MCF-method

The MCFS method is simple to use and fast. The technique is however not general applicable and shows severe dynamic errors. 

In the case of intermolecular interactions between polar molecules Otto and Ladik proposed the so-called mutually consistent field (MCF) method [135-136]. They discussed various aspects of the MCF approach in a series of papers [137-139], and compared it with the conventional SCF supermolecule and perturbational calculations. 

The main advantage of the MCF method as compared to the supermolecule calculations is that the dimensionality of the variational calculation can be considerably reduced. Nevertheless a large portion of the intermolecular integrals are still... 

The MCF method was successfully applied, for example, to the study of hydration of the glycine z witter ion with 6 and 12 water molecules [138]. It has been concluded that mutual polarization effects were quite important in the first hydration shell, but presumably the water molecules in more distant hydration shells are not polarized appreciably by the solute therefore their effect can be represented by the electrostatic potential of the corresponding unperturbed charge distributions. 

Unfortunately the symmetry requirements for the perturbation operator has not been respected in several previous applications of the SCMP model [157-161] which may have lead to inconsistencies in the calculations. These come from an uncritical use of asymmetrical integral approximations, as discussed previously in the context of the MCF method. 

Theoretical methods for the investigation of interactions between polymer chains are described in Chapter 6. Besides the theoretically clear-cut but, in the case of polymers with larger unit cells, numerically unfeasible, superchain approach, theoretical perturbation methods and the mutually consistent field (MCF) procedure recently developed at Erlangen are reviewed. The first application of the MCF method, which takes into account both the electrostatic part and polarization forces, to polynucleotide-polypeptide interactions (modeling DNA-protein interactions) is presented. 

The MCF method applied to generate an effective potential of the water environment surrounding polynucleotide chains is presented in Chapter 7. The respective positions of the water molecules and ions were taken from the results of extensive Monte Carlo simulations performed by dementi s group. The first results as to how this effective potential caused by the environment affects the band structure of a cytosine stack are also reviewed in this chapter. 

Two different methods have been developed for the successful representation of the potentials one in 1978 and the other in 1984. > Both methods give rather accurate results as compared to the supermolecule (SM) calculations, but the latter version is much faster. In order to understand the new version of the MCF method it is necessary to be familiar with the older one, which is the only one that has been applied to two interacting chains see Section 6.3. Therefore, both versions are described in the next two subsections. 

The first version of the MCF method described can be generalized to interacting chains in a straightforward manner. The one-electron part of... 

Despite all its successes, the MCF method with the point-charge representation of the potentials described above has one major disadvantage, namely if we have a molecule A, the values and positions of the point charges that represent its potential must be recalculated in every case that this molecule interacts with one or more other molecules, and this has to be done for every relative position of the interacting mole-... 

The first application of the MCF method (in its first version) to the interaction of two infinite chains, namely to the interaction of polyglycine (in different conformations) and different polynucleotide chains, was performed by Otto et This calculation represents the first step in the theoretiod treatment (at the ab initio level) for DNA-protein... 

Hence the MCF method was applied in the form appropriate to treat the interaction between polymer chains without the condition of commensurable cells. By computing the interaction between the MCF point chaiges (and nuclear charges) of both macromolecules, one obtains... 

The C stack calculation involved the positions (more precisely, the weighted averages of the probability distributions of the atomic nuclei) of five water clusters around a cytidine molecule (and five clusters in the planes above and below) computed by dementi s group with the aid of the Metropolis-Monte Carlo method. The five water clusters together contain 37 water molecules (see Figure 7.1). If three of their planes are selected, one has to construct the resultant effective potential of 111 water molecules. This was carried out with the help of the first (point-charge) version of the MCF method (see Section 6.2.1). 

After determining the proper point-charge representations of the water clusters, the potentials of the other water molecules situated around neighboring DNA subunits could be simply calculated by transforming the vectors r, which represent the positions of the point charges with the symmetry operation of the helix. After the chaise distribution of each water cluster was represented in this way, the clusters could be allowed to interact and the modification of their charge distribution as a result of the interactions had been taken into account via the first version of the MCF method (see Section 6.2.1). ... 

Secondly, the polarization effect just illustrated implies an effect on the conformation of the polymer chain. In the particular case of the polyethylene chain, the conformation where all the carbon atoms lie in the same plane will be twisted so as to bring the methylene groups 5 and 8 closer to the perturbing ion, while the methylene groups 2,3,4,9,10,11 will move away from it. This in turn will change the fields at the various atoms, and hence their polarizations. A more complete calculation would then have to follow the lines of the MCF method of Ladik and Otto. 

The method for cr electrons used here was proposed in ref.4 and the most recent review is given in re.5 here the interpretation of the atomic parameters as electronegativities is fully analized, following in ref.6. The MCF method was proposed in ref.7. 

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