Force fields, hierarchy

The accuracy of the embedding potential A hierarchy of force fields... 

Previous semiempirical QM/MM approaches with link atoms are based on intuitively reasonable model assumptions and implementations [186]. Recent work in our group [159,234] has attempted to define a hierarchy of semiempirical QM/MM models (A, B, C) and to achieve an optimum implementation for combinations of MNDQ or AMI with the MM3 force field [235, 236]. In the following we outline the main ideas of this development Consider a molecule X - Y, which is partitioned into an MM part X and a QM part Y (treated as Y-i with a link atom i = H). At the simplest level A, the total energy may be written in an obvious notation as... 

The computations required for accurate modeling and simulation of large-scale systems with atomistic resolution involve a hierarchy of levels of theory quantum mechanics (QM) to determine the electronic states force fields to average the electronics states and to obtain atom based forces (FF), molecular dynamics (MD) based on such an FF mesoscale or coarse grain descriptions that average or homogenize atomic motions and finally continuum level descriptions (see Fig. 1). 

Together with an appropriate closure for the pair and triplet distribution functions, one may restrict consideration in this limit to the first two equations in the hierarchy (23). Again, in this approximation, one may follow a course of the Debye-Hiickel approach to obtain the mean field potential, while image forces are accounted for. In this way, the distribution of ions in the system will be known, and interaction forces can be calculated on the basis of this distribution. 

A network model is quite similar to but more general than the hierarchical model. In a hierarchy, data have to be arranged such that one child has only one parent, and in many instances this is unrealistic. If we force the use of a hierarchical representation in such cases, data will have to be repeated at more than one location in the hierarchical model. This redundancy can create a number of problems. A record in a network model can participate in several relationships. This leads to two primary structural differences between hierarchical and network models. Some fields in the hierarchical model will become relationships in a network model. Further, the relationships in a network model are explicit and may be bidirectional. The navigation problem in a network data model can become severe. Because search of the database can start at several places in the network, there is added complexity in searching, as well. 

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