential-energy functions may be applied to correlate interaction virial coefficients. In the case where there are no, or insufficient, experimental data, but adequate data exist for the pure components, it may be possible to estimate with useful accuracy the unlike interaction parameters from combining rules such as ... 

The combining rules obtained from consideration of intermolecular potentials provide, at least by analogies similar to those invoked here, both information regarding the functional forms of the interaction parameters and estimates of their values. Some of the alternative forms proposed for eqs 5.26... 

Of course, other choices of combining rules are considered in the literature [210-214] but are not considerated here. In view of the fact that there are good reasons for also including three-body terms into the description of intermolecular interaction (see, e.g., [215, 216]), using simplified pair potentials of the type described in this section should only be considered as a reasonable approximate first step on the way towards a more rigorous modeling of interactions in real materials. 

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