The Mutually Consistent Field MCF Method

We saw in the previous section that the perturbation theoretical expressions governing two molecules (or linear chains) at medium distances (where a multipole expansion for the electrostatic term alone is insufficient) are rather complicated even in second order. On the other hand, perturbation theory in this form cannot describe the simultaneous interactions of more than two molecules (only with the aid of the still more complicated double perturbation theory), and it is also not very accurate. Therefore one must develop a new method, which is nearly as accurate as the supermolecule approach (which, for larger interacting molecules, is not feasible because of the prohibitively large amount of computer time), can treat an arbitrary number of interacting molecules (or linear chains) at medium intermolecular (interchain) distances, and is much faster than perturbation theory (PT). This problem was solved at Erlangen in a series of papers for both molecules and linear chains. 

The basic idea is that in the case of, say, three interacting molecules A, B, C (selected here only for the sake of simplicity) one solves not the HF equations of the three free molecules, namely 

Starting with unperturbed potentials V, F , and F one has to solve this system iteratively [for instance, recalculating with the changed HF wave functmns obtained from equation (6.22a) thus yielding a new potential which is then substituted into equations (6.22b) and (6.22c), etc.] until a mutually consistent solution is obtained [mutually consistent field (MCF)]. This means that the charge distributions and potentials of all the molecules would no longer vary if one were to continue the iterations. The real problem lies in how the classical electrostatic potentials 

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. 

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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. 

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. 

In this work we have used this version of the mutually consistent field method (MCF) (48) which has been developed to treat the interactions between polymer chains (69). Each subsystem is computed in the potential field of the partner system. The Coulomb potentials of the elementary cell of one chain, represented by a point charge distribution which are fitted to the Hartree-Fock Coulomb potential are included in the one-electron part of the Fock matrix of the other chain and vice versa (for more details see Section 2.4). The procedure of taking into account the effect of the mutually polarization is repeated until consistent solutions are obtained for the charge distributions. Computing finally the interaction between these point charge representations, one obtains the electrostatic and the polarization energy contribution together. 

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